Catalytic activity evaluation of industrial Pd/C catalyst via gray-box dynamic modeling and simulation of hydropurification reactor

Article abstract of DOI:10.1016/j.apcata.2014.10.048

In this paper, dynamic modeling and simulation of the hydropurification reactor in a purified terephthalic acid production plant has been investigated by gray-box technique to evaluate the catalytic activity of palladium supported on carbon (0.5 wt.% Pd/C) catalyst. The reaction kinetics and catalyst deactivation trend have been modeled by employing artificial neural network (ANN). The network output has been incorporated with the reactor first principle model (FPM). The simulation results reveal that the graybox model (FPM and ANN) is about 32 percent more accurate than FPM. The model demonstrates that the catalyst is deactivated after eleven months. Moreover, the catalyst lifetime decreases about two and half months in case of 7 percent increase of reactor feed flowrate. It is predicted that 10 percent enhancement of hydrogen flowrate promotes catalyst lifetime at the amount of one month. Additionally, the enhancement of 4-carboxybenzaldehyde concentration in the reactor feed improves CO and benzoic acid synthesis. CO is a poison to the catalyst, and benzoic acid might affect the product quality. The model can be applied into actual working plants to analyze the Pd/C catalyst efficient functioning and the catalytic reactor performance.

Full text of DOI:10.1016/j.apcata.2014.10.048

Applied Catalysis A: General 489 (2015) 262–271
Contents lists available at ScienceDirect
Applied Catalysis A: General
journal homepage: www.elsevier.com/locate/apcata
Catalytic activity evaluation of industrial Pd/C catalyst via gray-box
dynamic modeling and simulation of hydropurification reactor
a
a,∗
b
c
Abbas Azarpour , Sharifah R. Wan Alwi , Gholamreza Zahedi , Mazyar Madooli ,
d
Graeme J. Millar
a
Process Systems Engineering Center (PROSPECT), Faculty of Chemical Engineering, Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia
Chemical & Biological Engineering Department, Missouri University of Science & Technology, 1870 Miner Circle, Rolla, MO 65409, USA
PTA/PET Process Engineering Office, Shahid Tondgooyan Petrochemical Company, Petrochemical Economic Special Zone, 667 Mahshahr, Khoozestan, Iran
Science and Engineering Faculty, Queensland University of Technology, Brisbane 4000, QLD, Australia
b
c
d
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 12 May 2014
Received in revised form 18 October 2014
Accepted 25 October 2014
Available online 4 November 2014
In this paper, dynamic modeling and simulation of the hydropurification reactor in a purified terephthalic
acid production plant has been investigated by gray-box technique to evaluate the catalytic activity of
palladium supported on carbon (0.5 wt.% Pd/C) catalyst. The reaction kinetics and catalyst deactivation
trend have been modeled by employing artificial neural network (ANN). The network output has been
incorporated with the reactor first principle model (FPM). The simulation results reveal that the gray-
box model (FPM and ANN) is about 32 percent more accurate than FPM. The model demonstrates that
the catalyst is deactivated after eleven months. Moreover, the catalyst lifetime decreases about two
and half months in case of 7 percent increase of reactor feed flowrate. It is predicted that 10 percent
enhancement of hydrogen flowrate promotes catalyst lifetime at the amount of one month. Additionally,
the enhancement of 4-carboxybenzaldehyde concentration in the reactor feed improves CO and benzoic
acid synthesis. CO is a poison to the catalyst, and benzoic acid might affect the product quality. The
model can be applied into actual working plants to analyze the Pd/C catalyst efficient functioning and
the catalytic reactor performance.
Keywords:
Gray-box
Dynamic modeling
4
-Carboxybenzaldehyde
Catalyst
Artificial neural network
Deactivation
©
2014 Elsevier B.V. All rights reserved.
1
. Introduction
depends on the feed properties, especially the impurities low con-
centration [3].
Catalytic hydrotreating (HDT) is one of the elemental pro-
Purified terephthalic acid (PTA) is the key raw material to man-
ufacture polyethylene terephthalate (PET). PET is broadly utilized
in the production of synthetic fibers, beverage bottles, frozen food
trays, toiletries, cosmetics, household and pharmaceutical prod-
ucts, molding resins, X-ray and other photographic films, magnetic
tape, electrical insulation, printing sheets, and food packaging film
[4]. In the current technology of PTA production, the oxidation
of para-xylene (PX) to crude terephthalic acid (CTA) is catalyzed
cesses in the refinery and petrochemical industries which is
employed to improve the quality of products through catalytic
conversion or reduction of low polluting compounds such as
sulphur and aromatics [1]. The HDT reactions like hydrodeas-
phaltenization, hydrodesulfurization, hydrodemetallization, and
hydrodenitrogenation are processed in three phase fixed-bed cat-
alytic reactors (FBCRs) [2].
