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Technische Universität München
Department Chemie Lehrstuhl für Technische Chemie II
Prof. Johannes A. Lercher
Diffusion and Separation Characteristics of Binary
Hydrocarbon-Mixtures in MFI
Diffusions- und Trenneigenschaften von
Kohlenwasserstoffmischungen in MFI
Master Thesis
-----------------------------------------------------------------
Vorgelegt von Bsc. (TUM) Robin Kolvenbach
Betreuer: Prof. Dr. J. A. Lercher
Garching, April 2010
„Wer die erhabene Weisheit der Mathematik tadelt, nährt sich von Verwirrung“
Leonardo da Vinci
A Acknowledgement
Acknowledgement
There are a lot of people without whom this thesis had not been written and
whom I owe my deepest gratitude.
First of all Prof. Lercher for giving me the opportunity to work in his group and
trusting me with the most challenging issue for my work.
Then I would like to thank PD Dr. Jentys for guiding me through this thesis and
also over the last years during my study at Technische Universität München.
I would like to address my deepest gratitude to Oliver Gobin who is an
archetype for every scientist. I owe my gratitude to him for his guidance and
excellent advice throughout this thesis. The intense discussions we had
showed me how to perform scientific work in a proper way.
I would like to thank the whole group for their support during this thesis. I have
to address my special thanks to Xaver Hecht and the whole technical team
without whom this thesis would have been impossible.
Of course I would like to thank my wonderful parents and my family, brothers
and my sister for supporting me my whole live.
B Abstract
Abstract
The diffusion and separation characteristic of binary hydrocarbon mixtures
through zeolitic wafers were studied with a Wicke Kallenbach cell. Therefore,
the transport of a benzene/p-xylene mixture and a p-xylene/m-xylene mixture
was examined in ZSM5 powder pressed to wafers of 50, 100 and 150 mg. This
report analyzes the transport mechanism and tries to falsify two models, the
statistically dense membrane and the classical bed adsorber. Therefore several
parameters were varied: different measurement and activation temperatures as
well as compacting pressures were examined. It was found that the model of
the classical bed adsorber suits the experimental results. These were mainly an
equilibrium separation factor of 1 and the form of the transmission curves
which were both independent on the change of experimental conditions.
Considering the transport mechanism the diffusion through the mesopores was
found to be the rate determining step once the system was under stationary
conditions. The time until stationary conditions were reached as well as the
transmission time were clearly influenced by the capacity of the adsorber. The
capacity was determined by the temperature during the experiment and
activation as well as the weight of the wafer.
The steady state diffusion coefficients were 10-6 m2/g obtained by the Wicke
Kallenbach measurements, which are much faster than the diffusion
coefficients of 10-15 m2/g of the parent MFI as measured by pressure
modulation frequency response experiments and uptake rate measurements.
As a consequence the transport mechanism in the Wicke Kallenbach wafer can
be assumed to be Knudsen diffusion through the mesopores.
The pore size of the mesopores was confirmed either by calculations from the
Wicke Kallenbach experiments applying the theory of Knudsen diffusion or
nitrogen physisorption isotherms using DFT analysis. A pore size of 6 to 15 nm
was found in which the transport through the 6 nm pores seem to be the
determining step of the rate of diffusion.
C Zusammenfassung
Zusammenfassung
Die Diffusion und die Trennung einer Mischung bestehend aus zwei
Kohlenwasserstoffen wurde in einer Wicke Kallenbach Zelle untersucht. Hierbei
wurden Gemische aus Benzol/p-Xylol und m-Xylon/p-Xylol an einem Wafer aus
ZSM5 untersucht. Es wurden Pellets zu 50, 100, 150 mg durch Pressen des
Pulvers hergestellt. Dieser Bericht analysiert die Transportmechanismen
innerhalb des Wafers und falsifiziert zwei Modelle, zum einen die Idee einer
statistisch dichten Membran und den klassischen Bettadsorber. Hierbei
wurden verschiedene Parameter variiert, unter anderem die Experiment- und
Aktivierungstemperatur als auch den Pressdruck während der Herstellung des
Pellets. Es wurde festgestellt, dass das Modell des Bettadsorbers in der Lage
ist, die experimentellen Ergebnisse hinreichend gut zu beschreiben. Diese
waren vornehmlich ein Trennfaktor von 1 und die Form der Durchbruchskurve,
welche charakteristisch für Adsorber ist.
Der Transport durch den Wafer unter stationären Bedingungen wurde durch
die Diffusion in den Mesoporen determiniert. Hierbei hängt die Zeit bis zum
Erreichen des Gleichgewichts genauso wie die Durchbruchzeit von der
Kapazität des Adsorbers ab. Diese wiederum wurde beeinflusst von der
Experiment- und Aktivierungstemperatur als auch von der Dicke des Wafers.
Es wurden Diffusionskoeffizienten von 10-6 m2/g in den Wicke Kallenbach
Messungen gefunden welche im Vergleich zu 10-15 m2/g für das
korrespondierende Pulver deutlich größer waren. Die Diffusionskoeffizienten
des Pulvers wurden mittels pressure modulation Frequenz Antwort Methode
und Uptake Rate Messungen bestimmt. Anhand der gemessenen
Diffusionskoeffizienten kann angenommen werden, dass die Diffusion in den
Poren einer Knudsen Diffusion in den Mesoporen entspricht.
Die Porengröße wurde daraufhin durch zwei Methoden bestimmt. Zum einen
durch eine DFT Analyse einer Stickstoffphysisorptionsisotherme und zum
anderen durch Berechnung aus den experimentellen Wicke Kallenbach Daten
unter Benutzung der Theorie der Knudsen Diffusion. Es wurde eine Porengröße
von 6 bis 15 nm gefunden wobei der Transport in den 6 nm Poren den
gesamten Diffusionstransport determiniert.
D Abbreviations
Abbreviations
A amplitude of FR experiment
Aper poke surface area needed statiscally for one poke [m2]
Aper successful poke surface area needed statiscally for a poke leading to
sorption of the adsorbent into the pore system [m2]
AS surface species
Aw Cross section of the wafer [m2]
a parameter corresponding to the amount of adsorbate in the
pores cB and on the surface cA
B amount of gas present in the sheet
BP adsorbate inside the channel system
b parameter corresponding to the amount of adsorbate in the
pores cB and on the surface cA
C normalized gas phase concentration
Ct time dependent concentration [mol/l]
C∞ concentration at infinite time [mol/l]
c concentration of diffusing component [mol/m3]
c0 initial adsorbed phase concentration [mol/m3]
co equilibrium adsorbed phase concentration [mol/m3]
c∞ steady state adsorbed phase concentration [mol/m3]
cA concentration in the adsorbed phase [mol/m3]
ce equilibrium concentration inside the particle [mol/m3]
c(1,2), feed adsorbate concentration in the feed [mol/m3]
E Abbreviations
c(1,2), measurement adsorbate concentration in the permeate during the
measurement [mol/m3]
cp effective heat capacity of the adsorbent sample [J/kgK]
cs surface concentration [mol/m2]
D(c) concentration dependent diffusion coefficient
D0 pre exponential factor of the Arrhenius ansatz
Deff diffusion coefficient in the pore system [m2/s]
DK,eff effective Knudsen diffusion coefficient [m2/s]
DLS dynamic light scattering
dp pore diameter [m]
EA,D activation energy of diffusion [kJ/mol]
F volumetric flow rate [m3/s]
FHe volumetric flow rate of the sweep gas [m3/s]
Fmolecules Number of molecules transmitting through wafer per
second [molecules/s]
∆H heat of adsorption [J]
h external heat transfer coefficient [W/m2K]
J diffusive molar flow rate [mol/m2s]
K parameter proportional the slope of the adsorption
isotherm
KH Henry constant
k Boltzmann constant [J/mol]
ka rate constant of Adsorption [1/s]
L characteristic length of diffusion [m]
F Abbreviations
mean value of characteristic length of diffusion [m]
M molar weight [kg/mol]
MFC mass flow controller
m(t) mass dependent on the time
m0 starting mass
m∞ end mass
N statiscal number of successful pokes during the
transmission of the adsorbate through the wafer
NA Avogadro constant [1/mol]
n number of parallel transport processes
P partial pressure [Pa]
P0 standard pressure (1 bar)
Pe partial pressure of the diffusion component in the gas
phase at equilibrium condition [Pa]
p pressure amplitude of FR experiment
pB pressure amplitude of blak of FR experiment
Q dimensionless concentration in the adsorbed phase
Q0 equilibrium value of the average dimensionless adsorbed
phase concentration
R gas constant [J/molK]
r radius of the Wicke Kallenbach pellet [m]
ra rate of adsorption [mol/s]
S separation factor
SAd adsorption cross section [m2/mol]
G Abbreviations
Sw cross section of the adsorbent bed
SBET BET surface area [m2/g]
Sext external surface area [m2/g]
SEM Scanning electron microscopy
T temperature [K]
T0 experimental temperature (FR) [K]
TI initial and final steady state temperature [K]
TEM transmission electron microscopy
t time [s]
tHasley thickness of a monolayer of physisorbed nitrogen
according to the theory of Halsey [nm]
UHV ultra high vacuum
VFR volume of the FR system [m3]
Ve,FR equilibrium volume (FR) [m3]
Vma macropore volume [cm3/g]
Vme mesopore volume [cm3/g]
Vmi micropore volume [cm3/g]
vmicro,max maximum micropore volume [cm3/g]
Vmol molar volume [m3/mol]
Wsat maximum amount of adsorbed gas = W0 [mol/m2]
X adsorbate in the gas phase
XRD X-Ray diffraction
x space coordinate
H Abbreviations
xAdsorbate molar ratio of the adsorbate either in the feed or the
permeate
y length coordinate [m]
Zw Number of hits of a molecule with the wall [1/m2s]
I Abbreviations
Greek Symbols
α the dimensionless parameter describing the heat transport
β the dimensionless parameter describing the heat transport
δ characteristic function of FR experiment
mean value of the characteristic function of FR experiments
εp porosity factor
χ phase lag of the concentration inside the sheet
γ relative amplitude
κ rate constant of the surface barrier
η dimensionless radial coordinate
φ phase of the FR experiment
φB phase of the blank FR experiment
ρ effective density of the adsorbent sample [kg/m3]
ρB density of adsorbent bed
θ surface coverage
τ dimensionless time
τF tortuosity factor
υ amplitude of the perturbation
ω frequency of perturbation [1/s]
J Table of Contents
Table of Contents
Acknowledgement ............................................................................................. A
Abstract ............................................................................................................. B
Zusammenfassung ............................................................................................. C
Abbreviations ..................................................................................................... D
Greek Symbols.....................................................................................................I
1. Introduction ................................................................................................. 1
2. Theoretical Section ..................................................................................... 4
2.1 Zeolites ..................................................................................................... 4
2.2 Wicke Kallenbach Experiments ................................................................ 8
2.3. Frequency Response experiments ........................................................ 10
2.4. Uptake rate measurements ................................................................... 14
3. Experimental ............................................................................................. 19
3.1. Material .................................................................................................. 19
3.2. Wicke Kallenbach experiments ............................................................. 21
3.3.1 Sample preparation ......................................................................... 21
3.2.2 Experimental setup .......................................................................... 22
3.3. Frequency response experiments ......................................................... 25
3.3.1. Sample preparation ........................................................................ 25
3.3.2. Experimental Setup ......................................................................... 26
3.4. Uptake rate measurements ................................................................... 27
3.4.1 Sample preparation ......................................................................... 27
3.4.2. Experimental Setup ......................................................................... 27
4. Results ...................................................................................................... 29
4.1 Wicke-Kallenbach experiments .............................................................. 29
K Table of Contents
4.2. Frequency Response experiments ........................................................ 41
4.3. Uptake Rate measurements .................................................................. 43
4.4. Nitrogen physisorption isotherms.......................................................... 47
5. Discussion ................................................................................................ 49
6. Conclusion ................................................................................................ 69
Literature .......................................................................................................... 71
Appendix
1 Introduction
1. Introduction
The understanding of diffusion processes in porous media is crucial for the
development of new and more effective catalysts and molecular sieves.
Especially the diffusion in micropores became a very important field as this is
often the rate controlling step in a complex reaction network. Moreover it is
possible to increase the selectivity of a process by shape selective catalysts
[1,2]. Most of the time these are zeolites or related materials because the pore
structure can be tuned to favor the desired product. The difference in the
diffusivity of two components due to the pore diameter of a porous substrate
can also be used for separation by size exclusion. Sakai et al. showed the
separation of p-xylene from a ternary mixture of the xylene isomers with the
help of a MFI-type zeolite membrane [3].
Another approach to enhance the separation of hydrocarbons by zeolites was
recently published by our group. The enhanced separation is caused by a
surface modification with a silica layer of 3 nm thickness [4,5]. This over-layer
leads to a variation of the sticking probability on the modified surface which
speeds up selectively the sorption rate in the porous over-layer and has in
combination with the intrinsic size exclusion of the MFI micropores the
consequence of an enhancement of the sorption rate.
To be able to determine the intracrystalline diffusivity many different methods
were developed in the last decades among these uptake rate measurements
[6,7,8,9] as for instance zero length column [10,11], different NMR techniques
for example the widely applied pulsed field gradient method [12,13,14,15],
frequency response experiments [16,17,18,19] and rapid scan IR-
spectroscopy[4,5,19]. Furthermore microscopic IR techniques offer the
possibility to monitor the diffusion process in a sample [20,21].
Another widely used method is the measurement in a Wicke Kallenbach cell.
This experiment offers the possibility to determine the diffusive flow through a
micro-, meso- or macroporous wafer. Originally Wicke and Kallenbach
invented the method for monitoring the diffusivity of CO2 in active coal [22].
Since then the method was used for several different types of experiments
either in the classical form or modified to fit the requirements.
2 Introduction
Sun et al. applied the method to measure intracrystalline diffusivity of fast
transport processes such as methane in Silicalite 1 [23]: they mounted large
silicalite crystals (100x100x300 μm) at the center of an aluminum disk where
both sides of the crystals were exposed by using an epoxy resin. They
preformed the measurement with methane, ethane, propane and butane. The
experiments showed excellent results, which were in agreement with
previously reported intracrystalline diffusivities determined by frequency
response techniques.
Many other authors used zeolite membranes grown on a support, most of the
time alumina to investigate intrapore transport processes. Keizer et al.
demonstrated for example the possibility to separate mixtures of molecules
with small and large kinetic diameters [24]. N-hexane was chosen as small and
2,2-dimethylbutane as large molecule. Separation factors larger than 600 were
obtained in a temperature range between 298 and 473 K.
Tuchlenski et al. quantified the amount of surface diffusion of non adsorbing
gases in porous glass with a pore radius of 3.5 nm by applying a modified
Wicke-Kallenbach cell [25]. They obtained excellent results in describing the
diffusion of a non-adsorbing gas through the membrane by applying the dusty
gas model (DGM). Similar experiments were carried out by Arnóst et al. [26].
They examined the transport of ternary mixtures made of hydrogen, helium,
nitrogen or argon in mesoporous alumina wafers. They also tried to model the
transport processe with the DGM and in addition with the mean pore transport
mode model. Unfortunately they found out that it is impossible to model this
process as the molecules influence each other in the gas during the
transmission through the wafer.
The aim of this report is the examination and understanding of transport
phenomena of binary mixtures consisting of strong adsorbing substances
during the transmission through a pressed wafer of ZSM5 in a Wicke
Kallenbach cell.
The experiments should also give more insight in the separation behavior of
hydrocarbons of such wafers. They should answer the question if these wafers
act like a membrane or analogue to a bed adsorber. The experimental part
consists of Wicke Kallenbach experiments applying pressed wafers of ZSM5
3 Introduction
and binary mixtures of benzene and p-xylene as well as p-xylene and m-xylene
as adsorbates to see whether it is possible to separate these compounds.
To investigate the differences between the powder and the pressed wafer,
pressure modulation frequency response and uptake rate measurements were
performed. These techniques allow the determination of the time constant of
the diffusion and the examination of the transport mechanism by fitting the
experimental data to theoretical models.
The combination of all these different techniques should answer the question
which diffusion mechanism occurs in a pressed Wicke Kallenbach wafer and
shows if it is possible to separate hydrocarbons with a pressed zeolitic wafer.
4 Theoretical Section
2. Theoretical Section
2.1 Zeolites
Zeolites are microporous tecto-silicates which are nowadays widely used in
industrial processes [27]. Because every zeolite is a potential catalyst, adsorber
or cation exchanger they are applied in several processes [28] e.g. methanol to
gasoline [29] or selective catalytic reduction of nitric oxide by ammonia [30].
One of the most important operation areas is the petrochemical industry, in
particular fluid catalytic cracking [31], isomerization [32,33] and alkylation
[34,35].
The name Zeolite was used for the first time in 1756 by the mineralogist A.F.
