Heptane reforming over Pt-Re/Al2O3: Reaction network, kinetics, and apparent selective catalyst deactivation

Article abstract of DOI:10.1006/jcat.2001.3485

A lumped reaction network and its corresponding kinetics model for n-heptane reforming over an unsulfided Pt-Re/Al₂O₃ catalyst were developed by combining both the differential and the integral methods of analysis. When utilized along with previously developed coking kinetic model, the resulting reforming kinetics model is a power tool for a priori predictions of the evolution of catalyst coke profiles and a reforming product composition as a function of on-stream time, bed position, and operating conditions. This had a direct bearing on the simulation of the reforming reaction process and its catalyst regeneration process, since the coke profile is an initial condition for controlling and optimizing the catalyst's regeneration process. The infleunce of coke on the rates of different reactions in the reforming network could be quite selective.

Full text of DOI:10.1006/jcat.2001.3485

Journal of Catalysis 206, 188–201 (2002)
doi:10.1006/jcat.2001.3485, available online at http://www.idealibrary.com on
Heptane Reforming over Pt–Re/Al2O3: Reaction Network, Kinetics,
and Apparent Selective Catalyst Deactivation
∗, ,1
∗,2
K. Liu, † S. C. Fung,† T. C. Ho,† and D. S. Rumschitzki
∗
Department of Chemical Engineering, City College of the City University of New York, and GSUC–CUNY, New York, New York 10031;
and †Corporate Strategic Research Lab., ExxonMobil Research and Engineering Co., Annandale, New Jersey 08801
Received May 11, 2001; revised November 28, 2001; accepted November 28, 2001
ics model based on vibrational microbalance experiments
with a feed whose only hydrocarbon constituent is the coke
precursor. Thus, once armed with a reaction kinetics model,
we can combine it with the coking kinetics model to better
understand and predict reformer performance over cok-
ing time scales, on the one hand, and to predict the bed’s
coke profile based on the precursor’s dynamic profile, on
the other. This is the subject of this study.
This is a continuation of our previous work aimed at develop-
ing a fundamental, a priori model for predicting how a reforming
catalyst deactivates in a fixed-bed reactor due to coke formation.
Specifically, we construct a lumped reaction network for n-heptane
reforming on a bifunctional Pt–Re/Al2O3 catalyst using both dif-
ferential and integral rate data. The data are obtained from a vi-
brational microbalance and a multioutlet fixed-bed reactor with
n-heptane or reaction intermediates as the feed. The network, in-
cluding a five-membered naphthene lump that is the primary coke
precursor, has a minimum number of reactions and correspond-
ing adjustable rate parameters, almost all of which are individually
determined by targeted experiments. The resulting kinetic model,
coupled with a previously developed catalyst coking kinetic model,
correctly predicts the long-term spatiotemporal behavior of product
composition and coke-on-catalyst for a fixed-bed reformer. The re-
sults strongly suggest the need to partition the reforming reactions
into two subgroups: those that are significantly affected by coke
and those that are not. The approach taken here, which provides
both fundamental insights and a quantitative basis for improving
catalysts and processes, can also be extended to other catalytic
Specifically, the present study consists of two parts. The
first part addresses the reforming kinetics. We operate the
microbalance in differential mode to probe the relative im-
portance of individual lumped reactions, which helps elimi-
nate kinetically insignificant reaction pathways. Once a net-
work emerges as the leading candidate, the microbalance
further gives fairly tight estimates of the rate constants for
selected subsets of the network by using the reaction inter-
mediates as the feed. The remaining data are amassed in
an integral multioutlet fixed-bed reactor. These data allow
estimation and testing of the remaining rate constants by
using the already determined reaction paths and rate con-
stants. The resulting kinetic model has very few adjustable
parameters. The second part combines the reforming kinet-
ics model with previously developed coking kinetics to pre-
dict the development of reactor coke profiles and the evolu-
tion of product composition throughout the lifetime of the
catalyst. The agreement between theory and experiment is
excellent. A significant result suggested by this modeling
study is that the damaging effect of coke-on-catalyst may
be quite selective in that some reactions appear to be more
sensitive to coke than others. And the data suggest that the
deactivation process is primarily governed by certain metal
sites that are most vulnerable to coke deposition. Such a
selective deactivation phenomenon would have strong im-
plications for catalyst design and process development and
optimization.
systems.
ꢀc 2002 Elsevier Science (USA)
INTRODUCTION
In our previous paper (1), we assembled a preponder-
ance of experimental evidence that five-membered naph-
thenes (C5N) are the major coke precursors in n-heptane
reforming over an unsulfided Pt–Re/Al2O3 catalyst under
conditions close to those of a commercial reformer. If one
accepts the weight of this evidence and would like to predict
coke profiles in operating reformers, it is absolutely neces-
sary to have at one’s disposal a lumped reaction network
for n-heptane reforming that is simple, robust, and contains
C5N as one of its lumps. Moreover, such a model will be use-
ful for gaining a quantitative understanding of the catalyst
deactivation process. We have reported (2) a coking kinet-
The paper’s layout consists of an overview of prior work
on reforming kinetics, followed by experimental determi-
nation of reforming kinetics and lastly by the construction
of an a priori reactor model that ties reforming and catalyst
coking deactivation together.
1 Current address: International Fuel Cells, United Technologies Corp.,
195 Governor’s Highway South Windsor, CT 06074.
2 To whom correspondence should be addressed.
188
0021-9517/02 $35.00
c
ꢀ 2002 Elsevier Science (USA)
All rights reserved.