Catalyst deactivation, the catalytic activity and selectivity loss
over time, is a significant concern in the practice of industrial cat-
alytic processes. Industrial disadvantages of deactivation are the
production time loss and waste of investment. Catalyst deactiva-
tion is undoubtedly one of the most considerable issues in the
accomplishment of HDT processes. The rate of deactivation
by metals (Co2+, Mn ) and bromide (Br ) in acetic acid (AA) as
solvent. Purification of CTA requires at least one chemical step in
addition to the physical processes such as crystallization and wash-
ing. One of the major impurities is 4-carboxybenzaldehyde (4-CBA).
It is converted to para-toluic acid (pta) by catalytic hydrogenation
in an aqueous solution carried out in a trickle-bed reactor (TBR).
Artificial neural network (ANN) models can be very efficient
to simulate the processes which are very complicated and highly
nonlinear, improperly known, and taking much time to be ana-
lyzed with different empirical models. They are very flexible and
engage less model mismatched [5]. ANN can be applied into the
2+
1−
∗ Corresponding author. Tel.: +60 7 5535533; fax: +60 7 5588166.
E-mail addresses: shasha@cheme.utm.my, sr wanalwi@yahoo.com
S.R. Wan Alwi).
(
http://dx.doi.org/10.1016/j.apcata.2014.10.048
926-860X/© 2014 Elsevier B.V. All rights reserved.
0

A. Azarpour et al. / Applied Catalysis A: General 489 (2015) 262–271
263
Hybrid or gray-box model (GBM) is a combination of white box
and black box models, which can overcome the disadvantages of
both models. GBM takes over the benefits of both techniques (ANN
and FPM) and renders their constraints [11]. GBM has extrapolation
ability, where ANNs fail in this case and usually is more accurate
than FPMs [12].
Nomenclature
a(t)
deactivation parameter (–)
−
−
3
C
concentration (kmol m
)
1
ꢀ
H
k
K
Pi
q
Hr
heat of reaction (kJ mol
Henry’s constant (bar g m kmol
mass transfer coefficient (m s
)
3
−1
)
)
The application of hybrid models as an appropriate method to
simulate reactions kinetics models were recorded in many papers
−1
total gas–liquid mass transfer coefficient (m s−1)
partial pressure of component i (bar g)
z coordinate increment
[
13–15]. A gray-box model was devised to determine a dynamic
model in order to investigate the control objectives of an integrated
plant with recycle [16]. The simulation of the fermentation pro-
cess of ethanol was performed by a hybrid neural model which
was a combination of ANN and mass balance equations for lac-
tose, ethanol, and biomass [17]. A hybrid optimization method
combining variable population size genetic algorithm, bacterial
optimization, and shuffled frog leaping was employed to evalu-
ate the optimal operation of poly vinyl acetate production in an
industrial scale continuous stirred tank reactor (CSTR) [18]. Con-
trol of polymer molecular weight distribution was achieved by a
GBM devised for styrene polymerization in a CSTR [19]. Response
surface methodology and hybrid model of ANN-particle swarm
optimization were employed to determine the trace amounts of
methylene blue from water samples through the simulation and
optimization of the solid phase extraction [20]. Recently, a review
was done on the most established hybrid semi-parametric model-
ing and parameter identification techniques applied in the control,
process monitoring, optimization, and model reduction of chemical
engineering systems [21].
Q
Qf
r
t
u
total number of increments
feed flowrate (m s
3
−1
)
−
1
−1
s )
rate of reaction (kmol kgs
time (s)
superficial velocity (m s−1)
3
VB
x
bed volume (m )
datum value
z
axial coordinate (m)
Greek Letters
εB
ε
bed void fraction (–)
phase holdup (–)
εP
Á
ꢁ
particle porosity (–)
catalyst effectiveness factor (–)
Specific surface area of the phase interface (m m
2
−3
)
−3
ꢂB
bed bulk density (kg m
)
Subscripts
In the current study, a gray-box model has been employed to
simulate the catalytic hydropurification reactor in a PTA production
plant in order to analyze the activity of the industrial Pd/C catalyst
in terms of catalyst lifetime. The hydropurification reaction mecha-
nism and the deactivation trend of palladium supported on carbon
g
gas phase
i,j
in
k
index of components
inlet to the reactor
reaction index
liquid phase
l
(Pd/C) catalyst as kinetics-deactivation term has been determined by
out
P
outlet from the reactor
particle
an established ANN method as black box using the industrial reactor
data. Subsequently, the developed network output has been linked
with the hydropurification reactor FPM as white box. The devised
hybrid model has been solved through a numerical technique, and
the relevant codes have been written in MATLAB (version 2010b)
environment. The catalytic reactor performance has been assessed
in different process conditions focusing on the catalyst deactivation
and the concentration fluctuation of 4-CBA as the main impurity.
