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Influence of pelleting conditions on catalyst pore structure and effectiveness
Applied Catalysis,28 (1986)133-142 Ekevier Science Publishers B.V.,. Amsterdam - Printed in The NetherLands
Jan UCHYTIL, Institute
MiloE
KRAUS and Petr SCHNEIDER
of ChemicaT
Process
to’5 02 Prague 6-Suchdol, [Received
133
13 March
Fundamentals,
Czechoslovak
Academy
of Sciences,
Czechoslovakia,
1986, accepted
28 3uTy
1986)
The changes in textural and transport properties of v-alumina pellets caused by pellet compression are demonstrated. Transport properties were determined by ccombination a? binary countercurrent diffusion and permeation measurements. Changf5 in CdtdjytfC pWfof%TdfTCt? Of pkZljt?tS Wre teStP_d k3+3t?ri1TIeITtd~i'y USirTg gdS-phdSe ccyc~nhexano'~ dehydration; effectiveness factors of pe)>ets CDU~L) be yery accurately predicted using the theory of multicomponent diffusion in the transition region, the parameters obtained from measurements of pure transport processes and the reaction kinetics not influenced by mass transport.
INTRODUCT[ON One of the steps frequently ccata\ysts is tke formation influence
the intrinsic
structure
which,
the pellets. powdered
in
(one-sided, additives
of
variables
two-sided), {graphite,
activity
of alumina
fatty
in pore structure from evaluation parameters
substances
of mass
several
authors
explained applied. increasing
transport
affects active
of pellets
the pore
mass
within
by compression
of
the mode of compression
and the presence
of pelletization
reaction
pellets.
of pelletization
measured
pressure
rates using either
by transport
processes
inside
of the pellets
factors,
the pellets
on the powdered
the changes obtained
[1,2]. These
only and are independent
This based
parameters
on the
pellets
We have also characterized
materials
effectiveness
can be proved
by correct
solely on transaort
catalyst,
without
of
parameters
the inter-
transfer. of pelleting
pressure
[3-51. The observed
by structural
changes
compacting
pressure
on catalyst
significant
of the catalyst
In the case of V205-Si02
0166-9834/86/$03.50
the
pressure,
used for their evaluation.
of the pellet
The influence
the
the pore structure
and on the true kinetics, vention
the influence
by comparing
by crushing
of simple
of
acids or salts etc.,).
of the compressed
reflect
the gaseous prediction
granulometry
of industrial
this step does not usuaJ\y
utilization
in the preparation
the powder
pellets,
obtained
the
sequence
it significantly
are the pelletization
In this work we have studied or powders
Even tkDugh
activity,
determines
material
in the preparation
peJ\ets.
catalytic
turn,
The main
catalyst
employed
catalysts,
was ascribed
activity
increase materials
the decrease to diminished
0 1986 ElsevierScience Publishers B.V.
has been studied
in activity
by
[3,4] was
due to the high pressure of pellet
activity
pore diameters
[5].
with
134 In the present work, gas phase cyclohexanol v-alumina
at ZIO'C and atmospheric
evaluation
of the activities
and the corresponding
pressure
of pellets,
dehydration
to cyclohexene
was used as the model
obtained
at different
on
reaction
for
compacting
pressure,
powders.
wt.%
-50
0
loo
II*
10'
lo3 d , m
FIGURE
1
Integral
and differential
from a combination
particle
size, d, distribution
of sieve and sedimentation
of boehmit
analyses.
EXPERIMENTAL Cylindrical pression
pellets
of alumina
in a laboratory
containing
5 wt? of aluminium
(see Figure compacting pressure
level.
were
Figure
2. measurements
were
reaction
below
1. Their
performed
Reaction
runs aimed at obtaining
kPa by adding
determined
by adding
hydrogen water
possible
products
to calculate
(50-80
kPa).
reactor
on
was 60 to 100
to keep
the initial
by GLC.
crushed
pressure
to the feed. The inhibiting
to the feed
in
was used as inert
were analyzed
partial
weight
in
is shown
was high in order
the rate equation,
(0.16 - 0.4 mm) were used and cyclohexanol 100-700
air at 600°C for 2 hours.
form. Catalyst
feed. The space velocity
Five
at each
(A, B, C) were determined
in a glass differential-flow
and crushed
gauges.
prepared
pore size distribution
10%; it was, therefore,
rates as x/(W/F).
In kinetic
tensometric
in flowing
boehmit
size distribution
were
pellets
com-
from powdered
twenty
was kept at 210 f 0.5cC and hydrogen
of the cyclohexanol
the conversion
in Table
by two-sided
indicator,
using accurate
types of pellets
both in pellet
mg, the temperature diluent
were calcined
of three
and are summarized
all preparations,
prepared
and with broad particle
used and about
The pellets
properties
detail
Kinetic
stearate
1). The press was calibrated pressures
Textural
(5 by 5 mm) were
screw press with a torque
catalyst
was varied effect
samples
between
of water was
135 TABLE
1
Textural
properties
of u-alumina
pellets
A - C A
Property Compact
pressure,
B
62
MPa
C
92
170
Skeletal
densitya,
g/cm3,
P
2.87
Apparent
densityb,
g/cm3,
p
0.760
0.926
1.064
1.07
0.74
0.60
Pore volumeb, Porosity
cm3/g
P
(Z) totalC mesoporesd macropores
Specific
surface2,
Radii of most
e
m2/g
frequent
73.5
67.5
61.3
36.5
38.8
37.1
31.0
22.5
312
2.0
2.2
9.4
15.7
r
472
pycnometry
Micromeritics,
In
(AutoPycnometer
porosimetry
c1 - Pp/". d Pore radii ePore
159
parameters
F. 102
bMercury
2.2
244
379
macropores
aHelium
292
nm
mesopores
Transport
2.75
36.4
387 pores,
2.85
1320, Micromeritics,
up to 400 MPa (pore radii
6.1
317
149
USA).