HEPTANE REFORMING OVER Pt–Re/Al2O3
189
EXPERIMENTAL
Reactors and Procedures
We employed a novel vibrational microbalance (1) and
a multioutlet integral reactor for the present kinetics stud-
ies. The latter reactor has four outlets along its wall, which
allows us to take one gas sample at a time through a stream
selection valve. In this way one can amass conversion–space
time data for the kinetics analysis by either changing the
catalyst loading in different sections or varying the feed
rates, or both. Since the sample stream extracts less than
5% of the total volumetric flow traversing the catalyst bed,
there is little change in the space velocity due to the diver-
sion of the sample stream. The multioutlet reactor system
has been described in detail elsewhere (1, 14).
SCHEME 1. C−6 , cracking products; DMP, dimethylpentane + 3-
ethylpentane; MH, methylhexane; nC7, n-heptane; Tol, toluene.
LITERATURE ON REFORMING KINETICS
Kugelmans (3), McHenry et al. (4), and Mahoney (5) pro-
posed reaction networks for n-heptane reforming over the
Pt/Al2O3 catalyst. Surprisingly, though, there have been rel-
atively few attempts to determine the kinetics of n-heptane
reforming over the more industrially relevant Pt–Re/Al2O3
catalyst. Clem (6) proposed a reaction scheme as a basis
for a kinetics model of the n-heptane reforming for both
Pt–Re/Al2O3 and Pt/Al2O3 catalysts (see Scheme 1). The
model contains 14 parameters because it considers all pos-
sible reversible reactions in the network.
Van Trimpont et al. (7–9) studied n-heptane reforming
kinetics over both Pt/Al2O3 and Pt–Re/Al2O3 catalysts
for the range of 627–776◦K, 440–1650 kPa, and 400–
1550 kPa H2 partial pressures. They neglected direct dehy-
drocyclization and cracking of n-heptane. Sun et al. (10, 11)
reached a similar conclusion for the Pt–Sn/Al2O3 catalyst
in the temperature and pressure ranges of 733–773◦K and
800–1200 kPa. Ramage et al. (12, 13) developed a reform-
ing kinetics model for industrial feedstocks. In Scheme 2,
neglecting the C8 fraction, we show their lumped reform-
ing network for C7 hydrocarbons. Since normal paraffins
and isoparaffins give significantly different octane numbers,
Sun et al. (10, 11) segregated these into two distinct species
lumps.
A three-zone furnace with independent temperature
controllers provides varying heat input to different sections
of the reactor to facilitate isothermal operation. Also, di-
lution of the catalyst (1.6-mm extrudates) with inert, ran-
domly shaped quartz particles with an average diameter
of 1.0 mm is necessary to avoid axial temperature gra-
dients that would otherwise result from the highly en-
dothermic aromatization reaction. These measures give es-
sentially a uniform temperature profile along the 33-cm
reactor. A typical run’s loading consists of a total of 5 g
of catalyst, diluted with quartz particles, in the four cata-
lyst sections above outlet 4. Table 1 shows the different
loadings of the catalyst in the reactor’s four sections and
the corresponding space velocities. The amount of catalyst
above outlet 1 is labeled Section 1; the catalyst between
outlets 1 and 2 is Section 2, and so on. A 12 -in. section
of quartz particles separates the sections from each other
to avoid ambiguity in the amount of catalyst attributed to
each section. We vary the conversion either by changing
the feed rate for a given catalyst loading distribution or
by changing the catalyst loading of different sections for a
given feed rate. The reforming conditions for n-heptane on
the Pt–Re/A12O3 catalyst are similar to those in commer-
cial units. Specifically, temperatures are 733, 750, 772, 783,
and 794◦K at 517 kPa. At each temperature, three runs
totaling 12 liquid-weight hourly-space velocities (WHSVs)
constitute the kinetics data. Experiments at 207, 345,
517, and 1034 kPa at 750◦K provide the total pressure
dependence of the kinetics. To keep the number of manip-
ulated variables small, we fix the hydrogen-to-hydrocarbon
mole ratio in all experiments at 3, a value typical of com-
mercial operation.
From the foregoing literature review, one sees that there
are significant discrepancies among the published reaction
networks for nC7 reforming. In this study, we obtain both
differential and integral rate data using n-heptane and re-
action intermediates as the feeds. The resulting kinetics
model, while consistent with these data and with thermo-
dynamics, also passes the stringent test that it correctly
predicts the reactor coke profile as functions of on-stream
time.
The procedures used for catalyst pretreatment appear
in detail in (14) and a summary follows: After loading,
one heats the catalyst from room temperature to 789◦ at
3◦K/min under 2000 ml/min (at ambient conditions) of
H2 and maintains this temperature for 8 h to reduce the
catalyst in situ. A gradual, 3-h cooling of the reactor to
643◦K then precedes the introduction of the n-heptane
SCHEME 2. A, aromatics; C−, cracking products; C5N6, methylcy-
clopetanes; C6N6, cyclohexane; P,5paraffins.

190
LIU ET AL.
TABLE 1
Catalyst Loading and Corresponding Space Velocities of Different Sections
Run
Section 1
Section 2
Section 3
Outlet number
WHSV (g/h-g catalyst)
Catalyst loading (g)
4
2
3
4
2
10
1
110
0.09
4
6
3
14
2
26
0.9
1
120
0.25
4
8
3
18
2
57
0.4
1
133
0.3
2.5 1.5 0.91
2.85 1.0
2.8 1.5
reactor feed. A subsequent slow, 3-h heating of the reactor In most cases, the data between 30 and 40 h are used for
brings it to run temperature. On-stream time begins the evaluating kinetics parameters.
moment the reactor attains a preselected temperature. A
After terminating the run, we discharge the catalyst in
rotating selection valve directs the reaction products from discrete sections without mixing so as to be able to mea-
each of the outlets to an HP5880 GC equipped with a 50-m sure the coke content of each section by TPO. Fung and
capillary column coated with cross-linked methylsilicone Querini (15) have detailed the TPO technique. References
gum.
(1) and (2) detail the procedures for measuring reactor coke
At the end of the run the liquid feed is stopped, and the profiles in the multioutlet fixed bed reactor.
reactor is cooled to 643◦K over 3 h and maintained at this
As mentioned, in addition to the multioutlet integral
temperature for 5 h in hydrogen flowing at 430 ml/min (at reactor, we run the vibrational microbalance as a dif-
ambient conditions). This procedure strips the reversibly ferential reactor and check the existence and impor-
adsorbed hydrocarbons off the catalyst, so as not to con- tance of each individual reaction by feeding different hy-
tribute to the temperature-programmed oxidation (TPO) drocarbons (reactants, intermediates, and final products)
signal during the analysis of the catalyst coke. Following to the microbalance at WHSV = 30–80, H2/hydrocarbon
the 643◦K hydrogen stripping, the reactor is cooled to room molar ratio = 3, 750◦K, 30 psi, with 0.1 g of catalyst loaded.
temperature under flowing hydrogen.
Without going into great detail (1), we note that, in con-
Certain preliminary studies are necessary before begin- trast to traditional thermogravimetric balances, all of the
ning the bulk of the experimental work. Tests with various feed passes through the catalyst bed in the vibrational
mass velocities under otherwise identical reaction condi- microbalance, thereby determining the true space time over
tions reveal no external mass transfer limitations. Tests with the catalyst. Moreover, the gas concentrations that the dif-
different sizes of catalyst particles under otherwise constant ferential bed sees are essentially directly measured.
conditions to check for pore diffusion limitations show a
Materials
minimal effect of particle size. This is consistent with our
estimated effectiveness factor of about 0.9 for 1.6-mm ex-
The gases used in this research are cylinder hydrogen
of electrolytic grade (99.95%), cylinder helium (99.95%),
and cylinder nitrogen (99.95%). The liquid feed, n-heptane
(nC7), methylcyclopentane (MCP), ethylcyclopentane
trudates at 772◦K.
Catalytic reforming reactions often undergo very signif-
icant and rapid changes during the start-up period. Under
our operating conditions, the catalyst essentially lines out
(ECP), and 2-methylhexane (2MH) are all analytic pure
its activity within ∼30 h. It is generally accepted that the
grade (99 mol%). The bimetallic Pt–Re/Al2O3 catalyst, in
1
rapid formation of an initial coke level on the catalyst is
the form of 16 -in. extrudate in the reactor, contains 0.3 wt%
responsible for this catalyst “lineout” or “equilibration.”
Pt, 0.3% wt% Re, and 0.9 wt% Cl and has a BET specific
surface area of 200 m2/g. We neither presulfide the catalyst
nor add sulfur to the feed during the run. Catalyst particle
sizes are 177–250 µm in the microbalance experiments.
Clearly, a systematic kinetics study of the effects of space
velocity, temperature, pressure, or some other process vari-
able would be difficult in the rapidly changing period of the
catalyst itself. Despite the fact that the catalyst continues to
change during its life, its rate of change slows significantly
to a time scale that is long compared to reforming reaction
times after this lineout period. One can thus complete an
KINETICS MODEL
Our first task here is to implement an experimental pro-
isolated experimental study of reforming kinetics without gram to adequately justify an appropriate reaction network
considering catalyst deactivation over a narrow time win- that contains C5 naphthene as a single lump. Perhaps a
dow (<10 h) after the lineout period. In our work, we start safe way to do this, i.e., to investigate the reaction paths
each run with fresh catalyst and continue anywhere from that compose the reaction network over a wide range of
80 to 250 h. With such long experiments, we can clearly dis- conversions, is to use two reactor systems. One is the mi-
tinguish the lineout period from the long-term catalyst de- crobalance used as a differential reactor primarily for test-
activation and thus safely identify the postlineout period. ing the existence and importance of individual reactions.