s
solid phase
Superscripts
ind
S
sim
ss
industrial
surface of the catalyst
simulation
steady state
0
reactor inlet condition
2. Experiment
prediction of reaction parameters when there is not enough infor-
mation related to the reaction mechanisms [6]. Some classical
equations are usually employed to mathematically present the
deactivation model. When the deactivation mechanism of the cat-
alyst is not clearly understood, ANN is a very good tool to predict
it using the industrial reactor data. ANN models have the ability
to create quantitative relationships between the input and out-
put data without prior knowledge of the correlation between the
variables involved in the system [7].
Generally, there are three main methods to model the processes:
white box, black box, and gray-box [8]. White box, first principle
model (FPM) or deterministic model, is used when complete infor-
mation of the process is known, and the whole dominant equations
of the system are possible to be solved utilizing analytical or numer-
ical techniques [9]. ANN models are usually faster than FPMs. ANNs
are suitable for modeling, control, and optimization purposes [10].
Complex partial differential equations (PDEs) or complex algebraic
equations usually appear in FPM development which required to
be solved analytically or numerically. ANNs need large number of
training sets and have limited and weak extrapolation capacity.
The analysis of the CTA and PTA powder samples were carried
out in the laboratory of the industrial plant [22].
In order to measure the powders specifications some equipment
and materials have been used: HPLC machine with auto sampler
(HPLC Waters 600 Column C18 Novapack 4 ␮m), STRODS column
with 4 mm thickness and 150 mm length, class A 100 volumetric
flask, analytical scale with an accuracy of 0.1 mg, ultrasonic bath,
2 N ammonia solution, standard samples with specific amounts
of 4-CBA, pta, benzoic acid (BA), 4-hydroxymethylbenzoic acid
(4-HMBA), and mobile phase including acetonitrile (21 vol.%), tri-
fluoro AA (0.1 vol.%), and HPLC grade water (78.9 vol.%).
◦
−1
The HPLC machine was controlled at 50 C, 0.5 ml min , 230 nm
wavelength for BA and pta, 260 nm wavelength for 4-CBA and
4-HMBA. After injecting 20 ml of 0.5 N ammonia solution to the
machine by auto sampler, 0.5 ± 0.1 g of standard samples was
mixed with 10 ml of 2 N ammonia and deionized water to make a
solution of 100 ml. About 5 ml of the solution was filtered by syringe
type with specification of 0.45 mm. Then, it was transferred to auto
sampler machine vial. 10 ␮l of standard samples was injected to
the machine. The amounts of 4-CBA, pta, BA, and 4-HMBA were

2
64
A. Azarpour et al. / Applied Catalysis A: General 489 (2015) 262–271
calibrated by the generated peaks. Thereafter, the injection of 10 ␮l
of standard samples and the process of the solution filtration and
its transfer to the machine were repeated to calculate the necessary
values from the received chromatography.
reactor is crystallized, centrifuged, filterred in a rotary vacuum filter
(RVF), and dried. Dried PTA is transported to checking silos through
PCS. PTA powder is finally transferred either to the product silos
as on-spec material or sent back to CTA silos for reprocessing as
off-spec product.
3
. Hydropurification process description and problem
statement
3.2. Problem statement
3
.1. Hydropurification process description
The main challenge of PTA purification operation is to control
PTA powder quality and lengthen the lifetime of the expensive
Pd/C catalyst. There are some specifications which are considered
for the evaluation of the final PTA product as on-spec. The main
specifications of the product quality are the concentration of 4-
CBA (less than 25 ppm at the final product), delta-y as an indication
of black appearance of PTA powder, and b-value as an indication
of color degree of the product and its yellowish appearance. The
Purification of CTA is mainly carried out through the catalytic
hydropurification of 4-CBA to pta. Fig. 1 illustrates the purification
section of PTA production plant. CTA powder is mixed with filtrate
coming from the filtration section in a slurry feed drum (SFD). The
dissolved CTA along with compressed hydrogen is penetrated via
top entry to the hydropurification reactor. The liquid leaving the
Fig. 1. Layout of the purification section of PTA production plant (D: crystallizer; FC: flow controller; HE: heat exchanger; LC: level controller; NRV: not-return valve; PC:
pressure controller) [22].

