eth
.
matter in refineries and lots of investigations have been made concerning this issue. In this
a boiling temperature between 30 C and 200 C, and consti-
have an improved process its better to revamp naphtha
reforming strategies due to its impact on overall refinery
profits [5].
various hydrocarbons and related isomers. It is too complex to
represent the catalytic reforming reactions. In this regard,
the first significant attempt to model a reforming system has
been made by Smith [7]. He considered naphtha to consist of
three basic components including paraffins, naphthenes, and
* Corresponding author. Tel.: 98 711 2303071; fax: 98 711 6287294.
Avai lab le at www.sc iencedi rect .com
w.
i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 5 ( 2 0 1 0 ) 1 2 7 8 4e1 2 7 9 9E-mail address: [email protected] (M.R. Rahimpour).tutes typically 15e30% byweight of the crude oil. The catalytic
naphtha reforming reactions are carried out over commercial
Pt/Re/Al2O3 catalyst (0.3% Platinum, 0.3% Rhenium). Naphtha
and reformate are complex mixtures of paraffins, naph-
thenes, and aromatics in the C5eC12 range [1,2]. Naphtha
reforming plays a major role in improving the aromatic and
hydrogen production in petroleum refineries [3,4]. In order to
consider a detailed kinetic model taking into account all
components and reactions [6]. Studies on the catalytic
naphtha reforming process have been categorized in two basic
groups. The first group involves studies on the kinetics of
catalytic naphtha reforming process. Various attempts have
been made to find better lumped groups of reactions to1. Introduction
Full-range naphtha is the fraction of the crude oil with
2. Literature review
Naphtha as a complex reforming feedstock is composed ofReceived 21 May 2010
Received in revised form
15 July 2010
Accepted 23 August 2010
Keywords:
Axial-flow
Spherical packed-bed reactor
Catalytic naphtha reforming
Dynamic modeling
Hydrogen production
Aromatic production0360-3199/$ e see front matter 2010 Profedoi:10.1016/j.ijhydene.2010.08.124study, an axial-flow spherical packed-bed reactor (AF-SPBR) is considered for naphtha
reforming process in the presence of catalyst deactivation. Model equations are solved by
the orthogonal collocation method. The AF-SPBR results are compared with the plant data
of a conventional tubular packed-bed reactor (TR). The effects of some important param-
eters such as pressure and temperature on aromatic and hydrogen production rates and
catalyst activity have been investigated. Higher production rates of aromatics can
successfully be achieved in this novel reactor. Moreover, results show the capability of flow
augmentation in the proposed configuration in comparison with the TR. This study shows
the superiority of AF-SPBR configuration to the conventional types.
2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.Article history: Improving the octane number of the aromatics compounds has always been an importanta r t i c l e i n f o a b s t r a c tDepartment of Chemical Engineering, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz 71345, IranModeling of an axial flow, sphnaphtha reforming process indeactivation
D. Iranshahi, E. Pourazadi, K. Paymooni, A.M
journa l homepage : wwssor T. Nejat Veziroglu. Prical packed-bed reactor fore presence of the catalyst
Bahmanpour, M.R. Rahimpour*, A. Shariati
e lsev ie r . com/ loca te /heublished by Elsevier Ltd. All rights reserved.
Moreover, Brumbaugh has patented a modified novel axial-
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 5 ( 2 0 1 0 ) 1 2 7 8 4e1 2 7 9 9 12785aromatics industrially known as PNA. Thereafter, more
extensive attempts have been made to model reforming
reactions. Juarez and Macias [3] developed a new kinetic
model in which the most important reactions in terms of
isomers of the same nature (paraffins, naphthenes and
aromatics) were taken into account. The average deviation of
the new kinetic model from experimental data was reported
to be less than 3%. Weifeng et al. [8] developed a new kinetic
model including 20 lumped components and 31 reactions.