HEPTANE REFORMING OVER Pt–Re/Al2O3
191
The other is the multioutlet integral reactor for procuring
high-conversion data typical of commercial operation.
1.0
0.8
0.6
0.4
0.2
0.0
772oK
Basic Species, Lumps, and Kinetic Trends
The major products of nC7 reforming are toluene, iC7
(branched heptanes), and cracking products (C1–C6). Due
to the importance of the C5N contribution to coke forma-
tion (2), it is advantageous to segregate out all of the C5
naphthenes as a separate lump, even though this lump’s
concentration is much lower than that of other lumps. Re-
call that the reaction and deactivation essentially decouple
afterthe initial ∼30-hlineout, since the time scale ofcatalyst
deactivation becomes much longer than that of the main re-
actions. We use only the concentration data after ∼30 h and
within a narrow time window of less than 10 h in estimat-
ing the reforming kinetics parameters. As will be discussed
later, the long-term behavior of the catalyst is accounted
for through a deactivation function determined previously
(2). As illustrative examples, Figs. 1 and 2 plot reactant
and product concentrations versus space time for 750 and
772◦K at an on-stream time of 30–40 h and 517 kPa. (The
solid curves are model predictions to be discussed later.)
Both the iC7 and the C5N lumps show maxima, indicating
that they are reaction intermediates. The toluene (Tol) and
lighter hydrocarbon (C1–C6) yields increase monotonically
with space time, indicating that they are end products. After
10 min of space time, iC7 and nC7 decline concurrently and
their ratio remains fairly constant, which, along with the
fact that the iC7s themselves are roughly in an equilibrium
distribution, suggests that their interconversion reactions
may be much faster than all other interlump reactions at
these space times.
nC7
C1-C6
Tol
iC7
C5N
0.1
0.0
0.2
0.3
0.4
0.5
Space Time, hr
FIG. 2. Concentration versus space time data obtained from the mul-
tioutlet fixed-bed reactor, 772◦K, 517 kPa. Model (—) prediction, k6 and
k7, determined in microbalance with ECP.
tal data using the reactant (i.e., n-heptane in our case) as
the feed. Such a method can be very insensitive to changes
in network structure and for a particular network can lead
to more than one set of parameters that give equally good
fits. Moreover, it is well known that the requirement that a
multistepmodelkineticallydescribesthedatafromapartic-
ular experiment can tightly constrain certain parameter val-
ues while remaining extremely insensitive to variations in
otherparametervalues. Rather, aproperparameterestima-
tion procedure requires experiments using multiple feeds
including reactants, reaction intermediates, and products.
Each experiment is designed to make its result sensitive to
a particular parameter or to a small subset of the param-
eters. It is then critical to subject rate constants derived in
this way to some consistency checks, e.g., to see if they are
consistent with physicochemical laws and thermodynamics
(more on this later).
In kinetics studies, after postulating a reaction network,
one often estimates all of the rate parameters from the com-
parison of the integrated model equations with experimen-
Thus we examine the reaction networks proposed in the
following and perform specific experiments that target in-
dividual component reactions. Each experiment attempts
to ascertain whether a chemically plausible reaction occurs
at a relevant rate and if so, what its rate constant is. Only
after doing a number of such investigations do we examine
the integral data for nC7 feed to determine the parameters
not easily accessible by this direct method.
For example, Clem’s model (6) mentioned previously
contains 14 reactions, because it allows almost all possi-
ble (reversible) reactions between lumps. By feeding pure
toluene and hydrogen to the microbalance, one can test
whether toluene reacts to nC7 or to iC7. The result (data
not shown) shows that toluene is virtually unreactive at
750◦K, 207 kPa, H2/toluene molar ratio = 3, and 50 WHSV
[g feed/(g catalyst · h)]. Thus, there are no significant re-
verse reactions from toluene to nC7 and iC7 under these
conditions.
1.0
750oK
0.8
nC7
0.6
C1-C6
iC7
0.4
0.2
0.0
Tol
0.5
C5N
0.0
0.1
0.2
0.3
0.4
Space Time, hr
FIG. 1. Concentration versus space time data obtained from the mul-
tioutlet fixed-bed reactor, 750◦K, 517 kPa. Model (—) prediction, k6 and
k7, determined in microbalance with ECP.

192
LIU ET AL.
5
4
3
2
1
0
20
15
10
5
Feed: iC7
750oK
Feed: ECP
750oK
Tol
Tol
nC7
iC7
C1-C6
20
C5N
C1-C6
nC7
0
4
8
12
0
0
5
10
Time, hr
15
Time, hr
FIG. 3. Concentration versus on-stream time data obtained by feed-
ing 2-methylhexane (iC7) to the differential microbalance reactor at
750◦K, 207 kPa, H2/iC7 = 3, and 80 WHSV.
FIG. 5. Concentration versus on-stream time data obtained by feed-
ing ethylcyclopentane to the differential microbalance reactor at 750◦K,
207 kPa, H2/ECP = 3, and 35 WHSV.
McHenry et al. (4) and Clem’s (6) prior networks posit
that a dehydrocyclization ring closure of nC7 and iC7 pro-
duces toluene directly and rapidly. To test this pathway for
iC7, we run the microbalance using 2-methylhexane, the
major iC7 formed in nC7 reforming, as the feed at 750◦K,
207 kPa, H2/iC7 = 3, and 80 WHSV. As Fig. 3 shows, af-
ter the initial catalyst transient period, the major products
are nC7 and cracking products. The near absence of toluene
shows that ring closure of this iC7 molecule is not important
compared to that of nC7. Moreover, the presence of sig-
nificant cracking product without C5N or toluene suggests
that iC7 cracks directly, without an nC7 intermediate and
that the isomerization reaction, while fast, is not effectively
instantaneous relative to cracking. Note that the ratio of
the amounts of cracking product in Figs. 3 and 4 is approx-
imately the inverse of the ratio of their WHSVs. Since the
microbalance in this experiment is almost a differential re-
actor, this implies that the cracking rates of nC7 and of iC7
proceed at comparable rates.
When comparing Van Trimpont et al.’s model to that
of Ramage et al. (12, 13), one should ask, is the dehy-
drocyclization reaction (i) a direct six-membered ring clo-
sure, (ii) a five-membered ring closure to cyclopentane
intermediates (C5N) followed by ring expansion to cyclo-
hexane, or (iii) a simultaneous six- and five-membered ring
closure? To answer these questions, we feed pure ECP and
MCP (Figs. 5 and 6) as model compounds of C5N to the mi-
crobalance reactor and measure the rate of ring expansion
and ring opening in differential operation mode at 750◦K
and 207 kPa. Aromatics (toluene/benzene) and the normal
paraffins (nC7/nC6) are the major products of ECP/MCP
reforming. Cracking and isoparaffin formation rates are,
Feed: nC7
750oK
20
16
12
8
16
Feed: MCP
750oK
12
Bz
8
C1-C6
4
C5Ns
nC6
4
C1-C6
iC7
Tol
0
iC6
0
0
10
20
30
40
50
60
0
10
20
30
40
50
Time, hr
Time, hr
FIG. 4. Concentration versus on-stream time data obtained by feed-
ing n-heptane to the differential microbalance reactor at 750◦K, 207 kPa,
H2/nC7 = 3, and 30 WHSV.
FIG. 6. Concentration versus on-stream data obtained by feeding
methylcyclopentane to the differential microbalance reactor at 750◦K,
207 kPa, H2/MCP = 3, and 50 WHSV.