A. Azarpour et al. / Applied Catalysis A: General 489 (2015) 262–271
265
fluctuation of the operational parameters such as reactor feed
flowrate, feed concentration, and the impurities concentration
affect the catalytic reactor efficient performance. When the product
is off-spec, it might be either reprocessed or utilized by the down-
stream polyester plant. The following problems can be mentioned
in case that the product is off-spec:
Catalyst lifetime decrease.
Serious operational problems in the polyester plants.
Low quality product of polyester, especially its unfavorable
appearance.
PTA powder back-transfer operational problems.
Operational problems in its reprocessing, especially in filtration
and drying.
Partial or total cease of production.
Fig. 2. Research methodology.
Given a set of the data gathered from an industrial hydropu-
rification reactor operation, the reactor performance is going to be
sensitively analyzed. Most concerning issue of FBCRs modeling is
the accessibility of the reaction rate expressions and the deacti-
vation relation. Most reaction rate expressions are derived in the
environment that is far from the real operational conditions of
the industrial reactors. In addition, the deactivation mechanism
cannot exactly describe the real deactivation trend of the cata-
lyst. Therefore, employing a hybrid model to be able to predict the
reaction mechanism and deactivation trend through a special algo-
rithm such as ANN is a suitable method to deal with the mentioned
problems.
4
.1. Data collection
Table 1 includes the data of the samples analysis reported by
the laboratory utilized to establish the network and accomplish
the study.
4
.2. FPM development (white box)
The dynamic first principle model development is required to
4
. Methodology
analyze the catalytic performance of the reactor dealing with cata-
lyst deactivation. The steps of the modeling endeavor are explained
below.
Fig. 2 depicts the methodology of this study.
Table 1
Data employed to structure the network.
Day
Inlet
Outlet
CTA powder
Feed
PTA powder
4-CBA (ppm)
Reactor outlet
H2 (kg h−1)
pta (ppm)
H2 (kg h
−1
)
4-HMBA (ppm)
4-CBA (ppm)
pta (ppm)
1
3
4
6
7
9
1
1
1
1
1
1
1
2
2
2
2
2
2
3
3
3
3
3
3
3
4
4
5
0
5
0
5
0
1100
1200
1500
1400
1700
1000
1700
2000
2000
2000
1750
1700
2000
2500
2000
2200
2000
3000
2000
2000
2500
1900
2000
1500
2000
2000
2000
2000
230
270
250
330
250
300
300
250
350
400
200
250
300
350
280
300
350
280
300
350
300
500
270
400
350
400
330
380
6
6.5
8.6
8.3
8.5
9
9.3
9.3
10
9.9
9.8
9.5
9.6
9.8
10.1
10.2
10.1
10.2
10.3
10.2
10.9
10.5
11.5
11.9
12.2
13
11.4
12.2
13
100
90
100
90
95
82
3
250
256
292
289
321
323
332
358
389
392
403
416
433
439
449
460
468
472
486
491
506
517
521
541
547
562
564
581
3.2
4.2
4.1
4.2
4.4
4.6
4.5
4.8
4.8
4.8
4.7
4.8
4.6
5.2
5.2
5.2
5.4
5.6
5.7
5.7
5.8
6
13.8
14.6
15.4
16.2
16.9
17.7
18.4
19.4
19.8
20.4
20.9
21.4
21.8
22.2
22.6
23.1
23.5
24
05
20
35
50
65
80
95
10
25
40
55
70
85
00
15
30
45
60
75
90
05
20
90
100
105
85
70
95
110
60
100
90
120
150
130
100
110
90
100
105
100
90
24.5
25
25.5
26
26.5
27
27.5
6
6.2
6.4
6.6
6.8
13.4
13.5
110
125
The inlet and outlet values of BA in the reactor feed are 58 and 172 ppm, respectively, and the inlet and outlet values of CO in the reactor feed are nil and 27 ppm, respectively.
The inlet values of 4-HMBA to the reactor are considered nil.

2
66
A. Azarpour et al. / Applied Catalysis A: General 489 (2015) 262–271
Table 2
Reactor operational conditions and the catalyst specifications [22].
Item
Value
Item
Value
−
3
Pressure
Temperature
Feed flowrate
Hydrogen flowrate
TA concentration
Catalyst bed length
Catalyst bed diameter
Particle diameter
Specific surface area
73.5 bar g
Bulk density
475 kg m
0.44
0.61
◦
285
196 t h
C
Bed void fraction
Particle porosity
Pd
Activated carbon
Water content in wet catalyst
Particle size distribution
−1
−
1
13.2 kg h
23 wt.%
7.4 m
0.5 wt.%
99.5 wt.%.
