Hydrocarbon Processing - September 2021 - 61

Catalysts
ln Aobs ]− EA,obs
[
ln
⎡
⎣
⎢
⎢
3
(
dp/2
EA,true
2
)
1
RT
Since the second term on the left hand
side corresponds to that on the left hand
side, Eq. 7 indicates that the apparent activation
energy in the case of pore-diffusion
control is approximately half of the
true activation energy (Eq. 8):
EA,obs ≈
EA,true
2
(8)
FIG. 3 displays the effect of temperature
on the observed global rate constant,
as well as the region of each ratelimiting
step and its observed apparent
activation energy.
The unintentional shift of the ratecontrolling
step over temperature variation
represents another common pitfall
in the design scale-up of fixed-bed reactors
for highly exothermic and endothermic
reactions. Due to the unavoidable
difference in flow regimes between
laboratory/pilot reactors operated isothermally
and commercial reactors operated
adiabatically, experimental data
obtained in the lab reactor are useful for
determining the true reaction kinetics
and reaction scheme; those obtained in
a small-scale pilot reactor are useful for
investigating the conditions closer to the
commercial unit.
However, both types of data are often
insufficient for upscaling to a commercial
adiabatic reactor. In practice,
the commercial reactor is frequently designed
at a highly turbulent flow through
a packed bed of catalyst pellets to attain
high throughput with acceptable pressure
drop. Therefore, pore diffusion generally
becomes the rate-limiting step. When
adiabatic operation is adopted, an unintentional
shift from pore diffusion control
to film diffusion-or, more frequently,
intrinsic rate control-is likely to occur,
especially when a large temperature difference
exists between the inlet and outlet
of a catalyst bed. As a result, the designed
reactant conversion and/or product selectivity
may not be achieved if the facilities
and reactor are designed without considering
the above-mentioned shift.
1
=
RT
2De
(n + 1)
CAs
1−n × Atrue
1/2
⎤
⎦
⎥
⎥
Another common pitfall is the sub(7)
−
stantial
reduction of catalyst size in case
of exothermic reaction to increase production
rate by minimizing pore diffusion
limitation. This may lead to a runaway
reaction and can be handled by reducing
the catalyst pellet to an optimal size.
However, if the reaction is highly exothermic,
the adiabatic reactor may have to be
replaced by a multi-tubular reactor with
internal cooling.
A handy scaling correlation applicable
for non-isothermal reactors.
To enhance the upscaling success rate, the
effect of the three common rate-controlling
steps on the observed global rate as
a function of flow behavior and temperature
must be clarified. From Eq. 5, if the
reaction order can be approximated as
pseudo-first-order (n = 1), the effectiveness
factor becomes (Eq. 9):
3
η ≈
(
=
kobs
3
(
dp/2
)
De kIntr )1/2
(
constant is (Eq. 11):
kIntr = ATrue exp
(Eq. 12):
1
=
kobs
3
(
κ =
dp/2
⎛
⎜⎝
)
3
De
ATrue exp
⎡
⎢⎣
1
−Ea,true
RT
⎤
⎥⎦
⎞
⎟⎠
1/2
⎡
⎢⎣
1
+
−Ea,true
RT
⎤
⎥⎦
ψ
Rep
n
(12)
By defining a new parameter as (Eq. 13):
(13)
(
kobs
dp/2
)
=
exp
⎡
⎢⎣
DeATrue
Eq. 12, which expresses the global kinetic
rate as a function of flow behavior
and temperature, becomes Eq. 14:
1
κ
−EA,true
2RT
⎤
⎥⎦
+
ψ
Rep
n
(14)
FIG. 3. Effect of temperature on the observed
global rate constant, as well as the region of
each rate-limiting step.3
Hydrocarbon Processing | SEPTEMBER 2021 61
dp/2
)
yields (Eq. 10):
1
De
kIntr
(9)
The substitution of Eq. 9 into Eq. 2
1
+
ψ
Rep
n
(10)
The Arrhenius form of the intrinsic rate
(11)
Substituting Eq. 11 into Eq. 10 yields
TABLE 1. Effect of flow behavior and
temperature on each individual ratecontrolling
step
Rate-controlling
step
Film diffusion
Pore diffusion
Intrinsic
Flow
behavior
Ren
Temperature
~ Linear
Independent Exponential
Independent Exponential
Based on Eq. 14, TABLE 1 summarizes
the effect of flow behavior and temperature
on the individual rate controlling
step. Note that, as revealed in FIG. 3, the
exponential effect of pore diffusion rate
control is typically represented by an apparent
activation energy, which is half of
the true intrinsic value.
Estimating catalyst performance
in a commercial fixed-bed reactor.
To successfully scale up from a laboratory
and pilot reactor to a commercial
scale, the global kinetic correlation (Eq.
14) must be experimentally determined.
First, Eq. 14 is transformed to a linear
form by taking the natural logarithm of
both sides. If the experimental conditions
(mainly reaction temperature) are
chosen, such that the film diffusion is the
rate-limiting step, then Eq. 3 is valid. By
varying the Rep
n (proportional to fluid
velocity), the value of ψ can be obtained
from the slope of FIG. 2.
Next, experimental conditions (mainly
using sufficiently small catalyst pellet
size at relatively low temperature and
high fluid velocity) are chosen, such
that the surface reaction rate is the ratelimiting
step, the true intrinsic activation
energy EA,true
can be estimated from a plot
Hydrocarbon Processing - September 2021

Table of Contents for the Digital Edition of Hydrocarbon Processing - September 2021