HEPTANE REFORMING OVER Pt–Re/Al2O3
193
1.0
0.8
0.6
0.4
0.2
0.0
k1
k6
Feed: nC7
nC7
C5N
nC7
k4
-
C6
k7
k3
k5
k2
k4
iC7
C1-C6
iC7
Tol
Tol
FIG. 9. Lumped reaction network for n-heptane reforming over un-
sulfided Pt–Re/Al2O3 catalyst.
C5N
Finally, we do not need to include a saturated six-
membered naphthene lump explicitly in the nC7 reforming
kinetics scheme, because the dehydrogenation of methylcy-
clohexane to toluene is much faster than the other reactions
in the network and its concentration is extremely low.
In summary, Fig. 9 shows the simplest lumped reaction
network for nC7 reforming that summarizes these targeted
experiments from both the integral and the differential re-
actors.
0.0
0.1
0.2
0.3
0.4
0.5
Space Time, hr
FIG. 7. Model prediction obtained by neglecting direct dehydrocy-
clization of nC7, 750◦K, 517 kPa. Model (—) fails to predict toluene and
C5N concentrations.
by comparison, negligible after the initial transient period.
In fact, they may even require an nC7 intermediate. It is
now a simple matter to calculate the rate constants for the
C5N-to-toluene and C5N-to-nC7 reactions from these data.
Surprisingly the rate constant for C5N to toluene measured
this way is much smaller than Van Trimpont et al.’s (7–9)
value. This has some major consequences. Consider the in-
tegralreactordatafornC7 feedinFig. 7(ablow-upversionis
shown in Fig. 8). After the initial catalyst transient, the reac-
tion C5N → toluene, with the calculated rate constant, the
C5N concentration shown in the figure and with no other
parallel toluene formation pathway is incapable of produc-
ing anywhere near the amount of toluene observed. This
suggests that in addition to five-membered ring closure, a
simultaneous, direct six-membered ring dehydrocyclization
also produces aromatics.
Rate Equation and Parameter Estimation
Given the above lumped reaction network, the next step
is to evaluate the model parameters. This also provides a
test, albeit a weak one, of the network itself. Previous stud-
ies (6, 7–9, 13, 16) and our data show that when H2 is present
in large excess, all reactions in the network can be ade-
quately treated as pseudo first order. Note that the reactor
is practically isothermal. Despite the large excess of H2, the
net H2 production will somewhat increase the volumetric
flow rate along the bed. This change would only slightly
rescale the space time variable and therefore would not
significantly affect the relative rates of the reforming re-
actions. To simplify matters, we invoke the constant molar
volume assumption (more on this later). For a homoge-
neous plug-flow reactor free of mass transfer effects, the
pseudo-first-order rate constants can be estimated from a
nonlinear least-squares fit with
0.4
dc/dτ = −Kc,
[1]
where c is the concentration vector comprising all hydro-
carbon species shown in Fig. 9, K the rate constant matrix,
and τ the space time. The explicit forms of c and K will be
shown later in the section on modeling of the effect of coke
buildup on reactor performance.
Note that if one uses the Langmuir–Hinshelwood rate
expression and the data in early works (7–9, 13, 16), one
finds that the adsorption denominator is close to unity and
varies by less than 5% in our experiments even over the
largest difference in space times (0 and 30 min). For most
runs it is within the reproducibility tolerance.
measured
0.2
predicted
0.0
0.0
0.1
0.2
0.3
0.4
0.5
Space Time (hr)
We now use the experimental data to evaluate the
rate constants at each of five different temperatures. The
FIG. 8. Model prediction obtained by neglecting direct dehydrocy-
clization of nC7 (blow-up version of Fig. 7); —, model prediction.

194
LIU ET AL.
approach taken here is to consider the proposed reforming that adapts a modified Gauss–Newton method, which min-
network under the conditions of each of the differential re- imizes the weighted sum of squares and the cross products
actor runs and, for each, dissect out the subnetwork that is of the residuals between observed and calculated conver-
operative in that experiment. In this way we can estimate sions. At the beginning of the parameter evaluation, we did
the majority of the rate constants somewhat independently. not assume the same reaction rate constant values (k4 and
As discussed earlier, k6 and k7 are amenable to direct deter- kꢁ ) for nC7 and iC7 cracking. However, even with differ-
mination from differential reactor experiments such as the e4nt initial guesses for the two rate constants, the nonlinear
one in Fig. 5. This procedure assumes that the rate constants least-squares fit consistently generated almost identical fi-
for reactions of ECP are representative of those of all C5Ns, nal values for the two. At lower temperatures, this may
which was experimentally substantiated in (2). Moreover, be the result of k3 and k5 being about a factor of 5 larger
the mass balance of toluene argument discussed previously than k4 and k4ꢁ so that the two C7 isomers interchange fast
yields a good initial estimation of k2 based on the data ob- enough that one measures only the decay rate of nC7 plus
tained by feeding nC7 to the differential reactor (see Fig. 4). iC7 as an aggregate. This argument becomes less plausible
Next, consider the experiment feeding iC7 as shown in at the higher temperatures, where k3 and k5 are only about
Fig. 3. After the initial transient, toluene and C5N are twice k4. Despite this, the quasiequilibrium between nC7
present only in negligible concentrations and the major and iC7 may still be a good approximation for practical
products are nC7 and light hydrocarbons formed from purposes. Hence, to reduce the number of adjustable pa-
cracking. Apparently, the nC7 formed from iC7 does not rameters, we refitted the data assuming identical cracking
have enough time to significantly react further at the high constants k4 = kꢁ , leaving 7, rather than Clem’s 14 parame-
WHSV of 80. Thus the only reactions in the network that ters (6). Of thes4e 7, only 1 is truly free, and the others have
are significant in this regime are the isomerization reac- good initial guesses and tightly banded values.
tions (known to be faster than the other reactions involved
such as ring closure) between iC7 and nC7 and the cracking and experiment. The model (solid curves) fits the data quite
of iC7. well. Table 2 lists the resulting reaction rate constants for
Figures 1 and 2 exemplify the agreement between theory
The reduced model and these data give a value for k4ꢁ five temperatures. Figure 10 shows the Arrhenius plots for
and at least the ratio of k3/k5. Finally, a similar argument thedifferentrateconstants, andTable2liststhecorrespond-
(Fig. 4) with nC7/H2 feed yields a value for k1, an estimate ing apparent activation energies Ei for the ith reaction.
for k4, and another estimate for k3/k5. Before proceeding The nC7 dehydrocyclization and cracking have the high-
to the fixed-bed nC7 feed data, let us summarize: We have est apparent activation energies, while the nC7 isomeriza-
good values for k1, k6, and k7 and reasonable estimates, i.e., tion has the lowest Ei among all the reactions. Also, the
rather tight bounds on k2 (determined by feeding nC7 to the apparent activation energies of the reactions iC7 → nC7
differential microbalance reactor, Fig. 4), the ratio k3/k5, k4 and C5N → nC7 are comparable and are much lower than
and k4ꢁ . Moreover, we know from Figs. 3 and 4 that k4 and those of dehydrocyclization and cracking. Clearly, these ap-
k4ꢁ are similar in magnitude. This leaves only the magni- parent activation energies give a reasonable and consistent
tude of one of k3 or k5 as a totally free parameter, with explanation of the qualitative temperature effects reported
all others either fixed or free to vary only within narrow
bands. We take a conservative approach here, preferring to
carry over tight rate constant bands from the microbalance
differential reactor results to the integral fixed-bed reac-
k3
2
k5
tor parameter estimation analysis, rather than actual rate
constant values. The reasons for this caution are as follows.
k2
k7
k4
1
First, the microbalance run is for a particular iC7. In con-
trast, the fixed-bed reactor with an nC7 feed produces a
potpourri of iC7 s, not just 2MH. The rate constants k5 and
k4ꢁ for this mixture, those of interest, should be similar in
magnitude to those resulting from the 2MH feed, although
not necessarily identical. Finally, the microbalance is only
capable of running at a total pressure of 207 kPa as com-
pared to the more relevant value of 517 kPa in the fixed bed.
Thus, the theoretical accounting of how the total pressure
affectsspeciesconcentrationsandtheassumeduniformrate
constant–denominator values may be incomplete.
lnki
k6
0
k1
-1
0.00126
794 K
0.00129
0.00132
0.00135
0.00138
725 K
1/T (oK)
To obtain maximum-likelihood estimates of the remain-
ing parameters, we use a nonlinear least-squares algorithm stants.
FIG. 10. Arrhenius plots of the different pseudo-first-order rate con-