1.5 to IO4 nm) (Autopore
9200,
USA).
1.5 to 30 nm.
radii > 30 nm. experiments
aimed at comparison
weights
were
hexanol
and 63 ~01% of hydrogen binary
A - C were determined four gas pairs
(H2-N2,
at F/W = 0.159 mmol
countercurrent at laboratory He-N2,
cell, utilizing
Permeation temperature
and crushed
used for each pair and the feed mixture
Steady-state
diffusion
of whole
H2-Ar,
gas diffusion temperature He-Ar)
the validity
of pure gases
g
contained -1 -1 s .
fluxed
of Graham's
permeation
cell
equal
sample
37 ~01% of cyclo-
through
and atmospheric
in a modified
the pellets
pressure
for
Wicke-Kallenbach
law [6].
(H2, He, N2, Ar) through
in a pseudostationary
pellets,
pellets
was followed
[2,7] in the pressure
at room
range
0.5 - 40 kPa.
THEORY The information adsorption) effects
on reaction
pore system Direct
cannot
from porosimetry form a basis rate because
it provides
which may be involved
measurement
of diffusion
(mercury
and/or
for quantitative
only partly
and permeation
low temperature
treatment
nitrogen
of pore diffusion
a broad view of the complicated in mass
transport
of simple
gases
and catalysis. is more
relevant
136
0
1
3
2 Log r, nm
FIGURE
2
mercury
Pore radii, porosimetry.
r, distribution Arrows
to the real situation must be adopted given
in catalytic
as possible
between
requirement
follows
corporated
into other,
in pores and catalytic It has been found
sometimes
in this laboratory
for mass transfer model
(MTPM).
pores) active
be visualized
as a bundle
larger
the second the viscous
countercurrent these gases product
radius,
through
Thus,
must
is
be in-
for mass
transfer
the length
cylindrical
catalyst
pellets.
Optimum
can
capillaries
which
(with the
lie at an angle path can be
this is expressed and porosity
by
leads to characterizes
data on steady-state
inert gas pairs and permeation
From the low-pressure
separate
the
gradient.
from experimental of simple
supplies structure
third MTPM parameter
pores due to pressure
gas diffusion
which
of the transport
of transport;
#$. The less important
of the
can be based on the mean
transport
of tortuosity
modeling
only a part of the pores
The transport-pores
straight
the direction
can be evaluated
(r,) can be found.
purposes
for the mass
reactants.
Combination
in transport
binary
level
of the pore
for this description.
relations
that adequate
r, the first MTPM parameter)
along
MTPM parameter,
parameters
needed
equations
to this model,
of identical
of tortuosity.
flow
with
of transport.
than the length
the parameter
MTPM
surface
[1,2,6-91
and catalytic
According
is responsible
catalytically
to the direction
a description
relations
complicated
of the pore structure
The complexity
conversion.
transport-pore
mean transport-pore
rather
A, B and C from
r.
a model
from the fact that these
pore structure
(the transport
Anyway,
the real structure.
as possible
pellets
radii,
the need for as accurate
and as simple
The latter
of y-alumina
transport-pore
reactions.
which will simplify
by a compromise
system
curves
show mean
values
permeability
of
the
of r and $ are then evaluated
137 by least their
squares
product
fitting
equals
catalyst
pore structure
of gases
and processes
pressure
employed.
diffusion
for transport
used for determining
They
are, therefore,
pore structure
catalysts
accompanying
data under constraint
[1,2]. The MTPM parameters
available
differing
in the following
of the binary
(&)permeab
and are independent
them as well
suitable
procedure
reaction
for prediction
the
of the kind
as the temperature
for comparison
and also for predicting
a catalytic
that
only reflect
the mass transport
[8,9]. These
pellet
with
in porous
properties
of the catalyst
and
of catalysts
are utilized
effectiveness
factor. For a stoichiometrically
n c i=l
simple
(irreversible)
reaction
':iAi = 0
taking
(I)
place
density,
inside an isobaric
porous
Nl, of the key component
catalyst
pellet,
A, is expressed
the molar
diffusion
in the form of Fick's
flux
law
N, =-D,ct(dy,ldz)
(2)
using the modified the transition effective
Stefan-Maxwell
region
diffusion
coefficient
(D,)-’ = (Dlk)-’ + : i=l
According
to MTPM,
diffusivities, transport
IYi
-
k 0, = $ F r,;
which
takes
gas mixture
of the key component
i”i/‘,
the effective
Dyi, are obtained
parameters
equation
in a multicomponent
into account
diffusion
in
[IO]. D, is the global defined
as
)Y, l/D~i
Knudsen
diffusivity,
in the following
Dlk, and effective
way with
bulk
the use of the MTPM
r and 4 [1,2,6,7].