Cronsted who observed bubbles while heating the mineral Stilbite. The origin
of the name zeolite are the two greek words “zeon”(to boil) and
“lithos”(stone) [36]. Nowadays over 180 different zeolite structures are
known among them 40 natural and 140 synthetic topologies. They are
identified by a three letter code defined by the IUPAC (International Union of
Pure and Applied Chemistry) [37] and the IZA (International Zeolite Association)
[38] e.g. FAU = Faujasite.
Figure 1:Primary and secondary building units (PBU, SBU) of zeolitic frameworks.
Zeolites consist of SiO44- and AlO4
5- tetrahedrons as primary constitution which
built up a three dimensional secondary structure by linking through the oxygen
atoms (Figure 1). These secondary building units (SBU) can be separated in 20
5 Theoretical Section
different unique polyhedrons. The combination of the primary and secondary
units leads to huge and complex structural diversity with three dimensional
channel- and pore - systems, cages and super – cages [38].
Due to the regular structure of the material the pore size distribution is very
sharp. Figure 2 shows the pore size distribution of several different adsorbents
in comparism. The pores have a diameter below 1.3 nm which means they are
in the range of kinetic diameters of molecules. This property gives the
opportunity to perform size exclusive as well as shape selective reactions.
Additionally selective adsorption of a molecule from a reaction mixture
becomes possible because molecules larger than the pore openings cannot
enter in contrast to smaller ones.
Figure 2: Pore size distribution of zeolites in comparism to the standard adsorbents silica gel and active cole [39].
The isomorphous exchange of Si4+ by Al3+ opens out into a negative charge
which has to be compensated either by an inorganic or organic cation
consequently an alkali, earth alkali cation, quaternary ammonium ion or proton
[40] (Figure 3).
The general elemental formal for zeolites is Mx/m[(AlO2)x(SiO2)y]•wH2O where m
is the charge of the cation and w the number of water atoms is the cage.
6 Theoretical Section
Thereby the Si/Al ratio is defined by the ratio of y/x and has to be greater than
1 due to the Löwenstein rule [41]. This rule indicates that Al-O-Al linkages are
forbidden in zeolite frameworks. Si/Al ratios from 1 to infinity which describes
pure silica zeolites are common.
Figure 3: Structural formulas showing the effect of isomorphic exchange of silicon by aluminum
and the compensation by either an inorganic or organic cation M+ (a) or proton (b) [42].
The aluminum content is one of the characteristics determining the reactivity of
a zeolite by the density of negative charge in the framework. This has
enormous consequence for the density and strength of the Brønstedt acid
sites, the ion exchange capability, the thermal stability and hydrophilic
properties [43]. This dependence provides the opportunity to tune the reaction
properties of a zeolite by altering the degree of aluminum in the framework.
Summarizing the physical and chemical properties [44] of zeolites it may be
adhered that they have a high surface area, a molecular dimension of the
pores, a high adsorption capacity, high ion-exchange capability, high thermal
and hydrothermal stability, the possibility of modulation the electric properties
of the active sites and the possibility for pre-activating the molecules in the
pores by strong electric fields and molecular confinement.
Although the microporousity is one of the main advantages of zeolites it is a
disadvantage at the same time. The reason for this is the slow diffusion in the
micropores which leads to limitations of the rate of chemical reactions. To
solve this problem intense activities are ongoing over the last years.
7 Theoretical Section
There are mainly two ways to overcome this problem. One is to make nano
sized particles [45] and the other one is to synthesize mesoporous materials
like MCM-41 [46].
The synthesis of zeolites is usually performed under hydrothermal conditions
using reactive gels in alkaline media at 80 – 200 °C. These reactive gels are
produced from hydrated aluminum and silicon species e.g. hydroxides. Metal-
powder or salts dissolved in sodium hydroxide solution usually serve as
aluminum source. The silicon source which is normally the colloidal dioxide is
combined with the aluminum containing solutions under hydrothermal
conditions [47].
Figure 4: Two different method of ZSM5 synthesis [48].
A structure directing agent (SDA) is added to the reaction mixture to control
zeolite growth in means of pore size and network dimensions. Usually tertiary
amines serve as SDA e.g. a tertiary-propyl-ammonium salts in the case of
ZSM5. The pH of the reaction mixture is adjusted between 9 and 13. In this
high temperature and pressure conditions a reactive gel is formed. Inside this
gel zeolitic nuclei occurs which then starts the crystal growing. Depending on
the synthesis method zeolite crystals or polycrystalline zeolite material is
formed. These two different methods are described in Figure 4.
8 Theoretical Section
During the last 50 years many other preparation methods were developed.
They were extensively reviewed before [49,50,51,52] and will not be discussed
here.
2.2 Wicke Kallenbach Experiments
This method for investigating the diffusivity in porous media was developed by
Wicke and Kallenbach in 1941 [22]. In principle two countercurrent gas flows
graze the sample wafer in a 90° angle. One of the flows is loaded with probe
substances and the other one contains of pure sweep gas (Figure 5). The
sample is placed into the cell as a wafer which is either produced by
compacting of powder or as a grown membrane.
The diffusion through the wafer is driven by the concentration difference
between both flows. The pressure on both sides of the cell has to be the same
to avoid pressure driven transport through the sample. Therefore, the
volumetric flow rate of the loaded and the unloaded stream has to be the
same.
Figure 5: Flow scheme of the Wicke Kallenbach cell showing the fluxes going in and out of the cell and indication where the diffusive transport takes place.
If the experiment is performed with two or more substances it is possible to
determine the ability of the sample to separate the adsorbates by comparing
the feed concentration to the concentration in the permeate. Hence it is
possible to calculate a separation factor by:
(2.2.1)
If a separation is observed during the experiment the separation factor has to
differ from 1. Furthermore it is possible to calculate the diffusion coefficient of
9 Theoretical Section
the adsorbates inside the pellet from the steady state molar ratios of these
experiments by (2.2.2)
(2.2.2)
In this equation L is the characteristic length of diffusion, r is the radius of the
pellet, FHe is the volumetric flow rate of the sweep gas and xAdsorbate is the molar
ratio in the feed and in the permeate at steady state conditions, respectively.
In principle three different kinds of diffusion have to be considered in porous
media. In the case of molecular diffusion the mean free path of a molecule is
shorter than the pore diameter. As a result the diffusion process can be
described analogue to the free vacuity by the first fickian law by substituting
the diffusion coefficient by an effective diffusion coefficient (Deff). The latter
consists of an additional porosity factor (εp) which describes the ratio of pore
openings compared to the total surface area as well as a tortuosity-factor (τF)
specifying the differences of the pore geometry from the ideally assumed
cylinder [53].
(2.2.3)
If the pore size is small or the gas pressure is low the mean free path is longer
than the pore diameter. Consequently the molecules hit the pore walls much
more often than other molecules. In this case the so called Knudsen diffusion
is observed. The conditions for this kind of diffusion are summarized in the
following table [53]:
Table 1: Depence of the occurring of Knudsen diffusion on the partial pressure of the adsorbate and the pore size
dp [nm] <1000 <100 <1 <2
p [105 Pa] 0.1 1 10 50
The diffusive flow in the Knudsen theory can mathematically be expressed by
equation (2.2.4) [53].
(2.2.4)
10 Theoretical Section
In here dp is the pore diameter, R is the gas constant, T is the temperature, M is
the molar mass and c the concentration of the diffusing component. Analogue
to the fickian law the effective diffusion coefficient can be described by
equation (2.2.5) [53].
(2.2.5)
The third kind diffusive transport is the diffusion in pores with a diameter below
1 nm ocurring in zeolites. In this case the pore radius is in the range of the
minimum kinetic diameter of the diffusing molecule. Therefore the diffusion
coefficients found in zeolites are much lower than the molecular or Knudsen
coefficients.
The mathematical description is the first fickian law for a system in a steady
state as shown in (2.2.3). For non steady state situations the second fickian law
is used and calculated separately for each specific case. The solutions for all of
these constraints can be found in Crank et al. [54].
The dependence of the effective diffusion coefficient on the pore diameter is
shown in Figure 6.
Figure 6: Dependence of the effective diffusion coefficient on the pore size of porous adsorbents.
2.3. Frequency Response experiments
The frequency response method offers the opportunity to determine transport
pathways and their kinetics in a batch adsorber [60]. In this method the volume
of the reaction vessel is altered periodically by ±1 % while tracking the
pressure simultaneously. By changing the volume the adsorption/desorption
11 Theoretical Section
equilibrium is disturbed and tries to equilibrate again. This equilibration can be
followed by tracking the pressure (Figure 7).
Figure 7: Simulated data of a frequency response experiment with a square wave volume perturbation showing the signal of the magnet which describes the volume (blue) and the
corresponding pressure trend (red) against the time.
The experimental data is then compared to the solution of theoretical models in
order to find the best match. By matching the experimental data to the models
the mechanism of the transport process and its kinetic parameters can be
obtained.
The model equations used for the curve fitting can be found by solving the
mass balance in a closed volume as described previously by Yasuda et al. [16].
They obtained two characteristic functions characterizing the system:
(2.3.1)
(2.3.2)
(2.3.3)
Where p is the pressure amplitude of the experiment, pB is the corresponding
pressure amplitude in a blank experiment, φ is the phase of the experiment, φB
is the phase of the blank measurement and δ is the characteristic function.
Herein n is the number of parallel transport processes. Furthermore K is a
parameter proportional the slope of the adsorption isotherm, the temperature
(T), the volume of the system (VFR) and the gas constant (R).
Blank experiments are needed to exclude the non-idealities of the apparatus
itself from the outcome of the experiment [60]. The characteristic functions (δ)
are solutions of the second fickian law using the right boundary conditions. In
this work two different transport mechanisms are examined: the diffusion in an
12 Theoretical Section
infinite sheet and an infinite sheet with surface resistance. The mass balance of
an infinite sheet without surface barrier is defined as [17]:
(2.3.4)
where P is the pressure in the system, V is volume, R is the gas constant, T0 is
the experimental temperature and B is the amount of gas present in the sheet.
Assuming the volume is changed sinusoidal we can formulate the volume as:
(2.3.5)
herein Ve,FR is the equilibrium volume, υ is the amplitude of the perturbation, ω
is the frequency of perturbation and t is the time. The vapor pressure of the
diffusing substance and the concentration in the pores can generally be
described by:
(2.3.6)
(2.3.7)
where Pe is the partial pressure of the diffusion component in the gas phase at
equilibrium condition, ce is the equilibrium concentration inside the particle, p
(∆p/2) and γ are the relative amplitudes, φ and χ are the phase lags both
depending on the frequency ω.
The diffusion inside the pores is described by the second fickian law:
(2.3.8)
Herein c is the concentration in the pores, D(c) is the concentration dependent
diffusion coefficient and x is the space coordinate. Since the perturbations are
defined to be small fick´s law eases to:
(2.3.9)
In this work we consider the case of one dimensional diffusion in sheet with
plane boundaries at x=0 and x=L. The boundary conditions define the
concentration at the boundaries to be proportional to the sinusoidal changing
vapor pressure in the gas phase [55], [56]:
(2.3.10)
(2.3.11)
As a consequence the integral of the amount of gas present inside the sheet,
B, is given by:
(2.3.12)
13 Theoretical Section
Where Be is the equilibrium amount if gas present inside the sheet. The
amplitude A is expressed by [56]:
(2.3.13)
(2.3.14)
where KH is Henry´s law constant, p is the relative amplitude of the pressure, ω
is the frequency, L is the length of the sheet and D is the diffusion coefficient.
Furthermore the coefficient ψ in equation (2.3.12) is defined by:
(2.3.15)
Substituting (2.3.12) into the material balance (2.3.4) leads to the two equations
(2.3.1) and (2.3.2) where the in and out-of-phase functions are given by:
(2.3.16)
(2.3.17)
The other mechanism we want consider is surface controlled diffusion.
Therefore we have to add another equilibrium upstream to the one we
considered before describing the surface adsorption. This leads to the
following reaction network [57]:
X ↔ AS ↔ BP
where X is the adsorbate in the gas phase, AS is the surface species and BP is
the adsorbate inside the channel system. The corresponding material balance
is defined by:
(2.3.18)
The solution using the previously described terms for P, V and B result in these
in- and out of phase functions [16]:
(2.3.19)
(2.3.20)
where κ is the rate constant of the surface barrier and a and b are parameters
corresponding to the amount of adsorbate in the pores cB and on the surface cA
[60]:
14 Theoretical Section
(2.3.21)
(2.3.22)
Additionally the definition of the parameter K of the characteristic functions
(2.3.1) and (2.3.2) changed. In the case of a surface barrier it is defined by [57]:
(2.3.23)
Because most of the zeolites do not have a uniform particle size a normal
distribution is introduced which modifies the characteristic functions [60]:
(2.3.24)
Herein and describing the mean values of the characteristic function and
the thickness of the sheet, respectively.
2.4. Uptake rate measurements
To determine the kinetics of adsorption processes in porous materials a step
change of the adsorbate pressure is performed and the change in mass of the
sample is tracked. The altering of the pressure surroundings causes a shift in
the surface concentration of the adsorbate species which can be described by
the diffusional time constant (D/r2) [7].
The time constant and thereby the diffusivity can be obtained by matching the
experimental data to an appropriate model describing the diffusion process.
The method can be used for either macro-, meso- or microporous diffusion. A
general mathematical model is applied developed by Ruthven et al. [58] for
systems controlled by intracrystalline diffusion. It has the following
assumptions:
1) The sample consists of a ensemble of spherical particles
2) Intracrystalline diffusion is the only significant resistance to mass
transfer. Therefore the sorbate concentration at the surface of the
particles is always in equilibrium with the adsorbate in the
surrounding fluid phase.
3) The diffusivity is constant and the equilibrium relationships are linear.
4) The experiment is performed under isothermal conditions.
15 Theoretical Section
According to these approximations the system can be described by the
following differential equations. Based on the first fickian law the first one
defines the behavior of the dimensionless adsorbed phase concentration (Q)
dependent on the dimensionless time (τ):
(2.4.1)
(2.4.2)
(2.4.3)
in here η is the dimensionless radial coordinate, cA is the concentration in the
adsorbed phase, c0 is the initial adsorbed phase concentration and c∞ is the
steady state adsorbed phase concentration.
The second and third equation describe the average of the adsorbed phase
concentration over the particle (2.4.5) and its time dependence (2.4.6):
(2.4.5)
(2.4.6)
where Q is the dimensionless concentration in the adsorbed phase, η is the
dimensionless radial coordinate, ∆H is the heat of adsorption, τ is the
dimensionless time as defined in (2.4.3), ρ is the effective density of the
adsorbent sample, cp is the effective heat capacity of the adsorbent sample, c0
is the initial adsorbed phase concentration, c∞ is the final steady state
adsorbed phase concentration, T is the temperature, h is the external heat
transfer coefficient, TI is the initial and final steady state temperature, D is the
Diffusion coefficient and L is the radius of the particles
(= characteristic length of diffusion). Obviously the heat transfer has to be
taken into account even if it is disregarded later due to the isothermal
conditions. As a result the concentration of the adsorbed phase at the particle
surface can be defined by (2.4.7):
(2.4.7)
where cs is the surface concentration and co the equilibrium adsorbed phase
concentration.
This set of equations is solved with the initial boundary conditions (2.4.8) and
(2.4.9):
16 Theoretical Section
(2.4.8)
(2.4.9)
in here the first initial boundary condition indicates that the starting adsorbate
of the experiment is zero. The second one defines that the concentration of the
adsorbed phase does not change in the center of the particles.
The solution taking the boundary conditions into account can be obtained by
Laplace transformation and is shown in (2.4.10) and (2.4.11):
(2.4.10)
(2.4.11)
where qn is given by the roots of:
(2.4.12)
thereby Q0 is defines the equilibrium value of the average dimensionless
adsorbed phase concentration, α and β are the dimensionless parameters
describing the heat transport and are formulated by (2.4.13) and (2.4.14)
(2.4.13)
(2.4.14)
Considering the assumption of isothermic conditions (α ∞ and β 0) the
solution for the average dimensionless adsorbate concentration reduces to
(2.4.15):
(2.4.15)
This equation is then used to perform curve fitting with the fit parameter τ. By
knowing the length of diffusion the diffusion coefficient can be obtained.
2.5. Analysis of physisorption isotherms
The mostly applied method to analyze nitrogen physisorption isotherms was
developed by Brunauer, Emmett and Teller in 1938 [59]. It offers the possibility
to determine the surface area of a solid sample. In principle it is an extension of
the classical Langmuir isotherm, which is only valid for monolayer adsorption,
to multilayer adsorption.