HEPTANE REFORMING OVER Pt–Re/Al2O3
195
TABLE 2
Pseudo-First-Order Rate Constants ki and Apparent Activation Energies Ei
Temp
(◦K)
ki (1/h):
k1
k2
k3
k4
k5
k6
k7
Reaction: nC7 → C5N nC7 → Tol nC7 → iC7 C7 → C− iC7 → nC7 C5N → nC7 C5N → Tol
6
733
750
772
783
794
0.376
0.685
1.207
1.600
2.010
1.680
2.043
3.176
3.501
3.980
7.881
7.975
8.338
8.601
8.902
9.7
0.939
1.367
2.653
3.089
3.400
4.066
4.564
5.089
5.643
6.599
1.102
1.236
1.432
1.534
1.641
2.769
3.729
5.013
5.920
6.896
Ei (kJ/mol)
132.3
71.7
108.6
35.7
31.7
71.5
previously (1, 2); i.e., the higher the temperature, the more ing the differential and integral methods of experiment and
C5N, toluene, and cracking products produced and, rel- analysis, mightonearriveatarobustmodelforthefullrange
atively, the less iC7 formed. Finally, we remark that the of operating conditions of interest. We next further test the
pseudo-first-order kinetics implies low surface coverage. As adequacy of the model via thermodynamics considerations.
such, the apparent activation energies are lower than the
true activation energies for the surface reactions (Esi ); that
is, Ei = Esi − Hi , where Hi is the heat of chemisorption.
THERMODYNAMICS
The reaction scheme includes the reversible reactions
Sensitivity Analysis
nC7 ↔ iC7 and nC7 ↔ C5N. An independent check of the
rate constants is to compare their values with the equilib-
We now illustrate how insensitive a model with many
rium constant estimated from the free-energy ꢀG values
undetermined parameters is when fitting with only experi-
based on API-44 data (17). Table 3 compares the equi-
mental (integral) fixed-bed data. Consider the k2 ≡ 0 case,
librium constants measured at different temperatures in
this study to their literature values. The agreement is very
good. We note that equilibrium constants estimated from
the TRC Thermodynamics Tables (Thermodynamics Re-
search Center, Texas A&M University System) also agree
well with those listed in Table 3. This consistency test fur-
ther suggests that our model and its kinetics parameters
form an adequate representation of the reforming kinetics
i.e., without the direct six-membered ring closure of nC7
to toluene. Also, assume there is no direct nC7 cracking. If
one uses only the fixed bed and ignores the microbalance
data, the nonlinear least-squares fit finds another set of kꢁs,
completely different from those in Table 2, to fit the data.
Indeed, at 750◦K these k values with the corresponding ki-
netics model provide a good fit of this limited data set. But
the new k6 (15.7 h−1) and k7 (40.3 h−1) are much larger than
under the conditions employed.
those obtained from the ECP-feed differential microbal-
ance reactor data. Moreover, the reactions C5N → nC7 and
C5N → Tol become much faster than the isomeriaztion re-
SPATIAL AND TEMPORAL VARIATIONS OF CATALYST
actions nC7 ↔ iC7 (new k3 = 8.75 h−1 and k5 = 3.46 h−1),
COKE AND PRODUCT COMPOSITION
which is unreasonable on chemical grounds. Also, such fits
likely give negative activation energies for the same re-
The philosophy of our research has been that the chem-
actions. Clearly such comparisons for limited experimen- istry and kinetics of both the main reaction and the coking
tal data hardly discriminate among kinetics models. This reactions are intimately connected and that an adequate
illustrates the danger of inputting a reaction network with understanding of one requires deciphering how the other
many free parameters into a parameter-estimation program interacts with it. In particular, to understand the reforming
to fit integral reactor data without first doing a series of ex- reactions properly, one should be able to account for how
periments specifically designed to test the existence and the rates of its major reactions change over the long time
importance of each constituent reaction.
scale characteristic of catalyst deactivation. To claim to un-
Thus, experiments that only feed pure nC7, no matter derstand the coking, one should also be able to predict coke
whether they are differential and/or integral ones, are in- profiles as functions of on-stream time and of bed position
sufficient for the development of a robust reaction scheme based upon the knowledge of the precursor profile, either
and kinetics model. Though such kinetics models might cor- measured or predicted. Here, we tie all this together by
rectly predict the experimental data in a limited range, ex- combining the reforming kinetics with our coking kinetics
trapolation to other experimental conditions is dangerous model from (2) to address both of these expectations. For
and interpretation of the rate constants is suspect. Only by completeness, we first give a brief account of these catalyst
measuring different reaction steps separately and combin- coking kinetics.