", = (2/3)(8RgT/n
M,)1'2
(4)
(5)
Equation
(3) shows
at a given place mole fractions
that Dl depends
in the catalyst
of the non-key
y, in a linear way, making Using
the mole
the catalyst
D, = Dls (1 -
fraction
pellet,
A)/(1
on the composition
pellet.
components
it possible
of A, relative
c = y,/~,~,
- AC)
of the reaction
It was, however, (yi, i =2,
to express
mixture
[ll-131
that the
. . . . n) are accurately
D, as a function
to its value
it follows
shown
at the outer
for this dependence
to
of y, only. surface
of
[IO]
(6)
138 0,s is the global
effective
the outer
surface
of the catalyst
parameter
A is defined
diffusivity
valid
pellet,
for the composition
where
as A = 1 - (D,c/D,s),
at that point of the catalyst
exhausted
pellet
has the form
C"
+ CA/(1 - AC)1
Cc’
and c"
pellet
i = l,...,
D,c is the global
where
(radius
where
at
n. The effective
the key component
R sph), the materia 1 balance
is
(c')' = 8
[(I - Ac)/(l
are first and second
- A)] f(c)
derivatives
is related
the key component,R,; The linear
of the key com-
[IO]
relationships
67,(c). $ is the modified
Thiele
(7)
of c by x) with
x = 0, c' = 0; x = 1, c = 1. The dimensionless
WIS
yi = yis;
prevailing
(yl = 0).
For the spherical ponent
diffusivity
rate of disappearance
to the rate at the pellet yi = yi(y,)
boundary
conditions f(c), of
surfaced?,s:
can be employed
f(c) =
to express@,
as
modulus
t’*=Rzp/, (%'D1ctyls) The catalyst component
pellet
amount
the absence
effectiveness
that really
of intrapellet
factor,
reacts
n. defined
in the pellet
diffusional
as the ratio of the key
to that which
resistance,
would
can be obtained
react
in
[11] as
n = 3?(l)&*
(9)
The necessary integration
gradient
of c at the outer
of equation
surface
c' (1) is found
by numerical
(7).
RESULTS Textural
and transport
From the textural Figure
pressures
procedure;
higher (weight
same direction.
than those
Thus,
porosity
pellets
frequent
pores:
to maxima
density
1. On the other
increases
pore volume
constant.
markedly
and total
in macropores The same change
the mesopore
decreases
in MTPM parameters
radii r, correspond
in Table
is mainly
radius
A, B and C presented
skeletal
radius
in Table
is not affected
is true also for the pellets
volume)
the total
is nearly
the macropore
The trends
shown
The decrease
radii of the most whereas
this
per unit pellet
can be expected.
mesopore
data on selected
2 it can be seen that the v-alumina
the pelletization
density
properties
prepared
1 and by
under
hand, the apparent with
porosity
compaction, decrease
as
in the
(pores over 30 nm) as the can be observed
in the
stays at 2.0 - 2.2 nm
from 380 nm to 160 nm.
r and $ are similar:
of macropores
the mean
transport-pore
on the pore size distribution
curves
139 (arrows
I), indicating
in Figure
transport,
Assuming
Ema, the tortuosity
macropores,
macropores
of transport-pores
of transport
In this way, the following
$ = cma/q. pellets
that mainly
that porosity
pores,
tortuosity
A, B and C: q = 2.36, 3.30 and 3.69,
compacting
pressure
decreases
the volume
are responsible
equals
for mass
the porosity
q, can be evaluated
values
were obtained
respectively.
of macropores
Thus,
of from
for the
increasing
and increases
the
their
tortuosity. The agreement i.e., between
between
methods
use the same model y-alumina
pellets
the results
of porosimetry
that are based on completely suggests
for data evaluation,
is not far from the model
I
and of transport different
but which
that the pore structure
assumption
I
measurements,
processes
of cylindrical
of
pores.
I
0 8X %
0
o”
0 6-
@a A
B
a ?
4
I
I
I 0
-
200
KX
pressure, MPa
FIGURE
3
Cyclohexanol
prepared mmol/g
at different
conversion pressure.
over whole
(@
) and crushed
(0)
pellets
yls = 0.37, ~4~ = 0.63, ~2~ = y3s = 0, F/W = 0.159
s.
Dehydration
kinetics
The data for kinetic pelleting
pressures
the open points pressures the more
in Figure
indicate
were obtained
However,
3), whereas
increased
activity
data for crushed of y-alumina.
factors
pellets
effects
prepared
set (illustrated
pellets
prepared
The reason
for the corresponding
by using the rate equation positive
on crushed
100 MPa. They form a consistent
so, as the effectiveness
could be predicted pellets.
analysis
below
on activity
by
at higher
is not clear, whole
based on low-pressure
of compaction
under
pellets
crushed
have been reported
c3,41. The rate data were (21O"C,
atmospheric
correlated
pressure)
by the Langmuir-Hinshelwood
type rate equation
140 @, = ky,/(l
(IO)
+ K,Y, + $Y+
The form of the equation by cyclohexanol
accounts
and water
for the strong
inhibition
The constants
adsorption.
were
of dehydration
found
both
k = 0.92 mmol/g
s,
K, = 92, K3 = 66 (based on 115 data points).
TABLE 2 Effectiveness
factors
for v-alumina
pellets Pellet
Parameter
@ ,s, ymol/cm3
s
A
B
C
7.58
9.00
10.3
D Is. IO23 cm2/s
1.87
1.06
0.58
0
1.28
1.87
2.72
A Effectiveness
- 0.347
- 0.313
- 0.099
factor
calculated
with
A f 0
0.975
0.942
0.852
calculated
with A = 0
0.973
0.938
0.842
0.975
0.941
0.853
experimental
Dehydration Figure reaction
over pellets
3 shows that cyclohexanol rate region
with increasing over crushed Neglecting
pellets
remains
effectiveness
from 0.98 (pellet
The high effectiveness pores depend conditions
it.