Boyas and Froment [9] studied a fundamental chemistry of
naphtha. The current model imposed the equilibriums of
hydrogenation and dehydrogenations. Stijepovic et al. [10]
recommended a semi-empirical kinetic model for catalytic
reforming. Their lumping strategy was based on paraffins,
olefins, naphthenes and aromatics (PONA) analyses. Similar
studies in this field were carried out by Ramange et al. [11,12],
Krane et al. [13], Kmak [14] and Marin et al. [15]. The second
group involves studies on the modeling and improvement of
aromatics and hydrogen yields of the conventional reactors. Li
et al. [16] modeled and optimized a semi-regenerative cata-
lytic naphtha reformer by considering most of its key consti-
tutes. Taskar and Riggs [17] done a similar study as Li et al. But
they have used a reaction network composed of 35 reactions
for 35 pseudo components. Juarez et al. [18] modeled and
simulated four serially catalytic reactors for naphtha reform-
ing. Weifeng et al. [6] considered 18-lumped kinetic models to
simulate and optimize a whole industrial catalytic naphtha
reforming process by Aspen Plus platform. Stijepovic et al. [19]
introduced a new simulation and optimization approach for
CRs. They applied a new proposed objective function in which
economical and environmental performance was taken into
consideration. Khosravanipour and Rahimpour [4] presented
a membrane catalytic bed concept for naphtha reforming in
the presence of catalyst deactivation. Weifeng et al. [20]
examined a multi objective optimization strategy for a CR
process in order to obtain aromatic products. Rahimpour [21]
proposed a novel fluidized-bed membrane reactor (FBMR) for
naphtha reforming in the presence of catalyst deactivation.
He shows that the FBMR increases catalyst activity, aromatic
and hydrogen production rates.
In order to enhance the octane number of aromatic
compounds, the reaction conditions have to be improved.
Aromatics are enhanced by shifting the reactions (using
a hydrogen permeselective membrane) or decreasing the
pressure drop. In industrial plants, the pressure drop is
a serious problem in unit operations such as reactors. The
configurationswhich havemuch lower pressure drop than the
conventional fixed-bed reactors are radial flow spherical
packed-bed reactors (RF-SPBR) and radial flow tubular packed-
bed reactors (RF-TPBR). A complete literature review on the
RF-SPBR and RF-TPBR has been prepared by Iranshahi et al.
[22] have recentlymodeled the RF-SPBR for naphtha reforming
process in the presence of catalyst deactivation. They have
shown that in addition to pressure drop reduction through the
catalytic bed, the amount of aromatic production increases.
The AF-SPBR is an alternative configuration for pressure drop
reduction in high pressure processes such as naphtha
reforming. This novel configuration is not as well known asthe previous ones and little studies have been done on it.
Fogler has modeled the dehydrogenation of paraffins turningflow spherical reactor for naphtha reforming process [25].
The main goal of this work is to investigate the production
yield of aromatics in the AF-SPBR. A comparison between the
AF-SPBR and the TR are carried out in this study. The dynamic
modeling of this novel reactor is done by considering the
catalyst deactivation.
The AF-SPBR configuration is superior to the previous ones
(AF-TPBR and RF-SPBR) briefly as follows:
The AF-SPBR in comparison with the AF-TPBR:
Lower pressure drop is encountered in this configuration. Lower required material thickness (Material thickness fora spherical and a tubular pipe of the same radius, subjected to
action of an internal pressure, P, are tsph P$r=2s andttub P$r=s respectively.Where t is thewall thickness, s is thetensile stressand r is theradiusofthetubeandthesphere [26]).
Consequently the required surface has been decreasedwhich reduces effectively the costs of investment and
maintenance during the operation (this is a wise decision to
use membranes with lower costs of maintenance).
Smaller catalytic pellets with higher effectiveness factor canbe applied owing to the reduction of pressure drop in this
configuration.
Highermolar flow rate can be applied (due to lower pressuredrop) which increases the production rate.
Lower power supply of recompression is needed.
The AF-SPBR in comparison with the RF-SPBR:
The feed distribution has been improved (Utilizing the radialflow pattern to distribute the feed stream is not easily
applicable).
Modifications have been done on the reactor structure toprovide an effective contact between the reactant gas and
the catalytic bedwhen the quantity of the applied catalyst is
only a fraction of the designed quantity of catalyst [25].
Membrane technologies can be easily introduced in the AF-SPBR while it is hard to apply the membrane concept in
radial flow spherical packed-bed reactor (RF-SPBR).
A homogeneous one-dimensional model has been
considered. The basic structure of the model consists of heat
and mass balance equations. These equations must be
coupled with the deactivation model, and also thermody-
namic and kinetic equations, as well as auxiliary correlations
for predicting physical properties.
The effect of various parameters such as reactor length,
time, variable physical properties, and operating conditions
on the performance of the reactor has been investigated.
3. Reaction scheme and kineticsinto olefins and confirmed that the pressure drop in axial
spherical reactor decreases significantly [23]. Zardi et al. have
modeled the ammonia synthesis in an axial-radial reactor [24].Kinetics of multi-component reactions were presented by
Smith [7]. He assumed some pseudo components in order to
used, so the results are:
i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 5 ( 2 0 1 0 ) 1 2 7 8 4e1 2 7 9 912786simplify the feedstock of catalytic naphtha reforming. Four
dominant idealized reactions can be used to simplify the
catalytic reforming system. The following four reactions are
considered in the model:
(1) Dehydrogenation of naphthenes to aromatics.