38 wt.%
4–8 (mesh) = 97%
4.75–2.36 (mm)
Less than 4 (mesh) = 2%
Over 8 (mesh) = 1%
2.8 m
−
3
3.53 × 10
m
900–1100 m2
−1
g
4.2.1. Hydropurification reactions
4.2.4.2. Liquid phase.
The following reactions have been considered as the CTA
hydropurification reactions taking place inside the catalytic bed
23]:
ꢂ
ꢃ
∂
CH
∂CH
PH2
,l
,l
2
2
εl
= −ul
+ KH2,glꢁgl
− CH2,l
HH2
[
∂t
∂z
ꢀ
ꢁ
Pd/C
S
−
k
C
− C
(5)
C H O (4-CBA) + H −→ C H O (4-HMBA) ;
H2,lsꢁls
H2,l
H2,s
8
6
3
2
8
8
3
ꢀ
ꢁ
1
ꢀ
Hr = −83.82 kJ mol−
(1)
∂
Ci,l
∂Ci,l
∂z
ꢀ
ꢁ
S
i,s
εl
= −ul
+ ki,lsꢁls
C
− Ci,l
(6)
∂
t
Pd/C
C H O (4-HMBA) + H −→ C H O (pta) + H O;
8
8
3
2
8
8
2
2
ꢀ
ꢁ
4
.2.4.3. Solid phase.
1
ꢀ
Hr = −121.88 kJ mol−
(2)
3
ꢀ
ꢁ
ꢄ
∂Ci,s
S
i,s
εP(1 − εB)
= ki,lsꢁls Ci,l − C
±
r a(t)Á ꢂB
k k
(7)
C H O (4-CBA) −→ C7H O (BA) + CO;
ꢀꢀHr = 18.73 kJ mol−
ꢁ
∂t
k=1
Pd/C
1
8
6
3
6
2
where i are 4-CBA, 4-HMBA, pta, BA, and CO. The ‘+’ sign is for the
products, and the ‘−’ sign is for the reactants.
(
3)
4.3. Artificial neural network (black box)
4.2.2. Pd/C catalyst deactivation
Pd/C catalyst consisting of 0.5 wt.% palladium nanodispersed
While kinetics modeling of the main reactions is based on
particles is deactivated due to Pd sintering and the decline of Pd sur-
face atoms accessibility [24]. Palladium mobility over the surface
of carbon support is basically described by the surface structure, its
chemical composition and energy characteristics, sintering tem-
perature, and composition of reaction medium [25].
well-developed theory, deactivation models remain as yet mostly
empirical [31]. Therefore, a more accurate model is necessary as
the replacement of the traditional models for the catalyst deacti-
vation assessment. There are different models of sintering such as
empirical, phenomenological, probabilistic, and mechanistic which
cannot simulate the observed phenomena over sufficiently broad
extents of conditions [32].
4.2.3. Reactor operation and catalyst specifications
Table 2 gives information on the conditions of reactor operation
and the catalyst specifications.
In this contribution, ANN is used to predict the multiplication of
the reaction rate of the components and the deactivation parameter
(
r.a) as kinetics-deactivation term appeared in mass balance equa-
4
.2.4. Conservative equations
In the hydropurification reaction system, the main impurity
tions. The chemical reactions and the deactivation phenomenon are
usually described relying on the availability of the active sites of the
catalyst. Therefore, the rate of reaction and the deactivation trend
are interrelated with each other. The following relation reveals how
this term is determined from the industrial data of input and out-
put of the hydropurification reactor (targets) to feed the network
for each time step. It is developed for each component and each
reaction relying on the mass balance in the catalytic bed. Eq. (7)
is developed for the whole components in the solid phase. The
parameter a is a substitution of the whole parameters affecting the
catalyst deactivation, and the complicated mechanism of the sin-
tering phenomenon is ignored. Thus, the kinetics-deactivation term
facilitates the burdens of the accurate prediction of the mechanisms
of kinetics and deactivation.
flowrate compared with the reactor feed flowrate is minor. There-
fore, the system is under isothermal operation. The following
equations outline the mass balances of the components in each
phase of the catalytic bed of TBR considering the below-mentioned
assumptions:
Plug flow behavior is considered for both gas and liquid phases
[
26].
Back-mixing or axial dispersion is minimal [27].
Radial mass transfer is negligible [26].
Wall effect and heat transfer are not significant [28].
Pressure drop through the bed is small [29].
Particles wetting is nearly complete [30].