A) to 0.85 (pellet result
numerical
integration
as n
(Runge-Kutta-Gill
and parameters
Two cases were considered:
concentration.
along
rates
by
drop along
of diffusional
tend to 1. were
calculated
in runs depicted of equation
the pore
in
Thus the rates along
in the absence
effective
pellets,
For the
concentration
diffusion
A, as well as the resulting 0, changing
100 MPa.
can be approximated
dehydration
algorithm)
the global
under
of crushed
the local dehydration
factors
employed
linearly
the conversion
exp = Xcrushed'xpellet
reactant
rates
for cyclohexanol
(IO). Table 2 summarizes
Thiele moduli
from
the effectiveness
factors
pressures
rate is only moderate.
pellets A, B and C and for conditions
equation
because
decreases
of activity
this dependence
significantly
and, therefore,
The effectiveness
pellets)
C).
that even for a large
in reaction
the pores do not differ
evaluated
in the initial
conditions,
for pelleting
on the local cyclohexanol
follows
the pore the decrease
outside
for increase
factors,
factors
only weakly
over pellets
Under comparable
constant
in pellet A, for example,
f(c) 'I,cO.26,
resistance
no products
pressure.
the small and unaccounted
the experimental decrease
(i.e., with
pelleting
conversion
in Figure (7) using
3 by rate
coefficients,
effectiveness
length
for
(A taken
factors. from Table
2)
141
I
FIGURE
4
x
Cyclohexanol
and II, constant
4 shows
with
centres
kinetics
profiles
A, B, C.
the pore are not too
n which
of cyclohexanol
are, moreover,
concentrations
with the above qualitative
concentration
decreases
in
lower: h = 0.906,
toward
along dispellet
rate on this concentration
role of pore diffusion.
for f(c) 1, c), the effectiveness
be significantly
pellets
values.
of dehydration
the rate retardation
v-alumina
similar
A, B and C. In agreement
but the weak dependence
(i.e.,
inside
of 0, along
predict
it can be seen that cyclohexanol
obliterates
C would
the changes
experimental
the calculated
the pores of pellets cussion,
profiles
both alternatives
agreement
Figure
concentration
(A = 0). Because
large (A is small) excellent
1.0
05
0
factors
For the first order for pellets
0.824 and 0.707,
A, B and
respectively.
SYMBOLS A Ai C
parameter
(-)
reaction
component
relative
mole fraction
total molar
Di Dm.
effective
global Knudsen
effective
bulk diffusivity
dimensionless molar
Ki n
feed
number
coefficient
diffusivity
of the key component
of Ai (cm*/s)
of pair Ai-Aj
of pair Ai-Aj
(cm*/s)
(cm*/s)
rate of the key component
rate of the key component
rate constant adsorption
diffusion
reaction
(mol/s)
(mol/g s)
coefficients
of comoonents
(-)
(mol/cm3)
effective
bulk diffusivity
k
of the key component
concentration
of Ai (-)
of the reaction
mixture
(-)
(cm2/s)
2
142 molecular
Ml
molar
N1
weight
diffusion
F
mean
R
gas constant
RS sph
radius
41
CR; W
of A, (g/mol) flux density
transport-pore (J/m07
of spherical
radius
of A, (mol/cm's)
(nm)
K) pellet
(cm)
reaction
rate of the key component
(mol/cm3
reaction
rate of the key component
(mol/g
s)
s)
temperature catalyst
weight
dimensionless
(g)
geometric
coordinate
(x = 0 at the pellet
centre,
x = 1
at the outer surface) conversion
X
of the key component
mole fraction
Yl
geometric
coordinate
effectiveness Knudsen
Ki
factor
factor
stoichiometric
'i
Thiele
(-)
(-)
(-)
for Ai (equation
(4))
coefficient
modulus
geometric
parameter
MTPM
(-)
SUBSCRIPTS i
for reaction
component:
i = 3 water,
i = 4 hydrogen
i = 1 cyclohexanol,
S
for conditions
at the pellet
C
for conditions
at the point where
exhausted
outer
i =
2 cyclohexene,
surface the key component
is completely
(y, = 0)
REFERENCES 1 2 3 4 5
6 ii
9 IO 11 12 13
P. Schneider and D. Gelbin, Chem. Eng. Sci., 40 (1985) 1093. P. Fott, G. Petrini and P. Schneider, Collect. Czech. Chem. Commun., 48 (1983) 215. Y. Ogino and S. Nakajima, J. Catal., 9 (1967) 251. B. Parlitz, W. Hanke, R. Fricke, M. Richter, U. Roost and G. b)hlmann, J. Catal., 94 (1985) 24. H.-G. Jerschkewitz, G. Lischke and G. ihlmann, Appl. Catal., 6 (1983) 213. J. ValuS and P. Schneider, Appl. Catal., 1 (1981) 355. Fott and G. Petrini. ADDS. Catal.. 2 (1982) 367. Petrini and P. Schneider, Chem. Eng. Sci., 39 (1984) 637. P. Fott and P. Schneider, Chem. Eng. Sci., 39 (1984) 643. P. Schneider, Chem. Eng. Sci., 2 (1976) 155. P. Hugo, Chem. Eng. Sci., 20 (1965) 385, 975. P. Schneider, Chem. Eng. Commun., 1 (1974) 239. P. Schneider, Cat. Revs. Sci.-Eng., 12 (1976) 201.