17 Theoretical Section
The following assumption corresponds to this theory:
1) gas molecules adsorb in an infinite number of layers
2) each layer is treated independently which means that it has no
interaction with other layers
3) each layer can be treated with the theory of Langmuir adsorption
This leads to the BET equation:
(2.5.1)
with VAd equals the total amount of adsorbate adsorbed on the sample, P is the
partial pressure of the adsorbate, P0 is the standard pressure and Vm is the
volume of a monolayer.
2.5.1 is the linearized form of this equation. Based on this the monolayer
coverage can be obtained from the slope and the intercept of the resulting
graph shown in 2.5.2:
(2.5.2)
Furthermore it is possible to determine the surface area (2.5.3) if the adsorption
cross section of the adsorbing molecule is known.
(2.5.3)
In here Vm is the volume of a monolayer, Vmol is the molar volume of the
adsorbing gas, NA is the Avogadro constant, SAd is the adsorption cross section
of the adsorbing molecule and M is the molecular weight of the adsorbing
molecule.
Additionally it is possible to analyze the isotherm concerning the micro- and
mesopore volume. A the possible way is the t-plot method: the experimentally
obtained isotherm is compared to a standard isotherm by plotting them against
each other at the same P/P0 points.
The standard isotherm is thereby represented by the thickness of adsorbed
layers. In this thesis the method of Halsey [70] is used to produce the standard
isotherm. The corresponding equation is:
(2.5.4)
18 Theoretical Section
The obtained values are then plotted against the experimentally observed data.
Linear regions of the resulting plot correspond to regions where the standard
and the experimental isotherm have the same physical properties. These
regions can be described mathematically to determine the micro- and
mesopore volume.
The first linear region with a positive slope is defined as the point closely after
the micropores are completely filled and before the mesopore condensation
begins. It can be described by:
(2.5.5)
In here vmicro,max defines the volume of the micropores, kt is a coefficient
depending on the layer thickness, the units of vads and Sext. For standard units k
is defined by 1/(4.3532xtHasley) with tHasley representing the thickness of a
monolayer in the case of nitrogen 0.354 nm.
According to equation 2.5.5 the intercept of the first linear region defines the
micropore volume whereas the external surface area can be obtained from the
slope of the graph.
The second linear region with a positive slope describes the region shortly after
the mesopore condensation. Consequently the intercept of the second linear
region identifies the addition of the micro- and the mesopores. The last step is
to determine the mesopore volume. To do so the value of the combination
micro- and mesopore volume is subtracted by the previously obtained
micropore volume.
19 Experimental
3. Experimental
3.1. Material
Polycrystalline H-ZSM5 samples with a particle size < 100 nm and a Si/Al
ration of 45 [60] were provided by Südchemie AG. The nitrogen physisorption
isotherms were obtained using a PMI automated sorptometer at liquid nitrogen
temperature (77 K) after outgassing under vacuum for at least 6 hours. The
specific and the external surface area, the macro-, meso- and micropore
volume as well as the total pore volume (Table 2) were determined by nitrogen
physisorption (Figure 8) and applying the Brunauer-Emmett-Teller (BET) theory
in the range from 0.03 to 0.10. Between 0.1 and 0.3 mbar the plot was not
linear with a negative intercept (BET C constant).
1E-5 1E-4 1E-3 0.01 0.1 1
0
20
40
60
80
100
120
140
160
180
200
(b)
Am
ou
nt A
dso
rbe
d (
cm
3 S
TP
g-1)
Relative Pressure (-)
(a)
Figure 8: Nitrogen physisorption isotherms of the parent H-ZSM5 material (a) [5].
0.0 0.5 1.0 1.5 2.0
50
75
100
125
150
(b)
Vmi
Am
ou
nt A
dso
rbe
d (
cm
3 S
TP
g-1)
s
Vmi
+ Vme
(a)
Figure 9: αs plot of the parent (a) material. Two linear regions can be found at αs=0.5 corresponding to the micropore volume and at αs= 1.2 belonging to the sum of micro- and mesopore volume [4].
SBET
[m2/g]
Vmi
[cm3/g]
Vme
[cm3/g]
Vma
[cm3/g]
Sext
[m2/g]
Vtot
[cm3/g]
Parent 423 0.12 0.04 0.22 65 0.38
Table 2: [60,5]: Results of the nitrogen physisorption experiment for the parent ZSM5 sample. SBET is the total surface area determined by applying the BET theory, Sext is the external surface area and Vmi, Vme, Vma and Vtot are the micro-, meso and micropore volume obtained by using the αs comparative plot
Additionally the Langmuir surface area was determined by performing a
Langmuir plot in the relative pressure range up to 0.10 mbar. The macro-,
20 Experimental
meso- and micropore volumes were obtained by using a αs comparative plot
(Figure 9) [61] with nonporous hydroxylated silica [62] as reference adsorbent.
The particle size distribution was determined by dynamic light scattering (DLS)
and scanning electron microscopy (SEM). DLS measurements were performed
on a Malvern Zetasizer Nano ZS. Prior to the measurement the sample was
dispersed in water with help of an ultrasonic bath where it was kept for several
hours. The measurements were repeated at different concentrations several
times. SEM images were produced on a REM JEOL5900 LV microscope
operating at 25 kV with a resolution of 5 nm and a nominal magnification of 3.0
x 106. The samples were used without further purification. As shown in Figure
10 the particles contain of larger agglomerates of smaller particles with a
diameter of 0.36 ± 0.17 µm.
Figure 10: Scanning electron microscopy of the H-ZSM5 parent material [60].
The size of the primary particles was obtained by transmission electron
microscopy (TEM) and X – Ray diffraction (XRD) methods. The TEM images
were recorded on a JEOL-2011. The powdered samples were suspended in an
ethanol solution and dried on a copper-carbon grid prior to the measurement.
The powder diffraction patterns were measured on a Phillips X`pert Pro XRD
instrument operating at the Cu-Kα radiation at 40 kV with a Nickel filter to
remove the Cu-Kβ. The samples were used without pretreatment. Powder
patterns were produced using a spinner system with a ¼ inch divergence slit
between two angles of 5 an 70°. Step size was 0.017° with a scan time of 115s
per step. Both methods show that the primary particle size is below 100 nm
(Figure 11, Figure 12).
21 Experimental
Figure 11: TEM images of the parent H-ZSM5 sample[4].
Figure 12: XRD of the parent H-ZSM5 material showing the characteristic reflexes of ZSM5 [60].
The XRD of the parent material shows sharp reflexes at the characteristic
positions of ZSM5 (Figure 12).
Benzene and p-xylene (> 99.5 % GC standard) were supplied by Sigma Aldrich
and were used without further purification.
3.2. Wicke Kallenbach experiments
3.3.1 Sample preparation
All powdered samples were compacted into a stainless steel (b) ring at 20 kN
for 2 minutes using the pressing instruments shown in Figure 13.
The sample was then subsequently built into the Wicke Kallenbach cell and
was flushed with helium for 30 minutes. Afterwards the sample was activated
at 723 K for 1 hour in a helium flow of 50 ml/min for each of the two flows and
an incremental heating rate of 10 K/min.
The experiments were performed at a constant gas flow of 50 ml/min for each
of the two countercurrent flows. Thereby the loading with benzene was
22 Experimental
performed with a volumetric flow rate of 2 ml/min and p-xylene was saturated
with 18 ml/min. Assuming 100% saturation of the streams this leads to a ratio
of 1.33/1 bezene/p-xylene in the feed.
Figure 13: CAD model of the pressing instruments used to produce wafers for the Wicke Kallenbach cell containing of a plunger (a), the ring inserted in the cell (b) and the stamp pad
(c). The whole instrument consists of stainless steel.
To determine the temperature dependence of the separation, measurements at
130°C (403.15 K), 100°C (373.15 K) and 70°C (343.15 K) were executed. In
addition the sensitivity of the wafer thickness was examined in testing wafers
of 150, 100 and 50 mg. Also the influence of the compacting pressure and the
activation temperature was tested.
3.2.2 Experimental setup
The cell shown in Figure 14 is made of 6 pieces, two endplates (a,f) and two
rings, one holding the sample wafer (d) and the other holding the screws (c)
and two 2 mm thick graphite sealings (b,e). The flow rate is controlled by 4
mass flow controllers (MFC) Bronkhorst EL-flow select, two of them with a
range of 200 ml/min used for the sweep gas and the other two with a range of
20 ml/min leading to the saturators. These MFCs are computer controlled by
Flow DDE V4.41 and Flow View V1.09 (Bronkhorst).
The temperature of the cell is regulated via an Eurotherm 2404 PID controller.
The loading of the gas stream with benzene and p - xylene is performed via
two saturators, cooled down to 15°C in a thermostat (Huber K12-cc-NR) with a
1:1 glycol/water mixture as cooling agent to avoid condensation of the
adsorbate inside the system. Figure 15 shows a CAD Model of the saturators
23 Experimental
used. These saturators consist of two nearly identical parts which are
connected.
Figure 14: CAD Model of the Wicke Kallenbach cell containing two end plates (a,f), two sealings made out of graphite (b,e), an aluminum ring holding the screws (c) and the inner
stainless steel ring clamping the sample (d).
Figure 15: CAD Model of the saturator used to load the gas stream with adsorbates benzene and p – Xylene.
24 Experimental
The base body comprises a half inch t - piece and tube which is welded up
(a,b) and serves as a flask for the adsorbate. The gas flow enters the saturator
at point (c). The following 2 way valve controls the direction of the flow. It can
either enter the tube filled with adsorbate (a) or go through the bypass (e) back
into the system. The bypass is needed to clean the system before and after the
measurement.
To save the system from floating with adsorbate in the case of low-pressure
inside the system an empty second tube (b) is connected to the first flask. After
passing this station the stream gets back into the system through another 2
way valve (d) which connects the bypass (b) and the saturator.
An image of the total setup is shown in Figure 16.
Figure 16: Setup for the Wicke Kallenbach experiments containing the Wicke Kallenbach cell, the mass flow controllers (MFC) the saturators and the electronic for controlling the
temperature and the flows.
The permeate stream is connected to a vacuum system via a heated capillary
and differential pumped inlet system. The UHV is produced by a turbo-
25 Experimental
molecular pump TMH 071-003 (Pfeiffer Vacuum). This allows pressures down
to 10-9 mbar. During the measurements the vacuum is 10-5 mbar.
The permeate is analyzed by a mass-spectrometer (WR 13302, Hiden
Analytical) in the MID mode controlled by MASSoft Professional (Hiden
Analytical) computer software.
3.3. Frequency response experiments
3.3.1. Sample preparation
Two different kinds of samples, specifically powdered and pressed samples,
were used in this experiment. In the case of the powdered samples 35 mg
were carefully dispersed on glass-wool at the bottom of a quartz tube to have
isolated particles and thereby avoid bed effects.
Furthermore two types of pressed wafers were studied: Wicke Kallenbach-
wafers of 100 mg and IR wafers 6 mg weight. Both were carefully broken into
smaller pieces to fit in the quartz tube sample holder. Glass-wool was placed
at the bottom of the sample holder to have the same conditions as in the
experiments with powdered samples.
In both cases the glass-tube was connected to a UHV setup, placed into an
oven and pumped to 10-7 mbar. The samples were activated at 723K for 1 hour
with a temperature ramp of 10 K/min at ultra high vacuum conditions to
remove the adsorbed water.
The adsorbate was added with a partial pressure of 0.31 mbar at a
temperature of 373 K until the adsorption equilibrium was fully established.
During the experiment the volume of the setup was changed periodically in a
frequency range of 5 to 10-3 Hz and a square waved volume perturbation ±1%
in amplitude.
The pressure response was fourier transformed by obtaining the amplitude and
the phase lag. The resulting characteristic functions were fitted with the model
equations described in 2.3. by a nonlinear parameter fitting using a CMA
evolutional strategy in matlab [63]. The objective minimized to find the best
consistency was the root mean square error normalized to the variance of the
data. To be sure that the best parameters were found which is equal to the
26 Experimental
global minimum the calculation was performed three times with different
starting parameters.
3.3.2. Experimental Setup
An overview of the setup for the frequency response experiments is given in
Figure 17. The setup is basically a UHV unit equipped with volume perturbation
part which consists of two magnetically driven plates sealed with UHV bellows.
The UHV is produced by a turbo-molecular pump TMH 071-003 (Pfeiffer
Vacuum). This allows pressures down to 10-8 mbar. To enable the turbo pump
to start a zeolite trap is build into the system to produce vacuum of about 10-2
mbar.
Figure 17: Image of the frequency response setup showing the modulation unit, the vacuum chamber, the sample cell and the dosing system.
The pressure is recorded online via a Baratron pressure transducer (MKS
16A11TCC). The system is controlled via HP VEE based software. The
27 Experimental
adsorbing substrate is added by a separately pumped dosing system with an
all metal regulating valve UDV 040 (Pfeiffer Vacuum) to put the gas phase
corresponding to the liquid adsorbate into the system.
3.4. Uptake rate measurements
3.4.1 Sample preparation
A Wicke Kallenbach wafer of 100 mg was pressed as described in 2.1. and
broken afterwards into small pieces of 6 to 10 mg. One of these pieces was
subsequently filled into the quartz crucible which was then placed into the
balance.
The balance was connected to an UHV system and pumped 10-7 mbar. The
sample was activated at 723 K in UHV conditions to remove the adsorbed
water and cooled down to the experiment temperature of 373 K. The
adsorbate was added in a pressure jump with partial pressures of 0.1, 1, 2 and
10 mbar and was kept constant during the whole experiment while the sample
mass was monitored by a Seteram TG-DSC 111.
The mass of the sample was normalized afterwards by:
(3.4.1)
where m0 is the mass at the beginning of the experiment and m∞ is the mass at
the end. This normalized data was then fitted with theoretical models
described in 2.4. by nonlinear parameter fitting using a CMA evolutional
strategy in matlab [63]. The procedure was identical to the one described in
section 3.3.
3.4.2. Experimental Setup
The main item of the setup is a Seteram TG-DSC 111 microbalance (Figure 18)
equipped with quartz insertions and crucibles being heat insensitive. The
balance is connected to a UHV unit with a turbo-pump TMH 071-003 (Pfeiffer
Vacuum) which is able to produce a vacuum of 10-8 mbar. Additionally an oil
pump is connected to the system to produce on the one hand the fore-vacuum
of 10-3 mbar crucial for a turbo-pump system and on the other hand pumping
the inlet system for the adsorbates.
28 Experimental
The inlet system contains of a ¼ inch connection to fit the round bottomed
flask filled with adsorbate to the system. This fitting is linked to an all metal
regulating valve UDV 040 (Pfeiffer Vacuum) connecting the inlet part to the
vacuum system.
The whole system is operated by a Seteram controller which is connected to a
computer. A HP VEE based software is used to control the system and to track
all relevant data which is the mass, the pressure and the heat signal.
Figure 18: System used for uptake rate measurements consisting of a microbalance, vacuum system with a mass spectrometer, a dosing system and a controller.
29 Results
4. Results
4.1 Wicke-Kallenbach experiments
The diffusion and separation of benzene and p-xylene in H-ZSM5 have been
studied using the Wicke-Kallenbach method. In general the shape of the
benzene concentration curve was exponential with a clear overshooting. The
concentration gradient of p-xylene showed also an exponential form but
without the over-swinging behavior. Thereby the maximum of the over-
swinging of the benzene curve occured at the time the p-xylene uptake started.
This behavior was independent on the temperature during experiment and
activation, the thickness of the wafer and the compacting pressure.
The ratio between the equilibrium concentration of benzene and p-xylene had
a constant value around 1.43 for every performed experiment and hence
similar to the feed. This equals a separation factor of 1 valid for each
experiment. The uptake time of benzene and p-xylene differed by more than an
hour. An example of the concentration graph is shown in Figure 19 for 100 °C,
a wafer of 100 mg and 50 ml/min volume flow. In here the p-xylene
concentration was multiplied by the ratio of benzene and p-xylene (1.43).
Figure 19: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 100°C, 100mg wafer
weight and 50 ml/min volume flow.
0 10 20 30 40 50 60 70 80 90 10010
-10
10-9
10-8
10-7
10-6
10-5
10-4
time [min]
c [m
ol/l
]
Benzene
p-Xylene
30 Results
Because the uptake time for benzene and p-xylene differed as shown in Figure
19 the separation factor was clearly depending on the time. Figure 20 shows
this time dependence. It points out that the separation factor was 1 in the
beginning, started increasing very fast after 5 minutes and reached a sharp
maximum of 104 after 20 minutes corresponding to the maximum of the
benzene breakthrough curve. After 100 minutes the graph had a constant value
of 1 due to the equilibrium concentration of benzene and p-xylene.
Figure 20: Time dependence of the separation factor of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 at 100°C, 100mg wafer weight, a mixture of benzene/p-xylene
and 50 ml/min volume flow.
To study whether the uptake and thus the separation factor was influenced by
the temperature, experiments at 130, 100 and 70°C were carried out. Figure 21
displays the trend of the concentration of benzene at these three temperatures.