ꢀ
ꢁ
Ci,in − Ci,out Qf
r, a =
(8)
Á ꢂBεBVB
4
.2.4.1. Gas phase.
k
ꢀ
ꢁ
ꢀ
ꢁ
ꢂ
ꢃ
Feed-forward neural network (FFNN), which is applied to the
categorization and the approximation problems, has been chosen
as the network structure. An FFNN with one hidden layer and
∂
εgCH2,g
∂ ugCH
PH2,g
2,g
=
−
− KH2,g lꢁgl
− CH2,l
(4)
∂
t
∂z
HH2

A. Azarpour et al. / Applied Catalysis A: General 489 (2015) 262–271
267
Fig. 3. Layout of the gray-box model (GBM).
enough neurons (N) in the hidden layer can match any limited
input–output mapping problem.
and initial conditions for the solution of the set of PDEs are
following:
Initial conditions
For t = 0 at z = 0
For t = 0 at z > 0
Boundary conditions
For t > 0 at z = 0
4
.4. Training-validating-testing
0
Ci = Ci
SS
Ci = Ci
After structuring a network, it is required to train it, vali-
Ci = C0i
date it, and test it. Levenberg–Marquardt, BFGS Quasi Newton,
and Resilient Back-propagation trained the data more precisely
than the other training algorithms. Levenberg–Marquardt training
algorithm (trainlm) has been eventually chosen due to its better
performance. Trainlm is a network training function that updates
weight and bias values according to Levenberg–Marquardt opti-
mization.
where i is hydrogen for the gas phase, and i are 4-CBA, 4-HMBA,
pta, BA, and CO for the liquid and solid phases.
Fig. 4 shows the algorithm of the computer programs coded into
MATLAB 2010b environment for the solution of the hydropurifica-
tion reactor hybrid model.
4.8. Model validation
4.5. Estimation of kinetics-deactivation term
The validation of the proposed hybrid model has been carried
out utilizing percent relative error (RE) and root mean square error
RMSE). RMSE is defined as:
After the ANN preparation, it is ready to simulate each input data
to squash out the required information for FPM. Fig. 3 indicates the
layout of GBM incorporating FPM and ANN and the details of the
ANN (Black Box) giving the best results.
(
ꢅ
ꢆ
ꢆ
ꢇ
ND
ꢄꢀ
ꢁ
1
ND
2
ind
i
− x si im
RMSE =
x
(9)
4
.6. Parameters calculation
i=1
The parameters involved into conservative equations incorpo-
where xind and xsim are the industrial data and simulation results,
rating the physical properties of the components and the reaction
mixture are calculated relying on the proper correlations consider-
ing the real operation conditions [33].
respectively, and ND specifies the number of the data.
5. Results and discussion
4.7. Model mathematical solution
The catalyst deactivated by sintering phenomenon might be
The set of PDEs presenting the dynamic (Dyn) condition of the
regenerated, but usually the best strategy is to decline the rate of
deactivation process [34]. Therefore, it is quite helpful to model and
simulate the hydropurification reactor to evaluate the parameters
affecting the catalyst deactivation to extend its lifetime.
catalytic system is required to be solved in two approaches. At the
first approach, the initial conditions of the dynamic behavior of the
reactor for each increment (q as sectionized z coordinate) have to
be determined. Therefore, Eqs. (6) and (7) are developed for whole
components, and they are equaled to zero (Steady State: SS). In
this case, the catalyst is considered as fresh one (a = 1). The outputs
of this step are saved as the initial conditions for the dynamic state
determination. At the second approach, the set of PDEs developed
for whole components are transformed to ordinary differential
equations (ODEs) employing the finite difference method. The
kinetics-deactivation term (r.a) for each length increment (q) and
time step is predicted by the trained FFNN, and the values are
introduced to the FPM to solve the set of equations. The boundary
The industrial Pd/C catalyst bears strong stresses during its life-
time. It is heated up during startup and cooled down for shutdown
purpose encountering thermal expansion and contraction. More-
over, the mechanical strength of the catalyst is adversely affected
due to the fluctuation of the reactor pressure under abnormal con-
ditions. Also, the reaction phase is acidic which might result in
the leaching/corrosion reason of the deactivation. Furthermore, the
reaction temperature of the purification process is very close to the
Huttig temperature, which is an indication of the mobility of the
atoms at defects, for the Pd heterogeneous catalysis [34].

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A. Azarpour et al. / Applied Catalysis A: General 489 (2015) 262–271
Fig. 4. Computer algorithm for the hybrid model of the hydropurification reactor.
The first principle dynamic modeling of the hydropurification
are 2.85 and 1.67, respectively. This analysis suggests that the
employed hybrid model is about 32 percent more accurate than
FPM implying significant implications in relation to the predictions
of the reactor operation.
ANN can be employed for the complicated reaction systems.