(2) Dehydrocyclization of paraffins to naphthenes.
(3) Hydrocracking of naphthenes to lower hydrocarbons.
(4) Hydrocracking of paraffins to lower hydrocarbons.
The related reactions are
Naphthenes (CnH2n)4 Aromatics (CnH2n6) 3H2 (1)
Naphthenes (CnH2n) H24 Paraffins (CnH2n2) (2)
Naphthenes (CnH2n) n/3H2/ Lighter ends (C1eC5) (3)
Paraffins (CnH2n2) (n3)/3H2/ Lighter ends (C1eC5 (4)
Naphtha reforming reactions are limited by equilibrium. In
order to achieve higher aromatics production, the naphtha
reformingprocess should be carried out athigher temperatures.
The rate equations of these reactions are as follows:
r1 kf1Ke1
ke1pn pap3h
(5)
r2 kf2Ke2
ke2pnph pp
(6)
r3 kf3pt
pn (7)
r4 kf4pt
pp (8)
where kf and Ke are the forward rate constant and the
equilibrium constant, respectively. Rase [27] reported the
following equations for these constants.
kf1 9:87exp23:21 E1
1:8T
(9)
kf2 9:87exp35:98 E2
1:8T
(10)
kf3 kf4 exp42:97 E3
1:8T
(11)
Ke1 1:04 103exp46:15 46; 045
1:8T
(12)
Ke2 9:87exp7:12 8000
1:8T
(13)
where E is the activation energy of each reaction. The acti-vation energies depend on the catalyst which is used.
According to the previous works, the activation energy isE1 36,350E2 58,550E3 63,800
4. Process description
4.1. Conventional configuration
Naphtha reforming is amajor process practiced extensively by
petroleum refineries and the petrochemical industry to
convert paraffins and naphthenes into aromatics. A simplified
flow diagram of continuous catalytic reforming process is
shown in Fig. 1. The fresh naphtha feedstock (middle distillate
of atmospheric distillation column) is combined with a recy-
cled gas stream containing 60e90% (by mole) hydrogen.
Hydrogen can adjust the H2/HC molar ratio through the
reactors to prevent coking and also it sweeps the products
through the catalyst pores. The total reactor charges are
heated and passed through the catalytic reformers which are
designedwith three adiabatically operating reactors and three
heat exchangers between the reactors to maintain the reac-
tion temperatures at designed levels. The effluent from the
3rd reactor is cooled, and then it enters the separators. Off
gases and reformates are separated from the top and the
bottom of the separator [28]. Table 1 shows the specific
properties and operating conditions of the conventional
naphtha reactors. Boiling point ranges are determined by
Distillation Petro Test D86.
4.2. Spherical reactor setup
Although, tubular packed-bed reactors are used extensively in
industry [29], due to some disadvantages of this type of reac-
tors the spherical packed-bed reactors attract more atten-
tions. Some potential disadvantages of tubular reactors are
the pressure drop along the reactor, highmanufacturing costs
and low production capacity. In order to avoid serious pres-
sure drop in the TR, the effective diameters of the catalyst
particles are usually considered more than 3 mm which lead
to a certain inner mass transfer resistance. In this study, the
AF-SPBR is proposed for naphtha reforming process.found by minimizing the differences between the calculated
and the observed values of outlet temperature and aromatic
yield of bed simultaneously. A constrained optimization
procedure is used to find the activation energies. The activa-
tion energies are adjustable parameters. The objective func-
tion to be optimized is:
OF Xmi1
(NA cal NA plant
2X3i1
TOut cal TOut plant
2)(14)
where NA is the aromatic molar flow rate, T is the outlet
temperature of each bed and m is the number if data sets areFig. 2(a) shows the schematic diagram of the spherical
configuration setup. In the AF-SPBR, catalysts are situated
between two perforated screens. As depicted in Fig. 2(b), the
naphtha feed enters the top of the reactor and flows steadily
to the bottom of the reactor. Attempts should be made to
have a continuous flow without any channeling in the
reactor. The goal is to achieve a uniform flow distribution
through the catalytic bed, because the flow is mainly occur-
ring in an axial direction. The two screens in upper and lower
parts of the reactor hold the catalyst and act as a mechanical
support. Since the cross-sectional area is smaller near the
inlet and the outlet of the reactor, the presence of catalysts in
these parts would cause substantial pressure drop and
spherical packed-bed reactors [30]. In this study, a homoge-
Compressor
EX
-1
R-1
EX-2 EX-3
R-2
Naphtha Feed
R: Reactor
EX: Heat
Exchanger
S-1: Separator
S-2: Stabilizer
Fig. 1 e A simple process flow diagram for conv
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 5 ( 2 0 1 0 ) 1 2 7 8 4e1 2 7 9 9 12787Table 1 e Specifications of reactors, feed, product andcatalyst of plant for fresh catalyst.