It points out that the time to the breakthrough of benzene varied between 7
minutes for 130 °C and 18 minutes for 70 °C. It shows as well that the benzene
uptake curve kept its exponential form thus the over swinging got stronger with
increasing temperature.
The breakthrough time of p-xylene was also temperature dependent changing
from 15 minutes for 130°C to 37 minutes in the case of 70°C as shown in
Figure 22.
0 50 100 150 200 250 300 35010
-2
100
102
104
106
time [min]
Sepe
ratio
n Fa
ctor
[-]
31 Results
Figure 21:Concnetration vs. time diagram of benzene breakthrough curves at 130°C (black), 100°C (red) and 70°C (blue) in a Wicke Kallenbach experiment with a pressed H-ZSM5-wafer
of 100mg, a mixture of benzene/p-xylene and a volume flow of 50ml/min.
Figure 22: Concentration vs. time diagram of p-xylene breakthrough curves at 130°C (black), 100°C (red) and 70°C (blue) in a Wicke Kallenbach experiment with a pressed H-ZSM5-wafer
of 100mg, a mixture of benzene/p-xylene and a volume flow of 50ml/min.
The breakthrough time as well as the time to the equilibrium concentration
decreased with increasing temperature. As in the case of benzene the overall
form of the uptake curve stayed exponential but the graph got steeper the
higher the temperature was.
Similar time dependence was found in the separation factors. Figure 23 shows
that the maximum shifted from 15 minutes towards 37 minutes with decreasing
0 10 20 30 40 50 60 70 80 90
10-7
10-6
10-5
time [min]
c [m
ol/l
]
130 °C
100 °C
70 °C
0 50 100 15010
-9
10-8
10-7
10-6
10-5
10-4
time [min]
c [m
ol/l
]
130 °C
100 °C
70 °C
32 Results
temperature. But independent of the temperature the constant value 1 was
reached.
Figure 23: Seperation factor vs. time diagram at different temperatures of 130 (blue), 100 (red) and 70°C (black) in a Wicke Kallenbach experiment with a pressed H-ZSM5-wafer, a mixture of
benzene/p-xylene, a weight of 100 mg and a volume flow of 50ml/min.
To examine whether the amount of adsorbent or the thickness of the wafer had
an influence on the uptake or the separation factor pellets with weights of 50,
100 and 150 mg were used at constant temperature of 100°C keeping the
other experimental conditions untouched.
The obtained graph for benzene is shown in Figure 24. It can be seen that the
transmission time got longer the more material was used for the wafer and
hence with increasing thickness of the wafer. Considering the form of the
graphs it can be seen that curves were stretched increasing the thickness of
the wafer keeping the overall exponential form with an over-swinging before
reaching the equilibrium concentration. Consequently the chart got less steep
in exponential region and had a longer over-swinging period the higher the
weight of the wafer was. Furthermore the equilibrium concentration got smaller
with increasing thickness of the wafer.
20 40 60 80 100 12010
-2
100
102
104
time [min]
Sepe
ratio
n Fa
ctor
[-]
130°C
100°C
70°C
33 Results
Figure 24: Concentration vs. time diagram of benzene breakthrough curves with a wafer weight of 50mg (black), 100mg (red) and 150mg (blue) in a Wicke Kallenbach experiment with a
pressed H-ZSM5-wafer, a mixture of benzene/p-xylene, a temperature of 100°C and a volume flow of 50ml/min
Figure 25: Concentration vs. time diagram of p-xylene breakthrough curves with a wafer weight of 50mg (black), 100mg (red) and 150mg (blue) in a Wicke Kallenbach experiment with a
pressed H-ZSM5-wafer, a mixture of benzene/p-xylene, a temperature of 100°C and a volume flow of 50ml/min
Similar to the benzene curves the graph of p-xylene (Figure 25) got less steep
with increasing weight of the wafer. As in all other measurements before an
over-swinging is not observed.
As in the case of benzene the uptake time got longer with more material used
for making the wafer. Looking at the form of the breakthrough curves it is
0 50 100 150 200 250 300 35010
-8
10-7
10-6
10-5
time [min]
c [m
ol/l
]
50mg
100mg
150 mg
0 50 100 150 200 250 300 35010
-8
10-7
10-6
10-5
time [min]
c [m
ol/l
]
50 mg
100 mg
150 mg
34 Results
obviously exponential for all of the three weights but was also stretched for
thicker wafers.
The equilibrium concentration was smaller by the same percentage than in the
case of benzene. As a result the separation factor stayed 1 independent on the
thickness of the wafer. Remarkable is the time dependence of the separation
factors: similar to the uptake curves of benzene and p-xylene the maximum
separation factor shifted to longer time periods with increasing thickness of the
wafer (Figure 26).
Figure 26: Seperation factor vs. time diagram of wafers with weights of 150 (blue), 100 (red) and 50 mg (black) in a Wicke Kallenbach experiment with a pressed H-ZSM5-wafer, a mixture
of benzene/p-xylene, a temperature of 100°C and a volume flow of 50ml/min
In another experiment the influence of the activation temperature on the
separation was examined. In order to do so the activation was performed at
150 °C instead of 450 °C as in the previous experiments. As shown in Figure
27 and Figure 28 the overall form of the transmission curves was independent
on activation temperature. Differences could be observed in the breakthrough
time and the total uptake time.
The breakthrough time was shortened by 6 minutes from 12 to 6 minutes for
benzene and by 9 minutes from 26 to 17 minutes in the case of p-xylene. The
breakthrough curves got more flat in both cases which results in a less over-
shooting in the case of benzene and longer uptake times in both cases.
0 50 100 150
10-2
100
102
104
time [min]
Sepe
ratio
n Fa
ctor
[-]
150mg
100mg
50mg
35 Results
Figure 27: Concentration vs. time diagram of benzene breakthrough curves with a activation temperature of 150 (black), 450°C (red) in a Wicke Kallenbach experiment with a pressed H-
ZSM5-wafer of 100 mg, a mixture of benzene/p-xylene, a temperature of 100°C and a volume flow of 50ml/min.
Figure 28: Concentration vs. time diagram of p-xylene breakthrough curves with a activation temperature of 150 (black), 450°C (red) in a Wicke Kallenbach experiment with a pressed H-
ZSM5-wafer of 100 mg, a mixture of benzene/p-xylene, a temperature of 100°C and a volume flow of 50ml/min.
But even if the uptake time got longer a constant separation factor is reached
earlier specifically after 80 instead of 120 minutes (Figure 29). The constant
separation factor equals the previous experimental results with a value of 1.
0 50 100 150 200 250 300 350 40010
-8
10-7
10-6
10-5
10-4
time [min]
c [m
ol/l
]
150°C
450°C
0 50 100 150 200 250 300 350 40010
-8
10-7
10-6
10-5
10-4
time [min]
c [m
ol/l
]
150°C
450°C
36 Results
Figure 29: Seperation factor vs. time diagram with a activation temperature of 150 (black), 450°C (red) in a Wicke Kallenbach experiment with a pressed H-ZSM5-wafer of 100 mg, a
mixture of benzene/p-xylene, a temperature of 100°C and a volume flow of 50ml/min.
To check, whether the pressure of the compacting had an influence on the
result of the experiment a wafer of 100 mg were pressed with minimum force
of 10 kN. The curves shown in Figure 30 and Figure 31 revealed the same
behavior as the previously described with the over- swinging in the benzene
transmission curve but in a less extend as previously observed and the pure
exponential curve of the p-xylene graph.
Figure 30: Concentration vs. time diagram of benzene breakthrough curves with a compacting pressure of 10kN (black), 20kN (red) in a Wicke Kallenbach experiment with a pressed H-
ZSM5-wafer of 100 mg, a mixture of benzene/p-xylene, a temperature of 100°C and a volume flow of 50ml/min.
0 20 40 60 80 100 120 140 160 180 20010
-4
10-2
100
102
104
time [min]
Sepe
ratio
n Fa
ctor
[-]
150°C
450°C
0 50 100 150 20010
-8
10-7
10-6
10-5
time [min]
c [m
ol/l
]
10 kN
20 kN
37 Results
Figure 31: Concentration vs. time diagram of p-xylene breakthrough curves with a compacting pressure of 10kN (black), 20kN (red) in a Wicke Kallenbach experiment with a pressed H-
ZSM5-wafer of 100 mg, a mixture of benzene/p-xylene, a temperature of 100°C and a volume flow of 50ml/min.
Differences were seen in the breakthrough times. They were 7 instead of 12
and 19 instead of 26 minutes for benzene and p-xylene, respectively. Even if
the breakthrough time differed the overall uptake times stayed the same which
were 200 for benzene and 240 minutes in the case of p-xylene.
The separation factor was identical to the former experiments 1. The time
dependence of the separation factor is shown in Figure 32.
Figure 32: Seperation vs. time diagrams with a compacting pressure of 10kN (black), 20kN (red) in a Wicke Kallenbach experiment with a pressed H-ZSM5-wafer of 100 mg, a mixture of
benzene/p-xylene, a temperature of 100°C and a volume flow of 50ml/min.
0 50 100 150 200 250 30010
-8
10-7
10-6
10-5
time [min]
c [m
ol/l
]
10 kN
20 kN
0 20 40 60 80 100 120 140 160 180 20010
-1
100
101
102
103
time [min]
Sepe
ratio
n Fa
ctor
[-]
10kN
20kN
38 Results
The form stayed untouched of the compacting even the height of the maximum
is precisely the same with values around 700. The point of the maximum is
shifted from 20 to 15 minutes for 10 kN corresponding to the faster uptake for
the less compacted sample.
In addition the desorption (Figure 33) of benzene and p-xylene from the Wicke-
Kallenbach-wafer of 100 mg was evaluated at 100°C. Therefore, a normal
uptake procedure was performed as described before. After the concentrations
of the adsorbates reached a constant level the adsorbed species were
desorbed with unloaded sweep gas streams of 50 ml/min each until both
concentrations equaled zero.
Figure 33: Desorption-curve of benzene (blue) and p-xylene (red) at 100°C until 3090 min then the desorption was performed with a heating of 1°C per minute until 450°C and afterwards
cooled down stepwise to 100 °C again.
At that point an activation program with a heating rate of 1°C per minute was
started with a final temperature of 450°C. This temperature was then hold for 1
hour and subsequently cooled down stepwise to 100°C.
In here the desorption-curve of benzene was much steeper than the one of p-
xylene. It reached zero after 37 minutes and showed no more desorption even
if the temperature was raised. In contrast to that the p-xylene desorption curve
equals zero after 177 minutes and showed a clear maximum in desorption after
the temperature was increased corresponding to a temperature of 176°C.
0 200 400 600 800 1000 1200 1400 1600 1800 20000
0.5
1
1.5
2
2.5
3
3.5
4x 10
-5
time [minutes]
c [m
ol/l
]
Benzene
p-Xylene
39 Results
An identical Wicke Kallenbach experiment using a standard 100 mg wafer as
described previously was also performed with m-xylene and p-xylene as single
components due to experimental constraints. The result is shown in Figure 34.
Figure 34: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and consecutively p-xylene (black) and m-xylene (red), 100°C, 100mg wafer
weight and 50 ml/min volume flow.
As m- and p-xylene have the same mass distribution in a mass spectrometer it
was not possible to determine the separation in one experiment. Hence the
transmission of the single components was examined.
The form of both curves was identically exponential with a large slope in the
starting region. Differences could be found in transmission and the uptake
times. Thereby m-xylene showed a breakthrough time of 10 minutes whereas
p-xylene needed 40 minutes to transmit. In contrast the uptake time was much
longer for m-xylene than for p-xylene specifically 350 and 100 minutes for m-
xylene and p-xylene , respectively.
0 50 100 150 200 250 300 35010
-7
10-6
10-5
time [min]
c [m
ol/l
]
p-Xylene
m-Xylene
40 Results
Table 3: Experimental results of the Wicke-Kallenbach experiments
Sample Experiment
Number
Wafer
Weight
[mg]
Compacting
pressure
[kN]
Experimental
Temperature
[K]
Activation
Temperature
[K]
Breakthrough
Time
Benzene
[min]
Breakthrough
Time
m-xylene
[min]
Breakthrough
Time
pXylene
[min]
H-ZSM5 1 100 20 373 723 12 27
H-ZSM5 2 100 20 353 723 19 41
H-ZSM5 3 100 20 403 723 7 17
H-ZSM5 4 150 20 373 723 23 47
H-ZSM5 5 50 20 373 723 3 9
H-ZSM5 6 100 20 373 423 7 16
H-ZSM5 7 100 10 373 723 7 17
H-ZSM5 8 100 20 373 723 10 40
Experiment
Number
Uptake
Time
Benzene,
[min]
Uptake
Time
m-Xylene
[min]
Uptake
Time
p-Xylene
[min]
Equilibrium
Concentration
Benzene
[mmol/l]x102
Equilibrium
Concentration
m-Benzene
[mmol/l]x102
Equilibrium
Concentration
p-xylene
[mmol/l]x102
Separation factor
1 270 185 3.6 2.49 1.01
2 290 210 3.7 2.76 0.94
3 270 250 3.55 2.4 1.03
4 295 240 2.51 1.6 1.14
5 250 450 5.4 2.96 1.28
6 350 300 3.53 2.22 1.11
7 400 370 3.75 2.73 0.91
8 350 100 0.81 1.66 1.23
41 Results
The most important factor, the separation factor, was 1.23 in this experiment
taking the ratio of feed concentration into account which was 2.52 p-xylene/m-
xylene. All experiments are summarized in Table 3.
4.2. Frequency Response experiments
To understand which transport mechanism is rate determining in the Wicke
Kallenbach experiment three different frequency response experiments were
carried out. The first measurement was performed with a powdered sample,
the next with very thin wafers which were of a weight between 6 and 10 mg
and lastly with a wafer of the same type as used in the Wicke Kallenbach cell
with a weight of 100 mg. The wafers were broken into smaller pieces before
starting the measurement to fit into the quartz sample holder.
The characteristic functionns obtained from the measurements of the powder
and the thin wafer are compared in Figure 35 and Figure 36. The functions of
the Wicke Kallenbach wafer are not shown here because the time constant
(L2/D) was too large and therefore no suitable data was obtained.
The out of phase function (Figure 35) was nearly identical for both samples
showing a maximum at 0.02 Hz. This maximum corresponds to a time constant
of 50.25s using the method described by Gobin et al. [60] which defines the
reciprocal value of the maximum of the out-of-phase function to be the time
constant. In addition the diffusion coefficients were calculated by simply
dividing L2 by the time constant. Assuming a particle size of 0.4μm obtained by
SEM the diffusion coefficients were 2.15x10-15 and 2.36x10-15 m2/s for the thin
wafer and the powdered sample, respectively.
Curve fitting was applied employing the model equations described in 2.3.
using on the one hand a simple pore diffusion model in an infinite plane sheet
and on the other a more sophisticated model assuming a surface resistance
control. Both models were used with and without a particle size distribution to
see the impact of a non-uniform size distribution. The fits for the surface
resistance model are also shown in Figure 35 and Figure 36. The obtained
transport parameters for all theoretical models and both samples are
summarized in Table 4 and Table 5.
42 Results
Figure 35: Out of phase function of the ZSM5 sample in powdered state (black) and pressed to a thin wafer (red) including the fit (lines) with a surface resistance model in a non-uniform sheet.
Figure 36: In of phase function of the ZSM5 sample in powdered state (black) and pressed to a thin wafer (red) including the fit (lines) with a surface resistance model in a non-uniform sheet.
Both samples showed nearly the same parameters independent on the
assumed model. The time constant was in the range of 67 to 75 seconds, the
corresponding diffusion coefficient was between 2.16 and 2.59 x 10-15 m2/s. K
showed values between 0.24 and 0.27. All of the models had a apparently
good fitting probability confirmed by the normalized root mean square errors
which were in an acceptable range of 0.40 to 0.52. Thereby the model with
10-3
10-2
10-1
100
101
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
frequency [Hz]
out-
of-p
hase
cha
ract
eris
tic fu
nctio
n [-
]
NormRMS-Error = 0.44666
D = 2.5916e-015
K = 0.25392
powder
fit powder
fit thin Wafer
thin Wafer
10-3
10-2
10-1
100
101
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
frequency [Hz]
in-o
f-ph
ase
char
acte
rist
ic fu
nctio
n [-
]
powder
fit powder
thin wafer
fit thin wafer
43 Results
non-uniform particle sizes and a surface resistance had the best correlation
with the experimental data.