196
LIU ET AL.
TABLE 3
Measured Equilibrium Constants versus those Calculated from Thermodynamics
K16
Thermodynamics
K35
Thermodynamics
Kij = ki/kj
(temperature ◦K)
This work
0.341
This work
1.938
733
750
772
783
794
0.297
(1C2DMCP)
0.576b
1.539 (2MH)a
1.518(3MH)a
1.504 (2MH)
1.500 (3MH)
1.461 (2MH)
1.469 (3MH)
1.441 (3MH)
0.554
0.843
1.043
1.225
1.747
1.639
1.524
1.349
0.748b
1.144
(1C3DMCP)
1.289
1.422 (2MH)
1.445 (3MH)
(1C3DMCP)
a 2MH, 2-methylhexane; 3MH, 3-methylhexane.
b Average value of 1-cis-2-dimethylpentane (1C2DMCP) and 1-cis-3-dimethylpentane (1C3DMCP).
Kinetics of Catalyst Coking
the actual monolayer coke coverage is never complete in
a finite time, but rather equals [(1 − exp(−αCk)]/α. At the
same time multilayer coke formation accelerates. After a
significant portion of the active sites are coked, the rate of
multilayer coke buildup slows down.
The deleterious effect of coke formation on its reaction
rate r is generally represented by r = roφ = ro exp(−αCk),
where ro is its initial, coke-free rate. One sees that the
damaging marginal effect of coke becomes increasingly
weaker with increasing Ck, consistent with the multilayer
coke buildup mechanism. Analysis of the data obtained
from the vibrational microbalance and the corresponding
model in [2] leads to
As detailed in (2), the coking kinetics model is based
on the premise that site coverage is the sole cause of cata-
lyst deactivation. The sequence of events postulated in the
model that leads to coke laydown is that a small protocoke
molecule forms on an active site. Rather than automati-
cally depositing itself there, it samples both uncoked and
coked sites and then deposits randomly on one of them
and quickly polymerizes there. Let S0 and S be the active
site densities at time zero and t, respectively, and Ck be the
coke concentration on the catalyst. A pseudo-steady-state
assumption for the protocoke species leads to
dS
dt
dCk
dt
PC5N
= −αS
,
[2]
rc = r0φ = (κ1 + κ2/PH)
exp(−αCk),
[4]
PH
where α is a units conversion factor divided by S0. Since the
coke production (dCk/dt) is the product of its clean-catalyst
value r0(c) and the fraction φ of sites that are active, Eq. [2]
integrates to
relating the coking rate rc to instantaneous partial pres-
sures of C5N and H2, and coke-on-catalyst, where r0 is
the initial coking rate. The two deactivation rate constants
κ1and κ2 are functions of the initial acid and metal site den-
sities, adsorption equilibrium constants, and polymeriza-
tion initiation rate constant [2]. At 750◦ K, κ1 = 0.016
0.004 g coke/(g catalyst · h) and κ2 = 5.65 0.69 g coke kPa/
(g catalyst · h). Equation [4] demonstrates that coke slows
down its own formation rate, as it should.
ꢀ
ꢂ−1
ꢁ
t
φ = S/S0 = exp(−αCk) = 1 + α
r0(tꢁ) dtꢁ
,
[3]
0
which for time-invariant gas concentrations (as in the mi-
crobalance) is a hyperbolic decay of active sites with time.
This simple model lends itself naturally to the distinction
ofcokedepositingoncleansites(monolayercoke)andcoke
depositing on already coked sites (multilayer coke). The
Effect of Coke on Reforming Reactions
We now turn to the deactivation of the reforming re-
total coke concentration is the sum of the monolayer and actions due to coke buildup. In principle, as the coke-on-
multilayer coke concentrations. Physically, 1/α corresponds catalyst increases, there is no a priori reason why all re-
to the coke level for a complete monolayer coverage of actions occurring on the bifunctional catalyst should be
the active sites (excluding those sites that are lost during equally affected. After all, that selectivity changes as a cata-
the initial hydrocarbon adsorption and coking of the most lyst deactivates is not uncommon in heterogeneous cataly-
active sites not included in S0). For the catalyst here and in sis. Accepting this proposition, one can capture the salient
[2], the value of α is 56.8 g catalyst/g coke. As shown there, features of the deactivation process by focusing on only

HEPTANE REFORMING OVER Pt–Re/Al2O3
197
those reactions that are most sensitive to coke. To simplify the theory for two main reasons. First, all the rate constants
matters, we divide the reactions into two types: those that are predetermined and therefore not adjustable. Second,
are strongly affected by coke and those that are weakly we use the coking rate constants determined at low PH and
dependent on coke. If the difference in coke sensitivity of PH/PC5N to predict coke profiles at high PH and PH/PC5N
.
these two reaction types is sufficiently large, one can avoid Recall that κ1 and κ2 were determined from both reformer
the introduction of new adjustable parameters by simply and vibrational microbalance data, where the latter reac-
letting the coke dependence of type 1 reactions be equal tor operated at a PH and PH/PC5N much lower than that in
and neglecting the coke dependence of type 2 reactions. To the integral reactor where the reforming kinetics are mea-
switch off the coke dependence of some reactions we in- sured. So the microbalance produces a much higher coke at
troduce a switching constant δi such that the rate of the ith shorter on-stream times compared to the integral reactor.
reaction in the network takes the form
In the absence of a reforming kinetics model that contains
C5N as a kinetic lump and predicts its spatiotemporal evo-
lution, our previous attempts (1, 2) at predicting Ck(τ, t)
were simply empirical and heuristic.
ri (τ, t) = rio(τ)ϕi (t) ≡ rio exp(−αCkδi ) i = 1, 2, . . . , 7,
[5]
Before performing the integration, we need to discuss the
initial condition t = to. As reported previously (1, 2), the vi-
brational microbalance data show that there is an almost
instantaneous coke buildup of about 0.6 wt% upon intro-
duction of the n-heptane feed into the microbalance. We
thus need to account for this ”instantaneous” coke laydown
for the integral reactor as well. After this initial sharp rise,
thereisstillafurtherincreaseinCk during the ∼30-hreactor
start-up period, after which the ki are determined. Using the
ki values listed in Table 2, we can readily obtain analytical
expressions for Po(τ), Io(τ), No(τ), To(τ), and Lo(τ) corre-
sponding to t = to = 30 h. To march on the integration for
t > 30 h, however, we need to know the reactor coke profile
Cko(τ) at to = 30 h. This is estimated as follows. We inte-
grate Eqs. [6] to [13] from t = 0 up to t = 30 h by imposing
the following initial condition at t = 0: Ck = 0.6 wt% and
P = Po(τ), I = Io(τ), N = No(τ), T = To(τ), and L = Lo(τ).
The assumption here is that within the 30-h start-up period
Ck does not significantly affect the hydrocarbon concen-
trations. With the thus-obtained Cko(τ) at to = 30 h, we then
integrate Eqs. [6] to [13] again to calculate P, I, N, T, L, and
Ck for t > 30 h at any τ. The results are not sensitive to the
value assigned to to; for instance, the two cases to = 30 and
40 hgiveessentially thesameresults. Thenumerical method
used for integrating Eqs. [6] to [11] is a second-order finite
difference scheme with a mesh size ratio ꢀτ/ꢀt that avoids
numerical instabilities.
As alluded to earlier, we invoke the constant molar
flow rate assumption in estimating the rate constants ki .
However, this assumption needs to be relaxed to calculate
Ck accurately. One reason is that even a small gas dilution,
due to the production of light hydrocarbons (C6−) and H2,
can have a noticeable effect on the partial pressure of the
minute amount of C5N present. Another reason is that the
coking rate is sensitive to PH, although PH increases slightly
in the reactor’s downstream. These effects might cause a
rapid decline in Ck away from the reactor inlet region. Thus,
in calculating Ck at each grid point (τ, t), we also estimate
where rio is the initial (coke-free) rate, t the on-stream time,
ϕi = φδi, and δi = 1 or 0, depending on whether or not the ith
reaction is sensitive to coke. With Eq. [5] and the reform-
ing network shown in Fig. 9, one can construct a model of
the reformer’s long-term performance, as discussed in the
following.
Reactor Model
Let ct ≡ (P, I, N, L, T ), where P, I, N, L, and T are the
mole fractions of n-heptane, isoheptanes, C5N, light prod-
ucts from cracking, and toluene, respectively. The govern-
ing mass balance equations under the quasi-steady-state
assumption are
4
ꢃ
∂ P
= −
ki ϕi P + k5ϕ5 I + k6ϕ6 N
[6]
∂τ
i=1
∂ I
∂τ
= k3ϕ3 P − (k4ϕ4 + k5ϕ5)I
= k1ϕ1 P − (k6ϕ6 + k7ϕ7)N
= k2ϕ2 P + k7ϕ7 N
[7]
[8]
∂N
∂τ
∂T
∂τ
[9]
∂L
∂τ
= k4ϕ4(P + I)
[10]
[11]
∂Ck
∂t
= (κ10 + κ20/PH)PC5Nφ/PH.
The boundary (τ = 0) and initial (t = to) conditions are
τ = 0, P = 1, I = N = T = L = Ck = 0 [12]
for all t, and
t = to, Ck = Cko(τ), P = Po(τ), I = Io(τ), N = No(τ),
T = To(τ), L = Lo(τ) [13]
for all τ. These equations upon integration predict c(τ, t) the extents of C5N dilution and H2 production stoichio-
and Ck(τ, t), which would provide a very stringent test of metrically by assuming that the cracked products are from