Usual constraints of kinetic modeling of complicated chemical
reactions are insufficiently understood mechanisms [35], undesir-
able side reactions, inability in quantifying the concentration of
adsorbed surface components and gas phase radicals, and change
of the rate limiting steps in case of operational conditions fluc-
tuation [36]. Moreover, ANN can rectify the determination of the
reactor of PTA production was fulfilled considering the deactivation
of Pd/C catalyst due to sintering [33]. Following items include the
findings of the gray-box dynamic modeling of hydropurification
reactor focusing on the influences of the parameters on the reactor
run and the catalyst deactivation.
5
.1. Model validation
RMSE values of FPM and GBM have been calculated 0.46 and
.31, respectively. In addition, percent RE values of FPM and GBM
0

A. Azarpour et al. / Applied Catalysis A: General 489 (2015) 262–271
269
Fig. 6. The influence of 4-CBA inlet concentration on BA and CO synthesis in the
hydropurification reactor.
Fig. 5. The reactor outlet concentration of 4-CBA obtained from GBM and FPM in
comparison with industrial data over the course of time.
and penetrates into the final product leading to the product acidic
number increase.
deactivation rate of a porous catalyst which relies on a number of
factors: the actual decay reactions, the presence or absence of pore
diffusion slowdown, the way poisons affect the surface, pore mouth
blocking by deposited solids, equilibrium and reversible poisoning,
regeneration process, etc. [32].
5.4. Reactor feed flowrate
Fig. 7 illustrates that the rise of feed flowrate deteriorates the
catalytic activity of the catalyst and reduces the optimal perfor-
mance of the hydropurification reactor. The figure further depicts
the influence of increasing reactor feed flowrate by the amounts
of 7 percent and 14 percent compared with the normal opera-
tion flowrate indicating the decrease of the catalyst lifetime at the
amount of three and half months and six and half months, respec-
tively. The analysis has been made based on the maximum allowed
value of the main impurity (25 ppm) at the reactor outlet and the
normal lifetime of the catalyst (331 days). When the flowrate is
high, the residence time of the reaction mixture on the active sites
of the catalyst is not enough to fulfill the hydropurification reac-
tions. Moreover, more contaminants existed in the feed such as
5
.2. GBM and FPM comparison
Fig. 5 indicates that the results of GBM are nearer to the indus-
trial data than those of FPM. After about 11 months the catalyst was
deactivated and was not capable of converting the content of 4-CBA
lower than 25 ppm. In this condition, there is no remedy to regen-
erate the catalyst activity, and it has to be replaced. The high level
of 4-CBA content improves b-value leading to the reduction of the
transparent specialty of the powder. The source of 4-CBA builds up
from the improper control of the reactor feed concentration, high
flowrate of the feed, and insufficient control of PX oxidation reac-
tors. The high concentration of 4-CBA in PTA powder stimulates the
side reactions of PET polymerization and reduces the efficiency.
It means that 4-CBA can block the polymer chain and lessen the
molecular weight because of having acidic group [37]. Moreover,
4
-CBA can shorten the activity of antimony oxide catalyst due to its
aldehyde group in PET polymerization process.
5.3. Carbon monoxide and benzoic acid synthesis
Fig. 6 reflects the effect of reactor inlet concentration of 4-CBA
on the synthesis of CO and benzoic acid (BA) in the reactor. CO is
well known to be a poison to Pd catalysts. CO is able to change
the adsorption properties and catalytic surface conditions of palla-
dium catalysts [38] by strong interactions between CO molecules
and certain surface sites of palladium [39]. The quality of the hydro-
gen is also important. It sometimes happened that the product was
still off-spec after bringing back 4-CBA inlet concentration in the
normal range. After analysis of the hydrogen quality carried out by
the laboratory, it was realized that the inlet hydrogen was contam-
inated with CO. In addition, BA is initially produced from the side
reactions of PX oxidation in CTA unit and mostly removed through
a scrubber. Based on the efficiency of separation, it might remain in
the hydropurification reactor feed to a very little extent. In addition,
it is synthesized by 4-CBA hydrogenation side reaction. BA can be
crystallized during the downstream physical separation processes
Fig. 7. The influence of reactor feed flowrate on the Pd/C catalyst lifetime.

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A. Azarpour et al. / Applied Catalysis A: General 489 (2015) 262–271
Fig. 8. The influence of hydrogen flowrate increase on the Pd/C catalyst lifetime.
Fig. 9. The effect of the PTA production rate increase on the reactor catalytic effi-
ciency.
sulphur, oil, metallic terephthalates, and polymers pass through
the catalyst bed [40].