Table 4: Transport parameters for a powdered sample of ZSM5 obtained by curve fitting assuming theoretical models describing a uniform infinite sheet, a uniform infinite sheet with surface resistance control a non-uniform infinite sheet and a non-uniform infinite sheet with surface resistance control
Model L2/D [s] D x 1015
[m2/s]
K NRMS-error
Uniform infinite sheet 70.48 2.27 0.24 0.52
Uniform infinite sheet with surface
resistance
70.36 2.27 0.24 0.52
Non-uniform infinite sheet 61.74 2.59 0.25 0.45
Non-uniform infinite sheet with
surface resistance
67.24 2.38 0.25 0.44
Table 5: Transport parameters for a thin wafer of ZSM5 obtained by curve fitting assuming theoretical models describing a uniform infinite sheet, a uniform infinite sheet with surface resistance control a non-uniform infinite sheet and a non-uniform infinite sheet with surface resistance control
Model L2/D [s] D x 1015
[m2/s]
K NRMS-error
Uniform infinite sheet 68.40 2.34 0.26 0.43
Uniform infinite sheet with surface
resistance
68.32 2.34 0.26 0.44
Non-uniform infinite sheet 73.20 2.19 0.27 0.40
Non-uniform infinite sheet with
surface resistance
74.18 2.16 0.27 0.40
4.3. Uptake Rate measurements
The gravimetric uptake curves of an 8 mg piece of a 100 mg Wicke Kallenbach
wafer having a thickness of 1 mm were obtained at adsorbate partial pressures
of 0.1, 1, 2 and 10 mbar and 373 K. All of the curves showed an exponential
uptake with a large time constant (L2/D) between 3.58x102 and 5.77x103
seconds obtained by curve fitting with the theoretical model described in 2.4.
44 Results
Figure 37: Uptake curve of benzene in an H-ZSM5 Wicke Kallenbach wafer of 100 mg at a partial pressure of 1 mbar and 373K. The figure shows the experimental data (black) and the
result of the curve fitting (red) applying an infinite plane sheet model of 1mm thickness.
Figure 38: Fitted uptake curves of benzene in an H-ZSM5 Wicke Kallenbach wafer of 100 mg at 373K at partial pressures of 0.1mbar (black), 1mbar (red), 2mbar (blue) and 10 mbar (green).
Figure 37 shows an example of such an uptake curve for the case of 1 mbar
having a clear exponential behavior. It also shows the good quality of the fit
and therefore of the applied model. Figure 38 summarizes the uptake
measurements by showing the results of the curve fitting. Thereby the graphs
got steeper with increasing partial pressure of the adsorbate which is equal to
a decreasing time constant with the loading. This indicates a clear dependence
of the diffusion coefficient on the concentration which can be calculated by
0 500 1000 15000
0.2
0.4
0.6
0.8
1
1.2
1.4
time [s]
norm
aliz
ed c
once
ntra
tion
[-]
0 200 400 600 800 1000 1200 1400 16000
0.2
0.4
0.6
0.8
1
time [s]
norm
aliz
ed m
ass
[-]
0.1 mbar
1 mbar
2 mbar
10 mbar
45 Results
dividing L2 by the time constant. Thereby half of wafer thickness which is
0.5 mm equals L. The obtained parameters are summarized in Table 6.
Table 6: Summary of the parameters obtained curve fitting of the experimental data of a H-ZSM5 Wicke – Kallenbach wafer of 100mg applying a theoretical model describing an isothermal infinite plane sheet of the thickness 1mm
Partial pressure [mbar] L2/D x 102 [s] D x 1010 [m2/s] NRMS-error
0.1 57.7 0.43 0.30
1 18.3 1.37 0.26
2 7.75 3.23 0.73
10 3.58 6.98 0.64
To see how the diffusion coefficients of benzene in a ZSM5 Wicke Kallenbach
wafer depend on the partial pressure they were plotted with the partial
pressure on the x-axes and the diffusion coefficient on the y-axes. The
outcome is shown in Figure 39. A linear dependence is obtained.
Figure 39: Dependence of the diffusion coefficient on the partial pressure of Benzene in a Wicke Kallenbach wafer of 100mg.
To determine differences between the Wicke Kallenbach wafer and the
powdered sample the uptake rate of a powdered sample was also measured.
In order to do so 4.3 mg of the powder was dispersed on glass wool analogue
to the pressure frequency response experiments to avoid bed effects. The
adsorbate benzene was dosed into the system in steps of 0.1, 1, 2 and 10
mbar by simultaneously tracking the mass.
0,00E+00
1,00E+01
2,00E+01
3,00E+01
4,00E+01
5,00E+01
6,00E+01
7,00E+01
8,00E+01
0 2 4 6 8 10 12Dif
fusi
on
co
eff
icie
nt
x 1
01
1 [m
2 /s]
partial pressure [mbar]
46 Results
Figure 40:: Fitted uptake curves of benzene in H-ZSM5 powder at 373K at partial pressures of 0.1mbar (black), 1mbar (red), 2mbar (blue) and 10 mbar (green).
Data processing was performed identical to the other experiment by non-linear
parameter fitting using a CMA evolutional strategy in matlab which resulted the
fitting shown Figure 40 and Table 7.
Table 7: Summary of the parameters obtained curve fitting of the experimental data of a powdered H-ZSM5 applying a theoretical model describing isothermal infinite plane sheet of the thickness 0.4 μm
Partial pressure [mbar] L2/D x 102 [s] D x 1016 [m2/s] NRMS-error
0.1 2.22 7.21 0.29
1 2.7 5.93 0.25
2 3.4 4.71 0.36
10 6.14 2.61 0.28
The characteristic length of diffusion is defined here as the particle size of
0.4 μm. In contrast to the wafer the diffusion coefficient decreased with
increasing partial pressure which can also be seen in Figure 41. A linear
decrease of the diffusion coefficient with the pressure was obtained. This is
most likely due to non idealities of the experiment. Especially it is impossible to
perform the uptake of partial in a step function. Consequently the bigger the
change of partial pressure is the longer the uptake takes which means that it is
further away from the ideal step function. This means that the adsorption
0 50 100 150 2000
0.2
0.4
0.6
0.8
1
time [s]
norm
aliz
ed m
ass
[-]
0.1 mbar
1 mbar
2 mbar
10 mbar
47 Results
process of benzene in this MFI powder sample is too fast to get a reliable
result from the gravimetric uptake.
Figure 41: Trend of the diffusion coefficient of H-ZSM5 powder obtained by uptake rate measurements.
4.4. Nitrogen physisorption isotherms
The procedure of the nitrogen physisorption measurement of the Wicke
Kallenbach wafer was identical to the one described in the experimental
section (3.1). The outcome compared to the isotherm of the parent material is
shown in Figure 42 and Figure 43.
Figure 42:Nitrogen physisorption isotherms of H-ZSM5 parent powder material (black) and the same material pressed to a wafer of 100 mg (red).
0,00E+00
1,00E+00
2,00E+00
3,00E+00
4,00E+00
5,00E+00
6,00E+00
7,00E+00
8,00E+00
0 2 4 6 8 10 12Dif
fusi
on
co
eff
icie
nt
x 1
016 [
m2 /
s]
partial pressure [mbar]
0
50
100
150
200
250
300
350
0,00E+00 2,00E-01 4,00E-01 6,00E-01 8,00E-01 1,00E+00 1,20E+00
Vad
s[cm
3/g
]
P/P0 [-]
48 Results
Figure 43: Nitrogen physisorption isotherms of H-ZSM5 parent powder material (black) and the same material pressed to a wafer of 100 mg (red) in the range of 0.2 to 0.9 p/p0.
Both curves are typical type 4 isotherms. A remarkable change was observed
after pressing the powder to a wafer. The pressure region from the starting
point until 0.2 was nearly identical for either the powder or the wafer. At 0.2 the
hysteresis starts to open in the case of the wafer which occurred at 0.8 in the
case of the powder. Moreover the total size of the loop obtained was much
bigger in the case of wafer than for the powder. The data was then analyzed
applying the BET formula resulting in a BET surface area of 4 46 m2/g.
0
50
100
150
200
250
300
350
2,00E-01 3,00E-01 4,00E-01 5,00E-01 6,00E-01 7,00E-01 8,00E-01 9,00E-01
Vad
s[cm
3/g
]
P/P0 [-]
49 Discussion
5. Discussion
In order to understand how the ZSM5 wafer behaves during a Wicke
Kallenbach experiment two theories were postulated describing the wafer. On
the one hand a statistically dense membrane and on the other hand the
classical bed adsorber. Statistically dense membrane represents in this context
a mesoporous layered wafer in which the diffusing molecule has to pass at
least one particle during the diffusion process (Figure 44).
Figure 44: Principle of a statistically dense membrane.
This means the whole transport mechanism is controlled by the diffusion
through the particle which defines the kinetic of the pore diffusion as rate
determining. This model assumes a steady state during the diffusion; hence
the system is not in equilibrium at any time.
The other possible model is a flow adsorber showing transmissions curves as
described extensively before [53]. This model assumes an adsorption front
going through the particle bed until the adsorbent is saturated.
Figure 45: Principle of a classical bed adsorber [72].
In contrast to the dense membrane this model is based on the assumption of
thermodynamic control. Consequently it has an adsorption region (Figure 45)
50 Discussion
where the system is not in equilibrium but the overall rate is controlled by the
strength of adsorption. It assumes an established adsorption/desorption
equilibrium in the wafer after the breakthrough of the adsorbates is finished.
The first remarkable aspects in the obtained data were the breakthrough times.
The overall trend was that the breakthrough of benzene was faster than the
one of p-xylene. This behavior can be explained with both models. In the case
of the dense membrane the faster diffusing component would penetrate faster.
This assumption would be in good accordance with Gobin et al. [60] who found
intra crystalline diffusion coefficients of 5.28x10-13 and 2.46x10-13 m2/s for
benzene and p-xylene, respectively.
But on the other hand this breakthrough time distribution is also typical for flow
adsorbers. Based on the theory the weaker adsorbing substance penetrates
first. This matches the found breakthrough times which are in good agreement
with Mukti et al. who determined adsorption enthalpies of benzene and p-
xylene of -51 kJ/mol and 94 kJ/mol, respectively [64].
The next interesting result was the temperature dependence. A clear decrease
of the transmission time with increasing temperature was found which would
also be typical for both models. This can be explained for the membrane with
an increase of the diffusion coefficient with increasing temperature as
described in the literature [60]. The higher diffusion coefficient leads to a faster
transport through the pore system resulting in a decreased breakthrough time
at higher temperatures.
The explanation for the adsorber model is the decreasing capacity with the
increasing temperature as indicated by the isotherms. They show a decrease
of loading at increasing temperature. As a result less substance can be
adsorbed at the adsorbent which have to lead also to a decreased
transmission time.
Furthermore an influence on the wafer thickness was found. An increase of the
breakthrough time with increasing thickness was observed. This is in
agreement with both models. The explanation for the model of a statistically
dense membrane is simple, the thicker the wafer is the more particles have to
be passed statistically.
51 Discussion
On the other hand this observation agrees with the adsorber model. Increasing
the wafer thickness has the same effect as decreasing the temperature: it
results in a higher adsorption capacity. Based on this theory a higher capacity
leads to a longer breakthrough time [65].
The transmission times clearly decreased when the activation temperature was
decreased to 423K because the water was not removed completely from the
zeolite. This is inconsistent with the membrane model because a higher loading
makes it harder to diffuse through a particle. As a result the breakthrough time
should had been increased or at least stayed constant and not decreased as it
is shown in Figure 27 and Figure 28.
Considering the adsorber model a higher water loading lowers the capacity
because less adsorption places are reachable for the diffusing substance. As a
consequence shorter transmission times are expected. Thus, the experimental
data also agreed with the postulate of a bed adsorber analogue.
After discussing the breakthrough times the form of the transmission curve has
to be considered. In the experiments an overshooting in the benzene graph
and a pure exponential uptake of p-xylene was observed in every experiment
with H-ZSM5 as adsorbent independent on the temperature, wafer thickness,
activation temperature or compacting pressure. This type of breakthrough
curves is typical for bed adsorbers [53].
The overshooting arises due to the competitive adsorption of benzene and p-
xylene. In this case benzene adsorbs faster than p-xylene but the adsorption is
weaker. Consequently benzene is displaced by p-xylene which then occupies
the adsorption centers and by this leads to an accumulation of benzene in the
non-equilibrium zone. Once the equilibrium in the adsorber is established the
concentrations of benzene and p-xylene are constant. It follows that the
concentration of benzene shortly after the breakthrough is higher than the
steady state concentration which can be seen as an overshooting of the graph.
As discussed before the weaker adsorbing substance broke through first and
showed an overshooting. In contrast to this the adsorbate with the higher
adsorption enthalpy, in this case p-xylene [64], had a longer breakthrough time
and showed no overshooting at all. Therefore, the form of the transmission
curve can be explained by the model of a classical adsorber.
52 Discussion
To allow the comparison of the experimental data with the postulate of the
dense membrane the experimental data was tried to fit numerically. A solution
of the second fickian law derived by Crank et al. [54] for the diffusion through a
membrane was used:
(5.1)
where Cω is the concentration at infinite time, D is the diffusion coefficient
which was previously determined by Gobin et al. [60] and L is the characteristic
length of diffusion
Unfortunately it was impossible to fit the experimental data with a sufficient
goodness of fit. This means that it is not possible to describe the
experimentally obtained data with the model of a membrane. This strongly
suggests that the model of a statistically dense membrane is not describing
this particular Wicke Kallenbach experiments in a proper way.
The most important parameter for this process is the separation factor
because the aim of these wafers was the separation of benzene and p-xylene.
Unfortunately the separation factor in the experiments equaled independent on
any changes 1. This result can`t be explained with the dense membrane model.
If the transport process would had been controlled by pore diffusion a
separation factor higher than 1 had to be found because according to Gobin et
al. [60] the diffusion of benzene is by an order of 2 faster than the diffusion of
p-xylene inside the ZSM5 pore system. As the model assumes a kinetic control
the permeation flows of benzene and p-xylene must had been different from
each other which would had led to a separation.
According to Sun et al. [23] it is possible to calculate the concentration in the
permeate at steady state conditions by:
(5.2)
where AW is the cross section of the wafer, D is the intracrystalline diffusion
coefficient, KH is the Henry constant and L is the thickness of the wafer. The
concentration of p-xylene in steady can be calculated from the ratio of the p-
xylene/benzene concentration. This equals taking V>> AxDxK/L into account:
(5.3)
53 Discussion
According to 5.3 the separation factor can be mathematically described by
Dp-xylene/Dbenzene for the model of a membrane. Assuming this model it is possible
to calculate the theoretically expected separation factors according to the
previously reported diffusion coefficients [60]. The results are shown in Table 8.
Table 8: Theoretically expected separation factors of the Wicke Kallenbach experiment assuming a statiscally dense membrane applying the diffusion coefficients reported by Gobin et al. [60]
T [°C] Diffusion coefficient
Benzene x 10-15
[m2/s]
Diffusion coefficient
p-xylene x 10-15
[m2/s]
Seperation factor
[-]
70 3.96 0.97 4.08
100 7.34 2.48 2.96
130 12.9 6.02 2.14
Also a temperature dependence on the permeation flux [3,66,67] is expected
as the diffusion coefficient varies with the temperature which would had
influenced separation factor as well. But the results show that neither the
expected temperature dependence nor a separation factor at all was observed
in the experiments.
Furthermore the separation factor showed a clear dependence on the time
which means that it reached a maximum after 10 to 50 minutes depending on
the temperature, the wafer thickness, the compacting pressure and the
activation temperature. The observed behavior fits perfectly the model of an
adsorber. As expected the position of the maximum corresponded to the
capacity of the adsorber. The time until the maximum was reached increased
with increasing capacity produced by a lower temperature during experiment
and activation and a higher thickness of the wafer. The maximum of the
separation factor occurred at the same time as the maximum of the over
swinging of the benzene concentration curve. It was identical with the
breakthrough time of p-xylene.
To determine the amount of adsorbed species on the pellet a desorption
experiment was carried out. In order to do so adsorption until equilibrium
conditions was achieved, afterwards the adsorbate stream was stopped and
the adsorbate was desorbed with the help of sweep gas (50 ml/min). The
amount of adsorbed species was then determined by integration with respect
54 Discussion
to t of the resulted data. The obtained values were then multiplied by 2
because the desorption occurred in both directions of the cell but the amount
was only tracked at one of the streams. Hence, the concentration of adsorbed
species inside the wafer equals the integration with respect to t of the tracked
concentration signal multiplied by 2.
The integration resulted in a concentration of 5.86 x 10-4 and 1.33 x 10-3 mol/l
for benzene and p-xylene. This led to a ratio of benzene/p-xylene of 0.44 which
means that the concentration of p-xylene was more than two times higher than
the concentration of benzene. This result is in good accordance with the
adsorption enthalpies measured by Mukti et al. [64]. It is another hint for the
adsorber theory because this model predicts that the process is
thermodynamically controlled. By this means the concentration ratio inside the
sheet must be equal to the ratio calculated from the isotherms which depend
on the adsorption enthalpies.