198
LIU ET AL.
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
the primary cracking only and correct their concentrations
for these effects. This assumption is defensible because the
effect due to the H2-consuming secondary cracking is small.
The method of solution described earlier is repeated for
different sets of {δi } values to find the best match between
theory and experiment. In addition, the final {δi } chosen
must be mechanistically reasonable on chemical grounds,
as we discuss later.
Since the majority of catalyst life data are obtained at
750◦K and 517 kPa, we will test the reforming and coking
models against the product composition and coke profile
data collected under these conditions. With the ki values
listed in Table 2 for 750◦K, we integrate Eqs. [6] to [10]
analytically to give
complete monolayer coke
coke at 30th hr
0
5
10
15
20
25
30
Space Time, min
Po = 0.7250e−λ τ + 0.2742e−λ τ + 0.0008e−λ τ
[14]
[15]
1
2
3
FIG. 11. Coke profiles along the reactor using nC7 as feed; 750◦K and
517 kPa; dashed line, uniform deactivation for t = 240 h (δi = 1 for all i);
solid line, selective deactivation for t = 240 h (δ1 = δ2 = δ6 = 1, δi = 0 for
all other i); dotted line, selective deactivation for t = 30 h; horizontal line,
complete monolayer coke coverage.
Io = −0.585e−λ τ + 0.578e−λ τ + 0.007e−λ τ
1
2
3
No = −0.0457e−λ τ + 0.0668e−λ τ − 0.0211e−λ τ
[16]
1
2
3
To = 0.4433 − 0.0828e−λ τ − 0.3769e−λ τ + 0.0154e−λ τ
1
2
3
[17]
C5N profile, and thus the instantaneous coke buildup, is
monotonically increasing along the bed, resulting at 240 h
in an aggregate profile without a maximum. To portray the
observed behavior, given the fact that C5N concentration
is the main driver for coke production, reaction 7, that
depletes C5N and whose deactivation causes the C5N max-
imum to move downstream, must be coke-insensitive. For
chemical sensibility (see below) one may pick the selective
deactivation case with δ1 = δ2 = δ6 = 1, δi = 0 for all other
i. Among the three deactivating reactions, the fastest one,
measured by k2, is hurt more than the slow ones (k1 and k6).
This will free up some nC7 which would help to offset the
Lo = 0.5567 − 0.0121e−λ τ − 0.5425e−λ τ − 0.0021e−λ τ
,
1
2
3
[18]
where the three eigenvalues are λ1 = 15.826, λ2 = 2.147, and
λ3 = 4.997 (1/h). The system has three characteristic time
scales. The fastest, characterized by 1/λ1, is dominated by
the isomerization, dehydrogenation, and ring expansion re-
actions. The slowest, characterized by 1/λ3, is dominated by
the cyclization and ring opening/closure reactions.
Comparison of Theory and Experiment
The data used for comparison are Ck at t = 224 and 240 h coking of reaction 1 which produces C5N in the reactor’s
and c at t = 70, 100, and 130 h. Since the movement of the upstream. The C5N-to-toluene reaction (k7), being free of
coke profile is so slow, the data for t = 224 and 240 h can catalyst deactivation, will create a strong drainage for C5N,
be safely grouped together.
thereby causing a sharp decline of the C5N concentration
Figure 11, a snapshot of the state of catalyst coking in in the reactor’s downstream, thus giving a steep decline in
the integral reactor, shows the predicted and measured the cumulative coke made in the reactor’s downstream.
coke profiles along the bed. The predicted coke level is
Indeed, by setting δ1 = δ2 = δ6 = 1, and δi = 0 for all other
calculated for t up to the 240th h. The dashed line corre- i, we obtain the solid line that predicts the data very well.
sponds to the case where all reactions are deactivated by Note that the measured coke level near the reactor en-
coke, that is, uniform deactivation with δi = 1 for all i. This trance (Section 1, Table 1) is much higher than that pre-
case does not even give the correct trend, suggesting that dicted from the model. The very high coke level in Section 1
the deactivation is a selective phenomenon. Compared to is most likely caused by the contamination with the high-
the model prediction, the data show a faster coke buildup coke-content catalyst which dropped into Section 1 during
near the reactor entrance followed by a faster decline catalyst unloading (see Liu et al. (2) for details). We should
away from the reactor inlet region. What is going on is the also remark that the coke profile shown in Fig. 11 is quite
chemistry initially sets up a C5N profile with a maximum different from that reported in Refs. (9) and (16), which
about 1/4 down the reactor and decaying beyond. Since considered only 10 h of coking.
the coking rate is linear in C5N, the catalyst cokes fastest
We further test this choice (δ1 = δ2 = δ6 = 1, δi = 0 for all
at this maximum, the reactions slow down there and move other i) to see if it can correctly predict c(τ, t) for t = 70,
the maximum downstream. This process continues until 100, and 130 h. Figures 12 and 13 show the concentrations
the C5N maximum exits the reactor. From that point on the of n-heptanes, isoheptanes, toluene, and C1–C6 cracked

HEPTANE REFORMING OVER Pt–Re/Al2O3
199
1.0
0.8
0.6
0.4
0.2
0.0
70th hour
70th hour
0.04
0.03
nC7
0.02
iC7
C1-C6
0.01
Tol
0.00
0
5
10
15
20
25
30
0
5
10
15
20
25
30
Space Time, min
Space Time, min
FIG. 14. Mole fraction of five-membered naphthenes for t = 70 h;
750◦K, 517 kPa.
FIG. 12. Mole fractions of n-heptane, isoheptanes, toluene (ꢀ) and
C1–C6 cracking products (+); t = 70 h, 750◦K and 517 kPa.
stream. In contrast, the conditions used in the microbal-
ance experiments are so much more severe that essentially
a complete monolayer coke level is reached after 30 h even
at a much lower temperature of 717◦K (2).
products for t = 70 and 130 h, respectively. The agreements
are good. We do not show the results for the 100th hour
because they are very similar to those for the 70th and
130th hours. A more severe test is the prediction of the
C5N concentration whose very low values are susceptible
to large errors. As Figs. 14 (t = 70 h) and 15(t = 130 h) show,
the model does a good job in this respect.
We tried many other different combinations of δi values,
none of which gives a better fit than the earlier case. The
C5N and coke reactor profiles are more sensitive tools for
discriminating among different combinations of δi values.
We now extrapolate this model to the reactor start-up
period. Figure 11 also shows the predicted coke profile
(dotted line) at the 30th h, which is far below the level
of 0.6 + 1/α = 2.36 wt% (the horizontal line) for com-
plete monolayer coverage. Thus, a significant portion of the
active sites is still available for reforming after 30 h on
Tosumup, thecombinationofournewreformingkinetics
and catalyst coking models, when allowing for selective
deactivation, predicts both the temporal and the spatial
evolution of all the reaction participants, including the
coke, very well. This provides us with considerable insight
into the manner in which the catalyst deactivates. One
can use the present models for many simulation purposes.
Figure 16 is a three-dimensional plot of the spatial and tem-
poral variation of Ck at 750◦K and 517 kPa for t up to 240 h.
Some remarks on the practical implications of the forego-
ing results are in order. Since the formation of toluene from
C5N does not appear to be sensitive to coke, one would
expect that two feeds with different paraffins/naphthenes
130th hour
1.0
0.04
130th hour
0.8
0.03
0.02
0.01
0.00
nC7
0.6
C1-C6
Tol
iC7
0.4
0.2
0.0
0
5
10
15
20
25
30
0
5
10
15
20
25
30
Space Time, min
Space Time, min
FIG. 13. Mole fractions of n-heptane, isoheptanes, toluene (ꢀ), and
C1–C6 cracking products (+); t = 130 h; 750◦K and 517 kPa.
FIG. 15. Mole fraction of five-membered naphthenes for t = 130 h;
750◦K, 517 kPa.

