Hydrocarbon Processing - September 2021 - 60

Catalysts
of pseudo-steady-state approximation,
the following relation between the obresistance
of the stationary film around
the pellet is dominant, and this becomes
Generally, the effect of temperature
During each stage of upscaling of a new process/product
development-from catalyst development and testing
at laboratory and pilot scales to the up-scaled design
and adiabatic operation of a corresponding commercial
reactor-an unsuspected shift of the rate-controlling step
is a common prevalent pitfall to be handled appropriately.
served global, film-diffusion, pore-diffusion
and true-kinetic rate coefficients can
be derived (Eq. 1)1,2
:
1
=
kobs
kIntr
1
+
kPD aP/vP
(
1
)
+
kFD Sc/Vc
(
1
)
(1)
The effect of internal diffusion on the
observed reaction rate can be considered
by the so-called effectiveness factor (η),
which is defined as " the ratio of the real
reaction rate of the catalyst particle to the
imaginary reaction rate when the whole
particle is assumed to bathe in the surface
reactant concentration. " Meanwhile, the
effects of fluid velocity and flow regime
can be represented as a function of the
pellet-based Reynolds (Re) number. Eq.
1 can therefore be transformed to Eq. 2:
1
=
kobs
ηkIntr
1
+
ψ
Rep
n
(2)
As shown in FIG. 2, laboratory and pilot
reactors, which are generally small in
size and designed for low mass throughput,
frequently exhibit a laminar-flow
regime. As a result, the mass transfer
the rate-limiting step. The film resistance
dramatically decreases when the flow
regime becomes highly turbulent, as is
typical in a commercial reactor. In other
words, this shift from film diffusionrate
controlling to pore diffusion-rate
or surface-reaction controlling generally
occurs when upscaling to a high-capacity
commercial reactor. Pore diffusion rate
will dominate when the pellet size is relatively
large or the internal catalytic sites
have very high reactivity.
Rate-controlling mechanisms and
temperature. Another major difference
between laboratory/pilot and commercial
reactors is the effect of heat loss on
the surrounding area during operation.
Due to a high surface area per volume
of tubing and small piping, as well as a
small quantity of reaction heat generation
(or absorption) corresponding to
low mass throughput, most laboratory
and pilot reactors are run isothermally,
in practice. Their superficial fluid velocity
is relatively low and the flow regime is
mostly laminar or (at most) transitional.
Conversely, the corresponding efFIG.
2. The relationship between the inverse
observed kinetic rate constant and inverse
Re number that represents flow behavior in
isothermal operation.
60 SEPTEMBER 2021 | HydrocarbonProcessing.com
fect of significant heat loss in a largecolumn
commercial reactor with huge
mass throughput is essentially negligible.
Therefore, these reactors are generally
designed and operated in adiabatic mode.
Their superficial fluid velocity is quite
high and the flow regime is mostly turbulent.
The implication is that the ratelimiting
step for the former reactors is
typically film diffusion (particularly true
at high reaction temperature), whereas
for the latter it is pore-diffusion and/or
surface reaction. Since this discussion is
focused on individual catalyst pellets, the
influence between isothermal and adiabatic
operations is not considered here.
on the observed (or apparent) activation
energy is investigated by
carrying out experiments in
a laboratory reactor at sufficiently
high fluid velocity to
ensure a reasonably fast film
diffusion rate. Nevertheless,
in the significantly high temperature
range using catalyst
powder, the film diffusion
step would become rate-limiting
and the observed global
reaction resistance becomes
more or less proportional to
the external mass transfer film resistance.
From Eq. 2, we obtain Eq. 3:
ψ
1
≈
kobs
Rep
n
(3)
Since the gas density and viscosity
depend only slightly on temperature, so
does the corresponding Reynolds number.
In other words, according to Eq. 3,
the experimentally determined apparent
activation energy should be quite
small. Conversely, in the low temperature
range, the rate of reaction becomes
very slow and therefore the rate-limiting
step. The determined activation energy
becomes essentially equal to the true
activation energy defined by the Arrhenius
law.
In the intermediate temperature range
using a typical commercial catalyst pellet,
the pore-diffusion step becomes ratelimiting.
From Eq. 2, we obtain Eq. 4:
1
≈
kobs
ηkIntr
1
(4)
The effectiveness factor in the case of
an irreversible n-th order reaction is given
by Eq. 5:
3
η ≈
(
kobs
2
n + 1
kobs
dp/2
)
3
(
dp/2
)
kIntr
Applying the Arrhenius equation to
and kIntr
simplification:
in Eq. 6, Eq. 7 is obtained after
De
kIntr
CAs
1−n
2
n + 1
(5)
Substituting the effectiveness factor
from Eq. 5 into Eq. 4 yields Eq. 6:
De
kIntr
CAs
1 n
(6)
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