To confirm the theory of the adsorber the number of hits was calculated which
the molecules have with the pore wall during one transmission through the
wafer. This is important because it has to be shown that it is possible to
establish an adsorption/desorption equilibrium during the transmission time. If
it is impossible to build up an equilibrated state the whole adsorber theory is
no longer supportable.
The base of the calculation were the sticking probabilities obtained by
Reitmeier et al. [4] having values of 2.10x10-7 and 2.18x10-7 for benzene and p-
xylene. This parameter describes the probability that a poke between the
adsorbate and the outer surface of a porous material leads to a pore entering.
The starting point of the calculation is the overall number of wall collisions
depending on the partial pressure of adsorbate and the temperature derived
from the kinetical gas theory [68]:
(5.4)
where P is the partial pressure of the adsorbate in the feed, m is the mass of
one molecule, k is the Boltzmann constant and T is the temperature [K]. To be
able to calculate how many hits a molecule has with the walls of the
mesopores during the transmission through the wafer, the flow of molecules
per second entering the sample has to be calculated:
55 Discussion
(5.5)
In here p defines the partial pressure of the adsorbate in the feed, R in the gas
constant, T is the temperature, F(He) is the flow of the sweep gas and NA is the
Avogadro constant. With this data it is possible to determine the surface area
of the adsorbent needed for one poke of the adsorbate:
(5.6)
In the next step the surface area needed for poke leading to the sorption of the
adsorbate is identified by taking the sticking coefficient into account:
(5.7)
As the external surface area of the wafer is known the successful hits during
the transmission of the adsorbate through the wafer could be obtained by:
(5.8)
The results for temperatures of 343, 373 and 403 K and the adsorbates
benzene and p-xylene are summarized in Table 9.
Table 9: Results of the calculation considering the number of pokes leading to a pore entering during the transmission of benzene and p-xylene through the Wicke Kallenbach wafer
Adsorbate T
[K]
PFeed
[Pa]
Zw x 10-24
[1/(m2s)]
Fmolec.x10-16
[Molec./s]
Aper poke
x109
[m2]
Aper suc. poke
x102
[m2]
Nx102
[-]
Benzene 343 313,2 5.04 1.86 3.68 1.75 3.71
Benzene 373 313,2 4.84 1.81 3.75 1.78 3.64
Benzene 403 313,2 4.65 1.78 3.82 1.82 3.57
p-Xylene 343 234 3.23 1.32 4.10 1.88 3.46
p-Xylene 373 234 3.10 1.24 4.00 1.83 3.54
p-Xylene 403 234 2.98 1.21 4.06 1.86 3.49
The number of successful pokes is in the range of 350 per molecule during the
transmission through the wafer. This means that the establishing of an
adsorption/desorption equilibrium as postulated in the adsorber theory is in
good accordance with the previous determined sticking coefficients.
Consequently the theory of an adsorption zone is also valid.
Furthermore it is possible to estimate the length of the zone which is not in
equilibrium known as adsorption zone because it equals the length between
56 Discussion
two successful pokes. This value can simply be evaluated by taking the
reciprocal value of N and multiplying it with the total length of diffusion. This
leads to a length of the adsorption zone of 2.9x10-3 mm.
The final evidence for the assumed bed adsorber analogue gave the
comparison of the uptake curves of m-xylene and p-xylene which had to be
measured in two consecutive experiments due to experimental constraints.
The result is shown in Figure 34. Obviously m-xylene transmitted after 10
minutes where as breakthrough of p-xylene took 40 minutes. The form did not
change compared to the experiments of benzene and p–xylene and showed
both the same exponential form as p–xylene in the previous measurements.
This is due to the consecutive measurement: the overshooting as previously
seen in benzene is only observed if two adsorbates are present and the
adsorption enthalpies differ clearly [53].
The separation factor calculated as described in 2.2.1 had a value of 1.23
which equals 1 taking the error of the experiment into account. This is a totally
different behavior compared to the previously reported separation of p-xylene
from a mixture of o-, m- and p-xylene with the help of an MFI membrane [3].
Sakai et al. demonstrated that the differences in permeability due to the larger
minimum kinetic diameters of m-xylene in comparism to p-xylene lead to a
separation factor of 10 p-xylene/m-xylene at 373 K. This is significantly
different to our experiment. This experiment shows that the pressed Wicke
Kallenbach wafer did not act similar to a membrane and by this means the
theory of a statically dense membrane is not valid for this system.
In contrast to the theory a bed adsorber describes the experimental data very
good. The transmission times can be understood by the accessible adsorption
centers. M-xylene can only reach the outer surface having a BET surface area
of 65 m2/g. The sorption into the pores of the zeolite to adsorb at the
adsorption places inside the pore system is very slow due to the minimum
kinetic diameter. This process could be seen in the slow uptake in the late time
region of the uptake curve.
The other adsorbate p-xylene was able to access the pore system to adsorb
there which led to a transmission time of 40 minutes. Comparing this to the
observed BET total surface area of 446 m2/g of the wafer it can be concluded
57 Discussion
that the uptake time has a clear dependence on the accessible adsorbtion
centers. This is in good agreement with the postulated bed adsorber.
The fact that no separation occurred was due to the rate determining step
which was the Knudsen diffusion through the mesopores after the
adsorption/desorption equilibrium is established. As m-xylene and p-xylene
have the same mass the Knudsen diffusion coefficients have to be identical
(2.2.5) as the speed of this transport type is independent on the kinetic
diameter.
All these facts summarized in Table 10 show that the model of an adsorber
describes the wafer of the Wicke Kallenbach experiment bes
Table 10: Summary of the experimental facts and check of consistency to the adsorber and the statistically dense membrane model
Experimental Fact/Model Adsorber Membrane
breakthrough time consistent consistent
temperature dependence on breakthrough time of
benzene/p-xylene
consistent consistent
influence of wafer thickness on breakthrough time of
benzene/p-xylene
consistent inconsistent
dependence of the activation temperature on the
breakthrough time of benzene/p-xylene
consistent inconsistent
form of the uptake curves consistent -
equilibrium/ steady state separation factor = 1 benzene/p-
xylene
consistent inconsistent
equilibrium/ steady state separation factor = 1 p-xylene/m-
xylene
consistent inconsistent
missing temperature dependence on the separation factor
of benzene/p-xylene
consistent inconsistent
time dependence of the separation factor of benzene/p-
xylene
consistent -
sticking probalities consistent consistent
no activation energy of the diffusion consistent inconsistent
58 Discussion
Table 11: Summary of the results of the calculatng the diffusion coefficients of benzene and p-xylene in a Wicke Kallenbach wafer consisting of H-ZSM5. Furthermore the pore diameters calculated from these diffusion coefficients assuming Knudsen diffusion are reviewed
Sample Wafer
Weight
[mg]
Compacting
pressure
[kN]
Experimental
Temperature
[K]
Activation
Temperature
[K]
Diffusion
coefficient
Benzene x 10-7
[m2/s]
Diffusion
coefficient
p-xylene x 10-7
[m2/s]
pore diameter
calculated from
DBenzene x 10-9
[m]
pore diameter
calculated from
Dp-xylene x 10-9
[m]
H-ZSM5 100 20 373 723 6.51 6.39 6.14 7.02
H-ZSM5 100 20 343 723 6.74 7.20 6.53 8.14
H-ZSM5 100 20 403 723 6.39 6.18 6.11 6.54
H-ZSM5 150 20 373 723 6.56 5.77 6.18 6.35
H-ZSM5 50 20 373 723 4.88 3.60 4.61 3.96
H-ZSM5 100 20 373 423 6.32 5.62 5.96 6.18
H-ZSM5 100 10 373 723 6.61 7.16 6.24 7.88
59 Discussion
This fact leads to a characteristic length of diffusion equally to the thickness of
the wafer, in contrast to the radius of on particle as in the case of the
statistically dense membrane model. Consequently it was the possible to
calculate the diffusion coefficients by equation (2.2.2) from the equilibrium
molar ratios:
(5.10)
where L is characteristic length, r is the radius of the wafer, FHe is the flow rate
of the sweep gas helium and xAdsorbate is the molar ratio of the adsorbate in the
feed and the permeate at equilibrium conditions, respectively.
From the observed diffusion coefficients which were in the range of 10-6 m2/s
we could assume Knudsen diffusion. As a consequence it was possible to
calculate the radius of the pores by transposing (2.2.5). The transposed
equation is expressed by:
(5.11)
where R is the gas constant, T is the temperature, M is the molar mass. The
results of the calculation are shown in Table 11. The assumed Knudsen
diffusion is confirmed by the calculated pore diameters which are in the range
of 6 to 8 nm. Pores of this size were defined as mesopores [69] by the IUPAC
(International Union of Pure and Applied Chemistry). This means that the
diffusion in pressed wafers was limited by the transport in mesopores of 6 to 8
nm size.
Figure 46: SEM image of the surface of a Wicke Kallenbach wafer.
60 Discussion
This result fits to the impression of the SEM image which shows separated
particles (Figure 46)
It indicates as well that the wafer had pores of larger diameters than the
calculated ones of 6 to 8 nm but these pores were obviously not rate
determining. Thus, we can assume that the calculated pore diameters are the
smallest which occurred in the Wicke Kallenbach pellets as they determined
the transport rate.
The assumption of Knudsen diffusion determining the transport through the
wafer is also in good agreement with the physisorption isotherm of nitrogen.
Figure 47: t-plot produced with the method of Hasley for the H-ZSM5 Wicke Kallenbach wafer.
As previously described the isotherm had a much larger loop even at low
pressures of 0.2 P/P0 which corresponds to mesopores formed during the
pressing procedure. The BET surface area did not change from the powder to
the pressed disk and stayed at 420 to 450 m2/g.
The total volume of the micro- and mesopores was determined using a t-plot
(Figure 47) produced with the method of Halsey [70]. The results are
summarized in Table 12. It resulted in a total micropore volume of 0.147 cm3/g
and a mesopore volume of 0.232 cm3/g. A clear enhancement of the mesopore
volume was obtained compared to the pore volume of the parent material [5]
which was 0.147 cm3/g and 0.132 cm3/g micro– and mesopore volume. The
y = 0,048x + 0,147
y = 0,0095x + 0,3789
0
0,05
0,1
0,15
0,2
0,25
0,3
0,35
0,4
0,45
0,5
0 1 2 3 4 5 6 7 8 9
v ad
s[c
m3/g
STP
]
tHasley [nm]
61 Discussion
micropore volume stayed untouched which is the expected characteristic as
the micropores built up by the zeolite framework. This is not influenced by the
pressing of the powder and consequently the micropore volume had to stay
the same.
To have a closer look on the mesopores a DFT analysis of the physisorption
isotherm was performed to obtain the pore diameter of mesopores shown in
Figure 48.
Table 12: Results of the analysis if physisorption isotherms of H-ZSM5 in the powdered and the pressed form applying the BET equation [59] and the t-plot method [70]
Material SBET [m2/g] VMicro [cm3/g] VMeso [cm3/g]
powder 420 0.147 0.132
100 mg Wafer 446 0.147 0.232
The DFT analysis (Figure 48) showed an increase of mesopores with a
maximum of the distribution at a pore diameter of 17 nm. This is in good
agreement with the pore diameters calculated from the diffusion
measurements which were 6 to 8 nm. The huge pores indicated by the SEM
image are not found in the physisorption isotherm as they are larger than 65
nm.
Figure 48: pore size distribution of the parent H-ZSM5 material (black) and the Wicke Kallenbach wafer (red) obtained by DFT calculation.
0,00E+00
5,00E-04
1,00E-03
1,50E-03
2,00E-03
2,50E-03
50 150 250 350 450 550 650
dV
[cm
3/Å
/g]
pore size [Å]
62 Discussion
The assumption of Knudsen diffusion could also be confirmed by looking at the
activation energy which was determined by an Arrhenius ansatz describing the
diffusion coefficient by [66]:
(5.12)
(5.13)
In here D is the diffusion coefficient, EA,D is the activation energy of diffusion, R
is the gas constant and T is the temperature.
According to 5.13 it was possible to obtain the activation energy of the
diffusion of benzene and p-xylene for the rate determining step inside the sheet
by plotting 1/T against ln (D) (Figure 49).
Figure 49: Determination of the activation energy of benzene (black) and p-xylene (red) by an Arrhenius ansatz.
The calculation resulted in activation energies of -1.03 and -2.96 kJ/mol for
benzene and p-xylene, respectively. Taking the error of the system including
the inlet system and the mass spectrometer into account the activation energy
of diffusion was in the range of zero. Afterwards the ideal activation energy of
the Knudsen diffusion in the examined system was determined by calculation
the diffusion coefficients with:
(5.14)
The mean value of the obtained pore diameters from Table 11 was used for the
calculation. The results are shown in Table 13, Table 14 and Figure 50.
-14,4
-14,3
-14,2
-14,1
0,0024 0,0029
ln(D) [-]
1/T [1/K]
benzene
p-xylene
63 Discussion
Table 13: Calculated ideal Knudsen diffusion coefficients of benzene
T [K] D x 10-7 [m2/s]
343 6.38
373 6.65
403 6.91
Table 14: Calculated ideal Knudsen diffusion coefficients of p-xylene
T [K] D x 10-7 [m2/s]
343 5.47
373 5.70
403 5.93
Figure 50: Theoretical evaluation of the activation energy of benzene (black) and p-xylene (red) from the calculated Knudsen diffusion coefficients by a Arrhenius ansatz.
The results imply activation energies of 1.54 kJ/mol for both substances which
shows that the Knudsen diffusion has nearly no activation energy in this
system. Thus, the obtained activation energies of the measurements are in
good agreement with the theory and are consequently another hint for the
existence of Knudsen diffusion. This fact is also inconsistent with the
previously described theory of a dense membrane because the apparent
diffusion of benzene and p-xylene in the used ZSM5 sample has activation
energies according to Gobin et al. [60] of 23 and 35 kJ/mol, respectively.
Additionally curve fitting was preformed with the transmission curves of the
Wicke Kallenbach experiment. The aim of this method is to fit kinetic
-14,5
-14,4
-14,3
-14,2
-14,1
0,0023 0,0028
ln(D) [-]
1/T [1/K]
benzene
p-xylene
64 Discussion
parameters from the transmission curves of the Wicke Kallenbach
experiments. In order to do so a kinetic model was assumed and tried to fit the
experimental data. The data was fitted with a set of differential equations
describing an adsorber with an irreversible Langmuir adsorption.
The breakthrough curve was in this case specified by two differential
equations, one for the gaseous and one for the solid phase. These formulas
define the concentration dependent on time of the adsorbate where the solid
phase concentration is replaced by the surface coverage (Θ). Hence, the rate
of adsorption can be formulated by (6) [53].
(5.15)
In here Θ is the normalized surface coverage [71], ka is the reaction rate
coefficient and c is the concentration of the adsorbate in the gas phase.
The mass balance of the fluid phase describes the concentration of the
adsorbate dependent on the time [72]
(5.16)
These set of differential equations can be solved analytically according to
Bohart et. al [73]. The solution is shown in (5.17):
(5.17)
where C is the normalized concentration in the gas phase calculated by c/c0, ka
denotes the reaction rate coefficient, c0 is the concentration in the feed, t is the
reaction time, WSat is maximum amount of adsorbed gas, ρB is the density of
the bed, S is the section of the adsorbent bed and F is the gas flow rate.
Nonlinear parameter fitting was performed using a genetic algorithm
implemented in matlab. The fitting parameters were F and ka. The objective
minimized was the normalized root mean square error divided by t3 to get a
better fit in initial region of the curves. One example of the obtained fits is
shown in Figure 51.
65 Discussion
Figure 51: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 100°C, 100mg wafer
weight and 50 ml/min volume flow and the corresponding fit for benzene (black) and p-xylene (blue).
…
Figure 52: Trend of the parameter k with the temperature.
Due to the very primitive model and the in comparison to that very complex
adsorption behavior of the system the fits were poor. Nevertheless it was
possible to find trends for the strength of adsorption and the diffusion
coefficient. Hereby ka served as the parameter describing the limiting factor of
the adsorption on particle level which is according to Gobin et al. [60] the pore
entering step and F is proportional to the diffusion coefficient as the transport
through the pellet is a fully diffusive.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
x 104
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
t [s]
norm
aliz
ed c
once
ntra
tion
[-]
fit Benzene
measurement Benzene
fit p-Xylene
measurement p-xylene
0
0,01
0,02
0,03
0,04
0,05
0,06
0,07
0,08
0,09
60 70 80 90 100 110 120 130 140
k a [1
/s]
T [°C]
66 Discussion
The only trend observed was the dependence on the temperature. This can be
seen in the benzene fits. In here both parameters, k and F increased with
increasing temperature which was the expected behavior as activated
transport process getting faster with increasing temperature.