2
Jan UCHYTIL, Institute
MiloE
KRAUS and Petr SCHNEIDER
of ChemicaT
Process
to’5 02 Prague 6-Suchdol, [Received
133
13 March
Fundamentals,
Czechoslovak
Academy
of Sciences,
Czechoslovakia,
1986, accepted
28 3uTy
1986)
The changes in textural and transport properties of v-alumina pellets caused by pellet compression are demonstrated. Transport properties were determined by ccombination a? binary countercurrent diffusion and permeation measurements. Changf5 in CdtdjytfC pWfof%TdfTCt? Of pkZljt?tS Wre teStP_d k3+3t?ri1TIeITtd~i'y USirTg gdS-phdSe ccyc~nhexano'~ dehydration; effectiveness factors of pe)>ets CDU~L) be yery accurately predicted using the theory of multicomponent diffusion in the transition region, the parameters obtained from measurements of pure transport processes and the reaction kinetics not influenced by mass transport.
INTRODUCT[ON One of the steps frequently ccata\ysts is tke formation influence
the intrinsic
structure
which,
the pellets. powdered
in
(one-sided, additives
of
variables
two-sided), {graphite,
activity
of alumina
fatty
in pore structure from evaluation parameters
substances
of mass
several
authors
explained applied. increasing
transport
affects active
of pellets
the pore
mass
within
by compression
of
the mode of compression
and the presence
of pelletization
reaction
pellets.
of pelletization
measured
pressure
rates using either
by transport
processes
inside
of the pellets
factors,
the pellets
on the powdered
the changes obtained
[1,2]. These
only and are independent
This based
parameters
on the
pellets
We have also characterized
materials
effectiveness
can be proved
by correct
solely on transaort
catalyst,
without
of
parameters
the inter-
transfer. of pelleting
pressure
[3-51. The observed
by structural
changes
compacting
pressure
on catalyst
significant
of the catalyst
In the case of V205-Si02
0166-9834/86/$03.50
the
pressure,
used for their evaluation.
of the pellet
The influence
the
the pore structure
and on the true kinetics, vention
the influence
by comparing
by crushing
of simple
of
acids or salts etc.,).
of the compressed
reflect
the gaseous prediction
granulometry
of industrial
this step does not usuaJ\y
utilization
in the preparation
the powder
pellets,
obtained
the
sequence
it significantly
are the pelletization
In this work we have studied or powders
Even tkDugh
activity,
determines
material
in the preparation
peJ\ets.
catalytic
turn,
The main
catalyst
employed
catalysts,
was ascribed
activity
increase materials
the decrease to diminished
0 1986 ElsevierScience Publishers B.V.
has been studied
in activity
by
[3,4] was
due to the high pressure of pellet
activity
pore diameters
[5].
with
134 In the present work, gas phase cyclohexanol v-alumina
at ZIO'C and atmospheric
evaluation
of the activities
and the corresponding
pressure
of pellets,
dehydration
to cyclohexene
was used as the model
obtained
at different
on
reaction
for
compacting
pressure,
powders.
wt.%
-50
0
loo
II*
10'
lo3 d , m
FIGURE
1
Integral
and differential
from a combination
particle
size, d, distribution
of sieve and sedimentation
of boehmit
analyses.
EXPERIMENTAL Cylindrical pression
pellets
of alumina
in a laboratory
containing
5 wt? of aluminium
(see Figure compacting pressure
level.
were
Figure
2. measurements
were
reaction
below
1. Their
performed
Reaction
runs aimed at obtaining
kPa by adding
determined
by adding
hydrogen water
possible
products
to calculate
(50-80
kPa).
reactor
on
was 60 to 100
to keep
the initial
by GLC.
crushed
pressure
to the feed. The inhibiting
to the feed
in
was used as inert
were analyzed
partial
weight
in
is shown
was high in order
the rate equation,
(0.16 - 0.4 mm) were used and cyclohexanol 100-700
air at 600°C for 2 hours.
form. Catalyst
feed. The space velocity
Five
at each
(A, B, C) were determined
in a glass differential-flow
and crushed
gauges.
prepared
pore size distribution
10%; it was, therefore,
rates as x/(W/F).
In kinetic
tensometric
in flowing
boehmit
size distribution
were
pellets
com-
from powdered
twenty
was kept at 210 f 0.5cC and hydrogen
of the cyclohexanol
the conversion
in Table
by two-sided
indicator,
using accurate
types of pellets
both in pellet
mg, the temperature diluent
were calcined
of three
and are summarized
all preparations,
prepared
and with broad particle
used and about
The pellets
properties
detail
Kinetic
stearate
1). The press was calibrated pressures
Textural
(5 by 5 mm) were
screw press with a torque
catalyst
was varied effect
samples
between
of water was
135 TABLE
1
Textural
properties
of u-alumina
pellets
A - C A
Property Compact
pressure,
B
62
MPa
C
92
170
Skeletal
densitya,
g/cm3,
P
2.87
Apparent
densityb,
g/cm3,
p
0.760
0.926
1.064
1.07
0.74
0.60
Pore volumeb, Porosity
cm3/g
P
(Z) totalC mesoporesd macropores
Specific
surface2,
Radii of most
e
m2/g
frequent
73.5
67.5
61.3
36.5
38.8
37.1
31.0
22.5
312
2.0
2.2
9.4
15.7
r
472
pycnometry
Micromeritics,
In
(AutoPycnometer
porosimetry
c1 - Pp/". d Pore radii ePore
159
parameters
F. 102
bMercury
2.2
244
379
macropores
aHelium
292
nm
mesopores
Transport
2.75
36.4
387 pores,
2.85
1320, Micromeritics,
up to 400 MPa (pore radii
6.1
317
149
USA).