200
LIU ET AL.
of adjacent Ni atoms. Geometrically, one can see that it does
not take much Cu to break up the multiplets, which explains
the deactivation effect of Cu. In the case of cyclohexane de-
hydrogenation, by contrast, Cu has little, if any, effect on the
activity of Ni. Here the reaction, being much less demand-
ing than the hydrogenolysis reaction (C–C bond rupture),
does not require a multiplet of Ni sites.
3.0
2.5
2.0
1.5
1.0
The foregoing geometric effect can be carried over to our
system if we view coke as playing the role of Cu. We thus
proceed to propose that the formation or breaking of a ring
compound (k1, k6, and k2), the heart of reforming reactions,
requires a multiplet of metal atoms. As such, even a small
amount of coke can drastically reduce the concentration of
these multiplets. This should also be the case with the metal
hydrogenolysis activity. However, its contribution to the
formation of C1–C6 light products diminishes significantly
after the initial ∼30-h lineout period. In other words, the k4
value we measured essentially reflects acid cracking. On the
other hand, it is reasonable to propose that hydrogenation,
dehydrogenation, isomerization, ring expansion, and acid
cracking (k7, k3, k5, and k4) do not require multiplets and
they become relatively stable after the lineout period.
The foregoing argument helps to explain the results
borne out from our modeling study. The essential point here
is that just because coke can indiscriminately deposit on the
catalyst surface does not mean that all reactions are affected
equally. This reaction-sensitive deactivation phenomenon
is consistent with the fact that a paraffinic feed requires a
higher reforming temperature and more frequent catalyst
regeneration than a naphthenic feed. As coke builds up on
the catalyst, the aromatization of naphthenes remains unaf-
fected, whereas the aromatization of paraffins slows down
due to decrease in k1, k2, and k6. This in turn requires an
increase in the reformer temperature to maintain constant
product octane. A higher temperature increases the cok-
ing rate, thereby further lowering paraffin aromatization.
When the reformer reaches the maximum permissible tem-
perature, the catalyst is regenerated. Monitoring changes in
k1, k2, and k6 may improve reformer performance through
optimization of the catalyst regeneration schedule.
250
30
0.5
200
25
150
20
100
15
10
50
5
0
0
FIG. 16. Spatial and temporal variations of coke profile in reactor;
750◦K, 517 kPa.
ratios would exhibit quite different on-stream behaviors.
The lumped reforming network and its relation to catalyst
coking can be used for the development of process models
for commercial reforming feedstocks. It can also be used for
feed selection and blending. Joshi et al. (18) applied graph
theory to build the naphtha reforming model from rate data
on pure compounds.
On the fundamental side, the foregoing development
explains why the Pt–Ir/Al2O3 catalyst is more active and
stable than the Pt–Re/Al2O3 catalyst reported by Carter
et al. (19). They proposed that the high hydrogenolysis ac-
tivity of Ir helps to remove coke (and/or its precursors) from
metal surfaces, thus mitigating the deactivation effect on
paraffin ring closure reactions (i.e., k1, k2, and k6). The key
message of all this is that our results for the first time quan-
titatively point to the importance of selective deactivation
by coke, a phenomenon that deserves further investigation.
In the following, we propose a possible physical picture of
its origin.
Nature of Selective Deactivation by Coke
CONCLUSIONS
The question at hand is, why do some reactions in the
network appear to be much more sensitive to coke than
We have developed a lumped reaction network and its
other reactions? A short answer is that the high sensitivity corresponding kinetics model for n-heptane reforming
probably arises from the specific active site requirements over an unsulfided Pt–Re/Al2O3 catalyst by combining
demanded by those highly sensitive reactions.
both the differential and the integral methods of analysis.
To give a physical explanation of the selective deactiva- The resulting reforming kinetics model, when used along
tion, we draw an analogy with the Ni–Cu bimetallic cata- with previously developed coking kinetics model, provides
lyst system studied by Sinfelt et al. (20, 21). For ethane hy- us with a powerful tool for a priori predictions of the
drogenolysis, they observed that the addition of only a small evolution of catalyst coke profiles and a reforming product
amount of inactive Cu atoms substantially decreased the composition as a function of on-stream time, bed position,
catalyst activity. Their interpretation is that the surface in- and operating conditions. This has a direct bearing on the
termediates require bonding of carbon atoms to multiplets simulation of both the reforming reaction process and its

HEPTANE REFORMING OVER Pt–Re/Al2O3
201
catalyst regeneration process, since the coke profile is an Greek Letters
initial condition for the control and optimization of the
catalyst’s regeneration process.
α
deactivation constant, g catalyst/g coke
δi defined in Eq. [5], i = 1, 2, . . . , 7
Our modeling study indicates that while coke can indis-
criminately deposit on different active sites and on already
formed coke, its influence on the rates of various reactions
in the reforming network can be quite selective. This is a
very important consideration in both catalyst design and
process development. Further work in this area is needed;
for instance, it is definitely worthwhile to probe the genesis
of the apparent selective catalyst deactivation. Finally, the
present experimental and modeling protocol for investigat-
ing catalyst deactivation can also be extended to catalytic
systems other than reforming.
ϕi reaction-specific deactivation function, i = 1, 2, . . . , 7
φ
deactivation function
λi eigenvalues, i = 1, 2, 3
κ1 coking reaction rate constant of alkylcyclopentene
κ2 coking reaction rate constant of alkylcyclopentadine
τ
space time
ACKNOWLEDGMENT
Thanks are due to Dr. J. H. Sinfelt, who drew our attention to the selec-
tive deactivation phenomenon observed with the Ni–Cu catalyst system.
APPENDIX: NOMENCLATURE
REFERENCES
c
Ck
concentration vector ct = (P, I, N, L, T )
total amount of coke on catalyst, g coke/g
catalyst
five-membered naphthenes
six-membered naphthenes
cracking products of nC7 reforming
apparent activation energy of the ith reaction,
kJ/mol
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C6N
C6−
Ei
ECP
Hi
I
iC7
ki
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L
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mole fraction of C5N
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MCH
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nC7
P
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PC5N
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rc
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TOL
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WHSV weight-hourly space velocity (g feed/
(g catalyst · h))