These trends are shown in Figure 52 and Figure 53. But even if these
parameters show a trend in the temperature it is very difficult to interpret the
outcome with respect to the experiment.
In conclusion the curve fitting shows that the used model is much too trivial to
be able to describe the complex behavior of the Wicke Kallenbach system we
looked at. Nevertheless it was shown that the fitting gave the same information
as the experiment itself.
This can be a good starting point for applying a more sophisticated model and
try to understand the mechanism inside the pellet by mathematical modeling.
Figure 53: Trend of the parameter k with the temperature.
Looking at the frequency response experiments is as well interesting. It was
found that the diffusion coefficient of the powdered sample was about
2.5x10-15 m2/s for benzene in H-ZSM5 which is much slower than the measured
diffusion coefficients in particles with a larger diameter. As intensely discussed
by Gobin et al. [60] the rate determining step is in the case of such small
particles no longer the intracrystalline diffusion but the surface adsorption and
the pore entering step.
Interestingly the time constant did not change after pressing the particles to
thin wafers of 6 to 10 mg and diameters of 20 mm. It proves that the
0,00E+00
5,00E-12
1,00E-11
1,50E-11
2,00E-11
2,50E-11
3,00E-11
3,50E-11
4,00E-11
4,50E-11
5,00E-11
60 70 80 90 100 110 120 130 140
F [m
3 /s]
T [°C]
67 Discussion
characteristic length of diffusion equals the one for a powder and a thin wafer
which means that the rate controlling transport step is in both cases the same.
This denotes that the diffusion in a thin wafer can be described in the same
way as for a powdered sample.
The behavior changed dramatically if the powder was pressed to Wicke
Kallenbach pellets of 1 mm thickness. The characteristic functions for this
experiment were not interpretable due to a very large time constants as can be
seen in Figure 54. The maximum of the out-of-phase function was below 10-3
Hz which means that they are not in the range of the frequency response
experiment. Therefore, the uptake rate measurements were performed
because this method is able to determine large time constants.
Figure 54: In of phase (blue) and out of phase (red) functions obtained by a pressure frequency response experiment with a Wicke Kallenbach wafer of 100mg and benzene as adsorbate.
With this method time constants of 350 to 5700 s were found which are
impossible to obtain with the frequency response method. The characteristic
length of diffusion differed for the Wicke Kallenbach wafer as discussed before
which was half of the wafer thickness (0.5 mm), in contrast to the particles
(0.4 μm). This led to diffusion coefficients of 10-10 m2/s.
Taking into account the values obtained by the Wicke Kallenbach experiments
(10-6 m2/s ) valid for the mesopores and the diffusivities for the powdered
sample (10-15 m2/s) it can be assume that the adsorption in a Wicke Kallenbach
wafer is controlled by a mixture of both processes. But it can be seen from the
10-3
10-2
10-1
100
101
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Frequency [Hz]
char
acte
rist
ic fu
nctio
ns [-
]
fit-v1 in
fit-v1 out
68 Discussion
Wicke Kallenbach experiment that the flow through the wafer once the
adsorption desorption equilibrium is reached is only controlled by the transport
through the mesopores.
Applying the powder to the uptake rate measurement of benzene time
constants of 220 to 614 s were found. Surprisingly the time constant increased
with increasing benzene partial pressure which means that the diffusion
became slower with increasing vapor pressure. This behavior showed clearly
the non idealities of the system. It can be concluded that the dosing of
adsorbate into the system had the biggest influence on the result. This means
that it is impossible to perform a step change of the adsorbate concentration
with the used setup. Therefore, the diffusion of benzene in H-ZSM5 powder is
too rapid for uptake rate measurements. This is in good agreement with the
pressure modulation experiments and thereby with the previously reported
diffusivities [60].
69 Conclusion
6. Conclusion
The transport processes of strong adsorbing substances on pressed wafers in
a Wicke Kallenbach cell were investigated. In order to do so the system H-
ZSM5 with adsorbates benzene and p-xylene was examined. Experimental
results confirmed that the wafer could be described as a bed adsorber
analogue. The results leading to this conclusion were in particular the clear
dependences of the transmission time, the uptake time and the form of the
breakthrough curve on the temperature, the wafer thickness, the activation
temperature and the compacting pressure.
The wafer was a mesoporous accumulation of ZSM5 powder with the same
BET surface area as the non-compacted sample of 430 m2/g. During the
pressing procedure mesopores of 6 to 15 nm diameter were formed which was
confirmed by DFT calculations of the nitrogen physisorption isotherm and
calculations from the Wicke Kallenbach experiment.
At equilibrium conditions, which means after saturation of the wafer the
transport process was limited to the rate of diffusion through the mesopores.
Thus the separation factor is 1 independent of external parameters like
temperature, activation temperature, wafer thickness and compacting pressure
for molecules having a similar molar mass. This could be seen in the
experiments applying either p-xylene benzene mixtures or a blend of p-xylene
and m-xylene. Especially the measurement with m-xylene and p-xylene varified
that the wafer acted like a bed adsorber. The previously reported assumption,
that the pressed wafer acts like a grown membrane and could separate p-
xylene from a mixture of xylenes as described in the literature applying a MFI
membrane [3], proved to be wrong. So unfortunately it is impossible to
separate hydrocarbons with a pressed membrane of MFI particles.
The change in rate determining transport steps from the powder to the wafer
was also approved by the combination of pressure modulation frequency
response and uptake rate measurements. They show an increase of time
constants of two orders of magnitude by compacting the powder to a wafer
which is due to a increase of the charactistic length of diffusion from 0.4 μm to
1 mm. The diffusion coefficient previously reported by Gobin et al. [60] for the
70 Conclusion
parent wafer was confirmed whereas the uptake rate measurements showed
an increase in the diffusion coefficient by 5 orders of magnitude approving that
the uptake in the wafer is determined by a combination of Knudsen diffusion
and the pore entrance step. Nevertheless the Wicke Kallenbach experiments
showed that once the adsorption desorption equilibrium is established the
Knudsen diffusion controls the transmission rate.
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I Appendix A: Results
A. Results
A.1 Wicke Kallenbach experiments
A.1.1Variation of the temperature
Figure I: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 70°C, 100mg wafer weight
and 50 ml/min volume flow.
Figure II: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 100°C, 100mg wafer
weight and 50 ml/min volume flow.
0 50 100 150 200 250 300 35010
-10
10-9
10-8
10-7
10-6
10-5
10-4
time [min]
c [m
ol/l
]
Benzene
p-Xylene
0 50 100 150 200 250 300 35010
-10
10-9
10-8
10-7
10-6
10-5
10-4
time [min]
c [m
ol/l
]
Benzene
p-Xylene
II Appendix A: Results
Figure III: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 130°C, 100mg wafer
weight and 50 ml/min volume flow.
Figure IV: Time dependence of the separation factor of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 at 70°C, 100mg wafer weight, a mixture of benzene/p-xylene and 50
ml/min volume flow.
0 50 100 150 200 250 30010
-9
10-8
10-7
10-6
10-5
10-4
time [min]
c [m
ol/l
]
Benzene
p-Xylene
0 50 100 150 200 250 300 350
10-1
100
101
102
103
time [min]
Sepe
ratio
n Fa
ctor
[-]
III Appendix A: Results
Figure V: Time dependence of the separation factor of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 at 100°C, 100mg wafer weight, a mixture of benzene/p-xylene and
50 ml/min volume flow.
Figure VI: Time dependence of the separation factor of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 at 130°C, 100mg wafer weight, a mixture of benzene/p-xylene and
50 ml/min volume flow.
0 50 100 150 200 250 300 35010
-2
100
102
104
106
time [min]
Sepe
ratio
n Fa
ctor
[-]
0 50 100 150 200 250 300 35010
-2
10-1
100
101
102
103
time [min]
Sepe
ratio
n Fa
ctor
130
°C H
-ZSM
5
IV Appendix A: Results
A.1.2 Variation of the wafer thickness
Figure VII: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 100°C, 50mg
wafer weight and 50 ml/min volume flow.
Figure VIII: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 100°C, 150mg
wafer weight and 50 ml/min volume flow.
0 100 200 300 400 500 600 700 80010
-8
10-7
10-6
10-5
time [min]
c [m
ol/l
]
Benzene
p-Xylene
0 100 200 300 400 500 600 70010
-8
10-7
10-6
10-5
10-4
time [min]
c [m
ol/l
]
Benzene
p-Xylene
V Appendix A: Results
Figure IX: Time dependence of the separation factor of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 at 100°C, 50mg wafer weight, a mixture of benzene/p-xylene and 50
ml/min volume flow.
Figure X: Time dependence of the separation factor of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 at 100°C, 150mg wafer weight, a mixture of benzene/p-xylene and
50 ml/min volume flow.
0 100 200 300 400 500 600 700 80010
-2
10-1
100
101
102
103
104
time [min]
Sepe
ratio
n Fa
ctor
[-]
0 100 200 300 400 500 60010
-2
10-1
100
101
102
103
104
time [min]
Sepe
ratio
n Fa
ctor
[-]
VI Appendix A: Results
A.1.3 Variation of the activation temperature
Figure XI: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 100°C, 100mg wafer
weight and 50 ml/min volume flow, activated at 423 K.
Figure XII: Time dependence of the separation factor of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 at 100°C, 100mg wafer weight, a mixture of benzene/p-xylene
and 50 ml/min volume flow, activated at 423 K (black) and 723 K (red).
0 50 100 150 200 250 300 350 40010
-8
10-7
10-6
10-5
10-4
time [min]
c [m
ol/l
]
Benzene
p-Xylene
0 20 40 60 80 100 120 140 160 180 20010
-4
10-2
100
102
104
time [min]
Sepe
ratio
n Fa
ctor
[-]
150°C
450°C
VII Appendix A: Results
A.1.4 Influence of the compacting pressure
Figure XIII: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 100°C, 100mg wafer
weight and 50 ml/min volume flow, compacted with a pressure of 10 kN.
Figure XIV: Time dependence of the separation factor of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 at 100°C, 100mg wafer weight, a mixture of benzene/p-xylene and
50 ml/min volume flow, compacted with pressure of 10 kN (black) and 20 kN (red)
0 50 100 150 200 250 30010
-8
10-7
10-6
10-5
time [min]
c [m
ol/l
]
Benzene
p-Xylene
0 20 40 60 80 100 120 140 160 180 20010
-1
100
101
102
103
time [min]
Sepe
ratio
n Fa
ctor
[-]
10kN
20kN
VIII Appendix A: Results
A.2 Frequency Response experiments
A.2.1 H-ZSM5 powder
Figure XV: In- (black) and out-of-phase (red) functions of the batch FR experiment of H-ZSM5 powder. The fit was produced by applying a non-uniform infinite sheet model.
Figure XVI: In- (black) and out-of-phase (red) functions of the batch FR experiment of H-ZSM5 powder. The fit was produced by applying a non-uniform infinite sheet model with surface
resistance.
10-3
10-2
10-1
100
101
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
Frequency [Hz]
char
acte
rist
ic fu
nctio
ns [-
]
in-of-phase
out-of-phase
fit in-of-phase
fit out-of-phase
10-3
10-2
10-1
100
101
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
Frequency [Hz]
char
acte
rist
ic fu
nctio
ns [-
]
in-of-phase
out-of-phase
fit in-of-phase
fit out-of-phase
IX Appendix A: Results
A.2.2 H-ZSM5 thin wafer
Figure XVII: In- (black) and out-of-phase (red) functions of the batch FR experiment of an H-ZSM5 Wicke Kallenbach wafer. The fit was produced by applying a non-uniform infinite sheet
model.
Figure XVIII: In- (black) and out-of-phase (red) functions of the batch FR experiment of an H-ZSM5 Wicke Kallenbach wafer. The fit was produced by applying a non-uniform infinite sheet
model with surface resistance.
10-3
10-2
10-1
100
101
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
Frequency [Hz]
char
acte
rist
ic fu
nctio
ns [-
]
in-of-phase
out-of-phase
fit in-of-phase
fit out-of-phase
10-3
10-2
10-1
100
101
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
Frequency [Hz]
char
acte
rist
ic fu
nctio
ns [-
]
in-of-phase
out-of-phase
fit in-of-phase
fit out-of-phase
X Appendix A: Results
A.3 Uptake Rate measurements
A.3.1 H-ZSM5 powder
Figure XIX: Uptake curve of benzene in H-ZSM5 powder at a partial pressure of 0.1 mbar and 373K. The figure shows the experimental data (black) and the result of the curve fitting (red)
applying an infinite plane sheet model of 1mm thickness.
Figure XX: Uptake curve of benzene in H-ZSM5 powder at a partial pressure of 1 mbar and 373K. The figure shows the experimental data (black) and the result of the curve fitting (red)
applying an infinite plane sheet model of 1mm thickness.
0 50 100 150 200 2500
0.2
0.4
0.6
0.8
1
1.2
1.4
time [s]
norm
aliz
ed m
ass
[-]
experiment
fit
0 20 40 60 80 100 120 140 160 180 2000
0.2
0.4
0.6
0.8
1
1.2
1.4
time [s]
norm
aliz
ed m
ass
[-]
experiment
fit
XI Appendix A: Results
Figure XXI: Uptake curve of benzene in H-ZSM5 powder at a partial pressure of 2 mbar and 373K. The figure shows the experimental data (black) and the result of the curve fitting (red)
applying an infinite plane sheet model of 1mm thickness.
Figure XXII: Uptake curve of benzene in H-ZSM5 powder at a partial pressure of 10 mbar and 373K. The figure shows the experimental data (black) and the result of the curve fitting (red)
applying an infinite plane sheet model of 1mm thickness.
0 50 100 150 200 2500
0.2
0.4
0.6
0.8
1
1.2
1.4
time [s]
norm
aliz
ed m
ass
[-]
experiment
fit
0 100 200 300 400 500 600 700 800 9000
0.2
0.4
0.6
0.8
1
1.2
1.4
time [s]
norm
aliz
ed m
ass
[-]
experiment
fit
XII Appendix A: Results
A.3.2 H-ZSM5 Wicke Kallenbach wafer
Figure XXIII: Uptake curve of benzene in an H-ZSM5 Wicke Kallenbach wafer of 100 mg at a partial pressure of 0.1 mbar and 373K. The figure shows the experimental data (black) and the
result of the curve fitting (red) applying an infinite plane sheet model of 1mm thickness.
Figure XXIV: Uptake curve of benzene in an H-ZSM5 Wicke Kallenbach wafer of 100 mg at a partial pressure of 1 mbar and 373K. The figure shows the experimental data (black) and the
result of the curve fitting (red) applying an infinite plane sheet model of 1mm thickness.
0 200 400 600 800 1000 1200 1400 1600 18000
0.2
0.4
0.6
0.8
1
1.2
1.4
time [s]
norm
aliz
ed m
ass
[-]
experiment
fit
0 200 400 600 800 1000 12000
0.2
0.4
0.6
0.8
1
1.2
1.4
time [s]
norm
aliz
ed m
ass
[-]
experiment
fit
XIII Appendix A: Results
Figure XXV: Uptake curve of benzene in an H-ZSM5 Wicke Kallenbach wafer of 100 mg at a partial pressure of 2 mbar and 373K. The figure shows the experimental data (black) and the
result of the curve fitting (red) applying an infinite plane sheet model of 1mm thickness.
Figure XXVI: Uptake curve of benzene in an H-ZSM5 Wicke Kallenbach wafer of 100 mg at a partial pressure of 10 mbar and 373K. The figure shows the experimental data (black) and the
result of the curve fitting (red) applying an infinite plane sheet model of 1mm thickness.
0 200 400 600 800 1000 1200 14000
0.2
0.4
0.6
0.8
1
1.2
1.4
time [s]
norm
aliz
ed m
ass
[-]
experiment
fit
0 200 400 600 800 1000 1200 1400 1600 1800 20000
0.2
0.4
0.6
0.8
1
1.2
1.4
time [s]
norm
aliz
ed m
ass
[-]
experiment
fit
XIV Appendix A: Results
A.4 Nitrogen physisorption isotherms
A.4.1 H-ZSM5 powder
Figure XXVII: Nitrogen physisorption isotherm of ZSM-5 parent powder material.
Figure XXVIII: t-plot produced with the method of Hasley for H-ZSM5 powder.
0
50
100
150
200
250
300
0,00E+00 2,00E-01 4,00E-01 6,00E-01 8,00E-01 1,00E+00 1,20E+00
Vad
s[cm
3/g
]
p/p0
y = 0,0304x + 0,2787R² = 0,9908
y = 0,0542x + 0,1471R² = 0,9979
0
0,05
0,1
0,15
0,2
0,25
0,3
0,35
0,4
0,45
0 1 2 3 4 5
v ad
s[c
m3/g
STP
]
tHasley [nm]
XV Appendix A: Results
Figure XXIX: Linearization of the nitrogen physisorption isotherm in the low pressure range according to the BET theory of an H-ZSM5 powder sample.