1.5 to IO4 nm) (Autopore
9200,
USA).
1.5 to 30 nm.
radii > 30 nm. experiments
aimed at comparison
weights
were
hexanol
and 63 ~01% of hydrogen binary
A - C were determined four gas pairs
(H2-N2,
at F/W = 0.159 mmol
countercurrent at laboratory He-N2,
cell, utilizing
Permeation temperature
and crushed
used for each pair and the feed mixture
Steady-state
diffusion
of whole
H2-Ar,
gas diffusion temperature He-Ar)
the validity
of pure gases
g
contained -1 -1 s .
fluxed
of Graham's
permeation
cell
equal
sample
37 ~01% of cyclo-
through
and atmospheric
in a modified
the pellets
pressure
for
Wicke-Kallenbach
law [6].
(H2, He, N2, Ar) through
in a pseudostationary
pellets,
pellets
was followed
[2,7] in the pressure
at room
range
0.5 - 40 kPa.
THEORY The information adsorption) effects
on reaction
pore system Direct
cannot
from porosimetry form a basis rate because
it provides
which may be involved
measurement
of diffusion
(mercury
and/or
for quantitative
only partly
and permeation
low temperature
treatment
nitrogen
of pore diffusion
a broad view of the complicated in mass
transport
of simple
gases
and catalysis. is more
relevant
136
0
1
3
2 Log r, nm
FIGURE
2
mercury
Pore radii, porosimetry.
r, distribution Arrows
to the real situation must be adopted given
in catalytic
as possible
between
requirement
follows
corporated
into other,
in pores and catalytic It has been found
sometimes
in this laboratory
for mass transfer model
(MTPM).
pores) active
be visualized
as a bundle
larger
the second the viscous
countercurrent these gases product
radius,
through
Thus,
must
is
be in-
for mass
transfer
the length
cylindrical
catalyst
pellets.
Optimum
can
capillaries
which
(with the
lie at an angle path can be
this is expressed and porosity
by
leads to characterizes
data on steady-state
inert gas pairs and permeation
From the low-pressure
separate
the
gradient.
from experimental of simple
supplies structure
third MTPM parameter
pores due to pressure
gas diffusion
which
of the transport
of transport;
#$. The less important
of the
can be based on the mean
transport
of tortuosity
modeling
only a part of the pores
The transport-pores
straight
the direction
can be evaluated
(r,) can be found.
purposes
for the mass
reactants.
Combination
in transport
binary
level
of the pore
for this description.
relations
that adequate
r, the first MTPM parameter)
along
MTPM parameter,
parameters
needed
equations
to this model,
of identical
of tortuosity.
flow
with
of transport.
than the length
the parameter
MTPM
surface
[1,2,6-91
and catalytic
According
is responsible
catalytically
to the direction
a description
relations
complicated
of the pore structure
The complexity
conversion.
transport-pore
mean transport-pore
rather
A, B and C from
r.
a model
from the fact that these
pore structure
(the transport
Anyway,
the real structure.
as possible
pellets
radii,
the need for as accurate
and as simple
The latter
of y-alumina
transport-pore
reactions.
which will simplify
by a compromise
system
curves
show mean
values
permeability
of
the
of r and $ are then evaluated
137 by least their
squares
product
fitting
equals
catalyst
pore structure
of gases
and processes
pressure
employed.
diffusion
for transport
used for determining
They
are, therefore,
pore structure
catalysts
accompanying
data under constraint
[1,2]. The MTPM parameters
available
differing
in the following
of the binary
(&)permeab
and are independent
them as well
suitable
procedure
reaction
for prediction
the
of the kind
as the temperature
for comparison
and also for predicting
a catalytic
that
only reflect
the mass transport
[8,9]. These
pellet
with
in porous
properties
of the catalyst
and
of catalysts
are utilized
effectiveness
factor. For a stoichiometrically
n c i=l
simple
(irreversible)
reaction
':iAi = 0
taking
(I)
place
density,
inside an isobaric
porous
Nl, of the key component
catalyst
pellet,
A, is expressed
the molar
diffusion
in the form of Fick's
flux
law
N, =-D,ct(dy,ldz)
(2)
using the modified the transition effective
Stefan-Maxwell
region
diffusion
coefficient
(D,)-’ = (Dlk)-’ + : i=l
According
to MTPM,
diffusivities, transport
IYi
-
k 0, = $ F r,;
which
takes
gas mixture
of the key component
i”i/‘,
the effective
Dyi, are obtained
parameters
equation
in a multicomponent
into account
diffusion
in
[IO]. D, is the global defined
as
)Y, l/D~i
Knudsen
diffusivity,
in the following
Dlk, and effective
way with
bulk
the use of the MTPM
r and 4 [1,2,6,7].