5
.6. Misconception of getting more profit through production rate
enhancement
Fig. 9 demonstrates that to increase the production rate shortens
the lifetime of the catalyst and negatively affects the reactor run-
ning. The figure signifies that 10 percent and 20 percent increase
in the production rate compared with the normal operation rate
decreases the lifetime of the catalyst two and months and five
months, respectively. The assessment has been made regarding the
4-CBA outlet concentration and the catalyst normal lifetime. When
the concentration is high, more impurities contain into the reactor
feed, and the catalyst is not able to convert the main impurity to
less than the required value considered for the on-spec product.
Furthermore, the catalyst synthesis and the Pd dispersity are car-
ried out so that the catalyst is able to deal with a maximum defined
amount of the impurities. Therefore, the idea of getting more profit
through the boost of the production rate is not acceptable, and the
control of density meter and the concentration of the reactor feed
has to be carried out more carefully to avoid the rapid catalytic
weakness of Pd/C catalyst and improper purification process.
5
.5. Hydrogen flowrate
Fig. 8 denotes that when the inlet hydrogen flowrate increases,
the outlet of 4-CBA concentration declines implying more lifetime
of Pd/C catalyst. When the hydrogen flowrate steps up at the values
of 7 percent and 14 percent more than normal operation flowrate,
4
-CBA outlet concentration reduces, and the lifetime of the cat-
alyst improves about one month and two months, respectively.
It has been concluded relying on the topmost value of the 4-CBA
concentration in the final product and the normal lifetime of Pd/C
catalyst. It is to be mentioned that to enhance the hydrogen flowrate
more than the value suggested causes the difficulty in the control
of the reactor pressure resulting in the increase of delta-y. There
is a strong internal diffusion resistance for hydropurification of
4
-CBA over Pd/C catalyst. The hydrogenation rate enhances with
the increase of hydrogen flowrate which is demonstrated by the 4-
CBA outlet concentration reduction. When the hydrogen flowrate
improves, the amount of adsorbed hydrogen on the catalyst sur-
face increases due to the higher mass transfer rate and dissolved
hydrogen concentration. The other effect of the higher hydrogen
flowrate is that the leaching of precious metal like palladium can
be minimized by improving the availability of hydrogen in the liq-
uid reaction medium [38]. When 0.5 wt.% Pd/C catalyst is exposed to
hydrogen in high temperature, palladium hydride particles (PdHx)
migrate over the surface from the smooth areas to find the sites
where interaction with a particle is strong as stabilization centers.
At the same time, some Pd atoms diffusion can take place on the sur-
face which results in the development of large particles size and in
the decrease of small particles number. It was verified that the uti-
lization of carbon supports with a surface formed by the edge planes
of carbon micro-crystallite packs increases the catalyst tolerance
against deactivation for high temperature processes. Moreover, the
significant stabilizing effect of edge planes of carbon crystallite can
be provided, probably, by the strong interaction of acid-containing
functional groups of these planes with Pd particles. Yet, the changes
in the shape of Pd particles and the distribution over the surface are
observed for the process with hydrogen at the temperatures higher
than 573 K [25].
6. Conclusions
In this paper, a dynamic hybrid model as GBM has been
employed to evaluate the 0.5 wt.% Pd/C industrial catalyst deacti-
vation in the process of CTA hydropurification. The devised model
is a combination of FPM as white box and ANN as black box. The
research takes advantage of product quality analysis and opera-
tional data from an actual working plant.
The hybrid model is able to predict the catalytic performance of
the process more accurately than FPM. This achievement is impor-
tant since it is very critical to know at what degree the catalyst is
from deactivation orientation, and how the purification process is
being controlled. If PTA powder analysis reveals more 4-CBA con-
tent compared with the hybrid model output for a considerable
period of time, the source of the problem is to be searched imme-
diately to rectify it. 4-CBA concentration increase in the reactor
feed not only boosts the synthesis of BA which might penetrate
into the powder to affect the product quality but also increases
the CO production which is a serious poison to the catalyst. More-
over, even a minor increase of the reactor feed flowrate worsens the
activity of the Pd catalyst and shortens its lifetime. Furthermore,

A. Azarpour et al. / Applied Catalysis A: General 489 (2015) 262–271
271
hydrogen flowrate enhancement improves the lifetime of the cata-
lyst. Additionally, the idea of production rate enhancement due to
any reason such as compensation of raw material stock shortage
for PET production plant dramatically disturbs the catalytic reactor
performance. The proposed model can be applied into a real PTA
production plant to determine the lifetime of the expensive Pd/C
catalyst, to continue on-spec production, to analyze the catalytic
reactor operation, to teach the plant operators, to control the plant
more efficiently, and to encounter less number of shutdowns.
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