A.4.2 H-ZSM5 Wicke Kallenbach wafer
Figure XXX: Nitrogen physisorption isotherm of a H-ZSM5 Wicke Kallenbach wafer.
y = 0,0104x + 3E-06R² = 0,9999
0,00E+00
1,00E-04
2,00E-04
3,00E-04
4,00E-04
5,00E-04
6,00E-04
7,00E-04
8,00E-04
9,00E-04
0,00E+001,00E-022,00E-023,00E-024,00E-025,00E-026,00E-027,00E-028,00E-029,00E-02
(p/p
0)/
Vad
s*(1
-p/p
0) [
g/cm
3]
p/p0 [-]
0
50
100
150
200
250
300
350
0,00E+00 2,00E-01 4,00E-01 6,00E-01 8,00E-01 1,00E+00 1,20E+00
Vad
s[cm
3/g
]
p/p0 [-]
XVI Appendix A: Results
Figure XXXI: t-plot produced with the method of Hasley for a H-ZSM5 Wicke Kallenbach wafer.
Figure XXXII: Linearization of the nitrogen physisorption isotherm in the low pressure range according to the BET theory of an H-ZSM5 Wicke Kallenbach wafer.
y = 0,048x + 0,147R² = 0,9966
y = 0,0095x + 0,3789R² = 0,5502
0
0,05
0,1
0,15
0,2
0,25
0,3
0,35
0,4
0,45
0,5
0 1 2 3 4 5 6 7 8 9
v ad
s[c
m3/g
STP
]
tHasley [nm]
y = 0,0098x + 5E-08R² = 1
0
0,0001
0,0002
0,0003
0,0004
0,0005
0,0006
0,0007
0,0008
0,0009
0,00E+001,00E-022,00E-023,00E-024,00E-025,00E-026,00E-027,00E-028,00E-029,00E-02
(p/p
0)/
Vad
s*(1
-p/p
0) [
g/cm
3]
p/p0 [-]
XVII Appendix A: Results
A.5 Matlab source code
A.5.1 Processing of Wicke Kallenbach experimental data
function f_Trennfaktor_gegen_Zeit_und_TAbhaengigkeit [ filename dirpath ] = uigetfile ( '130'); [ MZ1 ] = textread ([ dirpath filename ]); t_MZ1 = MZ1 ( :, 1 ); Start1 = 2.17 .* ( 10 ^ 6 ); m1 = find ( t_MZ1 == Start1 ); t_MZ1 = MZ1 ( m1 : end, 1 ); I_MZB1 = MZ1 ( m1 : end, 3 ); I_MZX1 = MZ1 ( m1 : end, 4 ); c_MZB1 = 6936.1 .* I_MZB1; c_MZX1 = 10173 .* I_MZX1; c_MZX1 = c_MZX1 .* 1.44; S1 = c_MZB1 ./ ( c_MZX1 ); t_MZ1 = t_MZ1 - t_MZ1 ( 1 ); t_MZ1 = t_MZ1 ./ 60000; figure( 1 ) plot ( t_MZ1, S1, 'r+' ) xlabel ( 'time [min]' ), ylabel ( 'Seperation Factor 130 °C H-ZSM5' ),
title ( 'Trend of Seperation Factor' ) figure( 2 ) semilogy ( t_MZ1, c_MZB1, 'ks', t_MZ1, c_MZX1, 'r+') xlabel ( 'time [min]' ), ylabel ( 'c [mol/l]' ), title ( 'Zeolite H-
ZSM5 130 °C' ),legend ( 'Benzene', 'p-Xylene' ) [ filename dirpath ] = uigetfile ( '100'); [ MZ2 ] = textread ([ dirpath filename ]); t_MZ2 = MZ2 ( :, 1 ); Start2 = 2.93 .* ( 10 ^ 6 ); m2 = find ( t_MZ2 == Start2 ); t_MZ2 = MZ2 ( m2 : end, 1 ); I_MZB2 = MZ2 ( m2 : end, 3 ); I_MZX2 = MZ2 ( m2 : end, 4 ); c_MZB2 = 6936.1 .* I_MZB2; c_MZX2 = 10173 .* I_MZX2; c_MZX2 = c_MZX2 .* 1.44; S2 = c_MZB2 ./ ( c_MZX2 ); t_MZ2 = t_MZ2 - t_MZ2 ( 1 ); t_MZ2 = t_MZ2 ./ 60000; figure( 3 ) plot ( t_MZ2, S2, 'r+' ) xlabel ( 'time [min]' ), ylabel ( 'Seperation Factor 100 °C HZSM-5' ),
title ( 'Trend of Seperation Factor' ) figure( 4 ) semilogy ( t_MZ2, c_MZB2, 'ks', t_MZ2, c_MZX2, 'r+') xlabel ( 'time [min]' ), ylabel ( 'c [mol/l]' ), title ( 'Zeolite H-
ZSM5 100 °C' ),legend ( 'Benzene', 'p-Xylene' ) [ filename dirpath ] = uigetfile ( '70'); [ MZ3 ] = textread ([ dirpath filename ]); t_MZ3 = MZ3 ( :, 1 ); Start3 = 2.26 .* ( 10 ^ 6 ); m3 = find ( t_MZ3 == Start3 ); t_MZ3 = MZ3 ( m3 : end, 1 ); I_MZB3 = MZ3 ( m3 : end, 3 ); I_MZX3 = MZ3 ( m3 : end, 4 ); c_MZB3 = 6936.1 .* I_MZB3; c_MZX3 = 10173 .* I_MZX3; c_MZX3 = c_MZX3 .* 1.44; S3 = c_MZB3 ./ ( c_MZX3 );
XVIII Appendix A: Results
t_MZ3 = t_MZ3 - t_MZ3 ( 1 ); t_MZ3 = t_MZ3 ./ 60000; figure( 5 ) plot ( t_MZ3, S3, 'r+' ) xlabel ( 'time [min]' ), ylabel ( 'Seperation Factor 70 °C HZSM-5' ),
title ( 'Trend of Seperation Factor' ) figure( 6 ) semilogy ( t_MZ3, c_MZB3, 'ks', t_MZ3, c_MZX3, 'r+') figure( 7 ) xlabel ( 'time [min]' ), ylabel ( 'c [mol/l]' ), title ( 'Zeolite H-
ZSM5 70 °C' ),legend ( 'Benzene', 'p-Xylene' ) semilogy ( t_MZ1, c_MZB1, 'kx', t_MZ2, c_MZB2, 'ko',t_MZ3, c_MZB3,
'ks' ) xlabel ( 'time [min]' ), ylabel ( 'c [mol/l]' ), title ( 'Zeolite H-
ZSM5 T - Äbhängigkeit Benzol' ), legend ( '130 °C', '100 °C', '70 °C'
) figure( 8 ) semilogy ( t_MZ1, c_MZX1, 'rx', t_MZ2, c_MZX2, 'ro',t_MZ3, c_MZX3,
'rs' ) xlabel ( 'time [min]' ), ylabel ( 'c [mol/l]' ), title ( 'Zeolite H-
ZSM5 T - Äbhängigkeit p-Xylol' ), legend ( '130 °C', '100 °C', '70 °C'
)
XIX Appendix B: Simulation
B. Simulation
B.1 Curve fitting of Wicke Kallenbach experiments
Figure XXXIII: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 70°C, 100mg
wafer weight and 50 ml/min volume flow and the corresponding fit for benzene (black) and p-xylene (blue).
Figure XXXIV: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 100°C, 100mg
wafer weight and 50 ml/min volume flow and the corresponding fit for benzene (black) and p-xylene (blue).
0 0.5 1 1.5 2 2.5
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XX Appendix B: Simulation
Figure XXXV: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 130°C, 100mg
wafer weight and 50 ml/min volume flow and the corresponding fit for benzene (black) and p-xylene (blue).
Figure XXXVI: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 100°C, 50mg
wafer weight and 50 ml/min volume flow and the corresponding fit for benzene (black) and p-xylene (blue).
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XXI Appendix B: Simulation
Figure XXXVII: Concentration vs. time diagram of the Wicke Kallenbach experiment using a pressed wafer of ZSM5 and a mixture of benzene (black) and p-xylene (red), 100°C, 150mg
wafer weight and 50 ml/min volume flow and the corresponding fit for benzene (black) and p-xylene (blue).
Table I: Parameters obtained by non-linear curve fitting of the transmission curves of the Wicke Kallenbach experiments
Benzene p-Xylene
T [K] Weight [g] k [1/s] F [m3/s] k [1/s] F [m3/s]
343 100 0.029 2.14x10-11 0.013 1.1x10-11
373 100 0.053 3.08x10-11 0.012 9.94x10-12
403 100 0.082 4.50x10-11 0.014 2.00x10-11
373 50 0.047 3.00x10-11 0.014 2.45x10-11
373 150 0.300 1.71x10-11 0.010 7.54x10-12
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XXII Appendix B: Simulation
B.2 Matlab source code of Wicke Kallenbach curve fitting
B.2.1 Main program
function [] = f_Wicke_Kallenbach_curve_fitting ( start )
% In the first part the data is read and converted [ filename dirpath ] = uigetfile ( 'Xylol' ); [ Xylol ] = textread ([ dirpath filename ]); t = Xylol ( : , 1 );
% Then the normalized concentration vs. time diagram is calculated
from the % experimental data Start1 = start; n = find ( t == Start1 ); t = Xylol ( n : end, 1 ); I_Xylol = Xylol ( n : end, 3 ); I_Benzol = Xylol ( n : end, 4 ); C_Xylol = I_Xylol ./ max ( I_Xylol ); C_Benzol = I_Benzol ./ max ( I_Benzol ); t = t - t ( 1 ); t = t ./ 1000;
% Afterwards the curve fitting is performed applying a genetic
algorithm [ kB FB ] = f_Wicke_Kallenbach_ga_fit_breakthrough_curve_Benzene( t,
C_Benzol ) [ kX FX ] = f_Wicke_Kallenbach_ga_fit_breakthrough_curve_xylene( t,
C_Xylol )
%In the last step the solutions are plotted together with the
experimental %data Wsat = 0.0744; rhoB = 1.44 * 10 .^ 3; S = 4.18 * ( 10 .^ -8 ); x = 10 ^ -3; c0B = 0.13; c0X = 9.77 .* ( 10 .^ -2 );
for n = 1 : 1 : length ( kB )
XB = (kB ( n ) .* Wsat .* rhoB .* S ./ ( FB ( n ))) .* x;
TB = kB ( n ) .* c0B .* t;
CB ( :, n ) = exp ( TB - (0.9999 .* TB )) ./ ( exp ( TB - (0.9999 .*
TB )) + exp ( XB - (0.9999 .* TB )) - exp ( - 0.9999 .* TB ));
end
for m = 1 : 1 : length ( kX )
XX = (kX ( m ) .* Wsat .* rhoB .* S ./ ( FX ( m ))) .* x;
TX = kX ( m ) .* c0X .* t;
XXIII Appendix B: Simulation
CX ( :, m ) = exp ( TX - (0.9999 .* TX )) ./ ( exp ( TX - (0.9999 .*
TX )) + exp ( XX - (0.9999 .* TX )) - exp ( - 0.9999 .* TX ));
end
for n = 1 : 1 : length ( kB ) for m = 1 : 1 : length ( kX )
x = kB ( n ); y = FB ( n ); z = kX ( m ); u = FX ( m ); i = 3 + ( n - 1 ) .* length ( kX ) + m; figure ( i ) plot ( t, CB ( :, n ), 'k+', t, C_Benzol, 'r-', t, CX ( :, m ), 'b*',
t, C_Xylol, 'go' ) legend ( 'fit Benzene', 'measurement Benzene', 'fit p-Xylene',
'measurement p-xylene' ) text( 20000, 1,... ['kB = ',num2str(x)],... 'HorizontalAlignment','center') text( 20000, 0.75,... ['FB = ',num2str(y)],... 'HorizontalAlignment','center') text( 20000, 0.5,... ['kX = ',num2str(z)],... 'HorizontalAlignment','center') text( 20000, 1,... ['FX = ',num2str(u)],... 'HorizontalAlignment','center') end end
B.2.2 Genetic algorithm
% This script implements the Simple Genetic Algorithm described % in the examples section of the GA Toolbox manual. % % Author: Andrew Chipperfield % History: 23-Mar-94 file created % % tested under MATLAB v6 by Alex Shenfield (22-Jan-03) function [ kB FB ] =
f_Wicke_Kallenbach_ga_fit_breakthrough_curve_Benzene( t, CB_fit ) %imax = 3;
GGAP = .9; % Generation gap, how many new individuals are
created NVAR1 = 1; % Number of variables NVAR2 = 1; NIND = 40; % Number of individuals MAXGEN = 3000; % Number of generations PRECI = 20; % Precision of binary representation
% Build field descriptor FieldD1 = [rep([PRECI],[1, NVAR1]); rep([10^-5;1],[1, NVAR1]);... rep([1; 0; 1 ;1], [1, NVAR1])];
XXIV Appendix B: Simulation
FieldD2 = [rep([PRECI],[1, NVAR2]); rep([0.1 * 10^-10; 10^-5],[1,
NVAR2]);... rep([1; 0; 1 ;1], [1, NVAR2])];
% Initialise population Chrom1 = crtbp(NIND, NVAR1*PRECI); Chrom2 = crtbp(NIND, NVAR2*PRECI); % Reset counters Best = NaN*ones(MAXGEN,1); % best in current population gen = 0; % generational counter
% Evaluate initial population x = [bs2rv(Chrom1,FieldD1) bs2rv(Chrom2,FieldD2)]; [ObjV] = f_Wicke_Kallenbach_simulate_breakthrough_curve_Benzene_fit
( x, t, CB_fit ); ObjV = ObjV';
% Track best individual and display convergence Best(gen+1) = min(ObjV); figure(2) plot(log10(Best),'ro');xlabel('generation'); ylabel('log10(f(x))'); text(0.5,0.95,['Best = ',
num2str(Best(gen+1))],'Units','normalized'); drawnow;
% Generational loop while gen < MAXGEN,
% Assign fitness-value to entire population FitnV = ranking(ObjV);
% Select individuals for breeding SelCh1 = select('sus', Chrom1, FitnV, GGAP); SelCh2 = select('sus', Chrom2, FitnV, GGAP);
% Recombine selected individuals (crossover) SelCh1 = recombin('xovsp',SelCh1,0.7); SelCh2 = recombin('xovsp',SelCh2,0.7);
% Perform mutation on offspring SelCh1 = mut(SelCh1); SelCh2 = mut(SelCh2);
% Evaluate offspring, call objective function x = [bs2rv(SelCh1,FieldD1) bs2rv(SelCh2,FieldD2)]; [ObjVSel] =
f_Wicke_Kallenbach_simulate_breakthrough_curve_Benzene_fit ( x, t,
CB_fit ); ObjVSel = ObjVSel';
% Reinsert offspring into current population [Chrom1 ObjV]=reins(Chrom1,SelCh1,1,1,ObjV,ObjVSel); [Chrom2 ObjV]=reins(Chrom2,SelCh2,1,1,ObjV,ObjVSel);
% Increment generational counter gen = gen+1;
% Update display and record current best individual Best(gen+1) = min(ObjV); figure(2)
XXV Appendix B: Simulation
plot(log10(Best),'ro'); xlabel('generation');
ylabel('log10(f(x))'); text(0.5,0.95,['Best = ',
num2str(Best(gen+1))],'Units','normalized'); drawnow; end I = find(ObjV == (min(ObjV))); P1 = bs2rv(Chrom1,FieldD1); kB = P1 ( I ); P2 = bs2rv(Chrom2,FieldD2); FB = P2 ( I ); % End of GA
B.2.3 Fitness function
function [ObjV] =
f_Wicke_Kallenbach_simulate_breakthrough_curve_Benzene_fit ( x, t,
CB_fit )
ka = x ( : , 1 ); Wsat = 0.0744; rhoB = 1.44 * 10 .^ 3; S = 4.18 * ( 10 .^ -8 ); FB = x ( : , 2 ); x = 10 ^ -3; c0B = 0.13;
for n = 1 : 1 : length (ka)
XB = (ka ( n ) .* Wsat .* rhoB .* S ./ ( FB ( n ))) .* x;
TB = ka ( n ) .* c0B .* t;
CB = exp ( TB - ( TB .* 0.9999 )) ./ ( exp ( TB - ( TB .* 0.9999 )) +
exp ( XB - ( TB .* 0.9999 )) - exp( - TB .* 0.9999 ));
x = (( CB - CB_fit ) .^ 2 ); y = ( x ( 2 : end ) .* t ( 2 : end ) .^ 3 ) ./ ( 2 ); FitnV ( n ) = sum( y );
end
ObjV = FitnV;