", = (2/3)(8RgT/n
M,)1'2
(4)
(5)
Equation
(3) shows
at a given place mole fractions
that Dl depends
in the catalyst
of the non-key
y, in a linear way, making Using
the mole
the catalyst
D, = Dls (1 -
fraction
pellet,
A)/(1
on the composition
pellet.
components
it possible
of A, relative
c = y,/~,~,
- AC)
of the reaction
It was, however, (yi, i =2,
to express
mixture
[ll-131
that the
. . . . n) are accurately
D, as a function
to its value
it follows
shown
at the outer
for this dependence
to
of y, only. surface
of
[IO]
(6)
138 0,s is the global
effective
the outer
surface
of the catalyst
parameter
A is defined
diffusivity
valid
pellet,
for the composition
where
as A = 1 - (D,c/D,s),
at that point of the catalyst
exhausted
pellet
has the form
C"
+ CA/(1 - AC)1
Cc’
and c"
pellet
i = l,...,
D,c is the global
where
(radius
where
at
n. The effective
the key component
R sph), the materia 1 balance
is
(c')' = 8
[(I - Ac)/(l
are first and second
- A)] f(c)
derivatives
is related
the key component,R,; The linear
of the key com-
[IO]
relationships
67,(c). $ is the modified
Thiele
(7)
of c by x) with
x = 0, c' = 0; x = 1, c = 1. The dimensionless
WIS
yi = yis;
prevailing
(yl = 0).
For the spherical ponent
diffusivity
rate of disappearance
to the rate at the pellet yi = yi(y,)
boundary
conditions f(c), of
surfaced?,s:
can be employed
f(c) =
to express@,
as
modulus
t’*=Rzp/, (%'D1ctyls) The catalyst component
pellet
amount
the absence
effectiveness
that really
of intrapellet
factor,
reacts
n. defined
in the pellet
diffusional
as the ratio of the key
to that which
resistance,
would
can be obtained
react
in
[11] as
n = 3?(l)&*
(9)
The necessary integration
gradient
of c at the outer
of equation
surface
c' (1) is found
by numerical
(7).
RESULTS Textural
and transport
From the textural Figure
pressures
procedure;
higher (weight
same direction.
than those
Thus,
porosity
pellets
frequent
pores:
to maxima
density
1. On the other
increases
pore volume
constant.
markedly
and total
in macropores The same change
the mesopore
decreases
in MTPM parameters
radii r, correspond
in Table
is mainly
radius
A, B and C presented
skeletal
radius
in Table
is not affected
is true also for the pellets
volume)
the total
is nearly
the macropore
The trends
shown
The decrease
radii of the most whereas
this
per unit pellet
can be expected.
mesopore
data on selected
2 it can be seen that the v-alumina
the pelletization
density
properties
prepared
1 and by
under
hand, the apparent with
porosity
compaction, decrease
as
in the
(pores over 30 nm) as the can be observed
in the
stays at 2.0 - 2.2 nm
from 380 nm to 160 nm.
r and $ are similar:
of macropores
the mean
transport-pore
on the pore size distribution
curves
139 (arrows
I), indicating
in Figure
transport,
Assuming
Ema, the tortuosity
macropores,
macropores
of transport-pores
of transport
In this way, the following
$ = cma/q. pellets
that mainly
that porosity
pores,
tortuosity
A, B and C: q = 2.36, 3.30 and 3.69,
compacting
pressure
decreases
the volume
are responsible
equals
for mass
the porosity
q, can be evaluated
values
were obtained
respectively.
of macropores
Thus,
of from
for the
increasing
and increases
the
their
tortuosity. The agreement i.e., between
between
methods
use the same model y-alumina
pellets
the results
of porosimetry
that are based on completely suggests
for data evaluation,
is not far from the model
I
and of transport different
but which
that the pore structure
assumption
I
measurements,
processes
of cylindrical
of
pores.
I
0 8X %
0
o”
0 6-
@a A
B
a ?
4
I
I
I 0
-
200
KX
pressure, MPa
FIGURE
3
Cyclohexanol
prepared mmol/g
at different
conversion pressure.
over whole
(@
) and crushed
(0)
pellets
yls = 0.37, ~4~ = 0.63, ~2~ = y3s = 0, F/W = 0.159
s.
Dehydration
kinetics
The data for kinetic pelleting
pressures
the open points pressures the more
in Figure
indicate
were obtained
However,
3), whereas
increased
activity
data for crushed of y-alumina.
factors
pellets
effects
prepared
set (illustrated
pellets
prepared
The reason
for the corresponding
by using the rate equation positive
on crushed
100 MPa. They form a consistent
so, as the effectiveness
could be predicted pellets.
analysis
below
on activity
by
at higher
is not clear, whole
based on low-pressure
of compaction
under
pellets
crushed
have been reported
c3,41. The rate data were (21O"C,
atmospheric
correlated
pressure)
by the Langmuir-Hinshelwood
type rate equation
140 @, = ky,/(l
(IO)
+ K,Y, + $Y+
The form of the equation by cyclohexanol
accounts
and water
for the strong
inhibition
The constants
adsorption.
were
of dehydration
found
both
k = 0.92 mmol/g
s,
K, = 92, K3 = 66 (based on 115 data points).
TABLE 2 Effectiveness
factors
for v-alumina
pellets Pellet
Parameter
@ ,s, ymol/cm3
s
A
B
C
7.58
9.00
10.3
D Is. IO23 cm2/s
1.87
1.06
0.58
0
1.28
1.87
2.72
A Effectiveness
- 0.347
- 0.313
- 0.099
factor
calculated
with
A f 0
0.975
0.942
0.852
calculated
with A = 0
0.973
0.938
0.842
0.975
0.941
0.853
experimental
Dehydration Figure reaction
over pellets
3 shows that cyclohexanol rate region
with increasing over crushed Neglecting
pellets
remains
effectiveness
from 0.98 (pellet
The high effectiveness pores depend conditions
it.
A) to 0.85 (pellet result
numerical
integration
as n
(Runge-Kutta-Gill
and parameters
Two cases were considered:
concentration.
along
rates
by
drop along
of diffusional
tend to 1. were
calculated
in runs depicted of equation
the pore
in
Thus the rates along
in the absence
effective
pellets,
For the
concentration
diffusion
A, as well as the resulting 0, changing
100 MPa.
can be approximated
dehydration
algorithm)
the global
under
of crushed
the local dehydration
factors
employed
linearly
the conversion
exp = Xcrushed'xpellet
reactant
rates
for cyclohexanol
(IO). Table 2 summarizes
Thiele moduli
from
the effectiveness
factors
pressures
rate is only moderate.
pellets A, B and C and for conditions
equation
because
decreases
of activity
this dependence
significantly
and, therefore,
The effectiveness
pellets)
C).
that even for a large
in reaction
the pores do not differ
evaluated
in the initial
conditions,
for pelleting
on the local cyclohexanol
follows
the pore the decrease
outside
for increase
factors,
factors
only weakly
over pellets
Under comparable
constant
in pellet A, for example,
f(c) 'I,cO.26,
resistance
no products
pressure.
the small and unaccounted
the experimental decrease
(i.e., with
pelleting
conversion
in Figure (7) using
3 by rate
coefficients,
effectiveness
length
for
(A taken
factors. from Table
2)
141
I
FIGURE
4
x
Cyclohexanol
and II, constant
4 shows
with
centres
kinetics
profiles
A, B, C.
the pore are not too
n which
of cyclohexanol
are, moreover,
concentrations
with the above qualitative
concentration
decreases
in
lower: h = 0.906,
toward
along dispellet
rate on this concentration
role of pore diffusion.
for f(c) 1, c), the effectiveness
be significantly
pellets
values.
of dehydration
the rate retardation
v-alumina
similar
A, B and C. In agreement
but the weak dependence
(i.e.,
inside
of 0, along
predict
it can be seen that cyclohexanol
obliterates
C would
the changes
experimental
the calculated
the pores of pellets cussion,
profiles
both alternatives
agreement
Figure
concentration
(A = 0). Because
large (A is small) excellent
1.0
05
0
factors
For the first order for pellets
0.824 and 0.707,
A, B and
respectively.
SYMBOLS A Ai C
parameter
(-)
reaction
component
relative
mole fraction
total molar
Di Dm.
effective
global Knudsen
effective
bulk diffusivity
dimensionless molar
Ki n
feed
number
coefficient
diffusivity
of the key component
of Ai (cm*/s)
of pair Ai-Aj
of pair Ai-Aj
(cm*/s)
(cm*/s)
rate of the key component
rate of the key component
rate constant adsorption
diffusion
reaction
(mol/s)
(mol/g s)
coefficients
of comoonents
(-)
(mol/cm3)
effective
bulk diffusivity
k
of the key component
concentration
of Ai (-)
of the reaction
mixture
(-)
(cm2/s)
2
142 molecular
Ml
molar
N1
weight
diffusion
F
mean
R
gas constant
RS sph
radius
41
CR; W
of A, (g/mol) flux density
transport-pore (J/m07
of spherical
radius
of A, (mol/cm's)
(nm)
K) pellet
(cm)
reaction
rate of the key component
(mol/cm3
reaction
rate of the key component
(mol/g
s)
s)
temperature catalyst
weight
dimensionless
(g)
geometric
coordinate
(x = 0 at the pellet
centre,
x = 1
at the outer surface) conversion
X
of the key component
mole fraction
Yl
geometric
coordinate
effectiveness Knudsen
Ki
factor
factor
stoichiometric
'i
Thiele
(-)
(-)
(-)
for Ai (equation
(4))
coefficient
modulus
geometric
parameter
MTPM
(-)
SUBSCRIPTS i
for reaction
component:
i = 3 water,
i = 4 hydrogen
i = 1 cyclohexanol,
S
for conditions
at the pellet
C
for conditions
at the point where
exhausted
outer
i =
2 cyclohexene,
surface the key component
is completely
(y, = 0)
REFERENCES 1 2 3 4 5
6 ii
9 IO 11 12 13
P. Schneider and D. Gelbin, Chem. Eng. Sci., 40 (1985) 1093. P. Fott, G. Petrini and P. Schneider, Collect. Czech. Chem. Commun., 48 (1983) 215. Y. Ogino and S. Nakajima, J. Catal., 9 (1967) 251. B. Parlitz, W. Hanke, R. Fricke, M. Richter, U. Roost and G. b)hlmann, J. Catal., 94 (1985) 24. H.-G. Jerschkewitz, G. Lischke and G. ihlmann, Appl. Catal., 6 (1983) 213. J. ValuS and P. Schneider, Appl. Catal., 1 (1981) 355. Fott and G. Petrini. ADDS. Catal.. 2 (1982) 367. Petrini and P. Schneider, Chem. Eng. Sci., 39 (1984) 637. P. Fott and P. Schneider, Chem. Eng. Sci., 39 (1984) 643. P. Schneider, Chem. Eng. Sci., 2 (1976) 155. P. Hugo, Chem. Eng. Sci., 20 (1965) 385, 975. P. Schneider, Chem. Eng. Commun., 1 (1974) 239. P. Schneider, Cat. Revs. Sci.-Eng., 12 (1976) 201.
2