Parameter NumericalValue
Unit
Naphtha feed stock 30.41 103 Kg/hReformate 24.66 103 Kg/hH2/HC mole ratio 4.73 e
LHSV 1.25 h1
Mole percent of hydrogen in recycle 69.5 eDiameter and length of 1st reactor 1.25, 6.29 m
Diameter and length of 2nd reactor 1.67, 7.13 m
Diameter and length of 3rd reactor 1.98, 7.89 m
Distillation fraction of naphtha feed and reformate
TBP Naphtha feed
(C)Reformate
(C)IBP 106 44
10% 113 73
30% 119 105
50% 125 123
70% 133 136
90% 144 153
FBP 173 181
Typical properties of catalyst in use
dp 1.2 mm
Pt 0.3 wt%
Re 0.3 wt%
sa 220 m2/g
rB 0.3 Kg/l
3 0.36 eneous one-dimensional model has been considered. The flow
pattern in the AF-SPBR is assumed to be axial. The basic
structure of the model consists of heat and mass balance
equations. These equations must be coupled with the deac-
tivationmodel, and also thermodynamic and kinetic relations
as well as auxiliary correlations for predicting physical prop-
erties. In order to solve the equations, an element with theconsequently, reduce the efficiency of the spherical reactors.
The other advantage of these screens is to balance the free
zones (free catalyst zones) to find a desirable pressure drop
during the process. The radial flow is assumed to be negli-
gible in comparison with the axial flow. As a result, the
equations in the axial coordinate are being taken into
account exclusively.
5. Reactor modeling
5.1. Axial- flow spherical packed-bed reactor model (AF-SPBR model)
Rahimpour et al. have established the dynamic modeling of
R-3
S-1S-2
Hydrogen Rich Gas
Reformate to Storage
Off Gas
entional catalytic naphtha reforming (TR).length dz (as shown in Fig. 3) has been considered and the
material and energy balances are written upon this element.
Themass and energy balance equations for fluid phase can be
formulated as follows:
Dej1Ac
v
vz
AcvCjvz
1Ac
v
vz
AcuzCj
rBaXmi1
nijri 3vCjvt
j 1;2;.;n 15
keff1Ac
v
vz
AcvTvz
1Ac
v
vz
rAcuzcp
T Tref
rBaXmi1
DHiri
3vrcps
T Tref
vt
(16)
where a is the catalyst activity, i represents the reaction
number and j represents the component number, Dej is the
effective diffusivity of component j, C is the gas phase
concentration, rB is the catalyst bulk density, vij is the
i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 5 ( 2 0 1 0 ) 1 2 7 8 4e1 2 7 9 912788R-1 R-2
R: Reactor
EX: Heat Exchanger
S-1: Separator
S-2: Stabilizer
astoichiometry coefficient of the reactant j in the reaction i, ri is
the reaction rate, keff is the thermal conductivity of the gas
phase, T is the temperature, r is the density of gas phase, CP is
the heat capacity of the gas phase, 3 is the void fraction andDH
is the heat of the reaction.
Its worthmentioning that the cross-section area, Ac, in the
AF-SPBR is a function of reactor length. Therefore it must
remain between the parentheses of the derivative equation of
mass and energy balances. The formulation of cross-section
area, Ac, is described as follows [23]:
Ac phR2 z L12
i(17)
The boundary and initial conditions are as follows:
Compressor
EX
-1
EX-2 EX-3
Naphtha Feed
z+dz
z
dz
F1
Naphtha Feed
Product
F1
b
Fig. 2 e (a) Spherical axial-flow configuration for catalytic naph
specifications for spherical reactor in the catalytic naphtha refoR-3
S-1S-2
Off Gasz 0; Cj Cjo; T To (18)
z L1 L2 : vCjvz
0; vTvz
0 (19)
t 0; Cj Cssj ; T Tss; Ts Tsss ; a 1; (20)
where L1 and L2 represent the vertical distance from the center
of the reactor to the top and bottom screens in the axial
coordinate. The superscript ss represents the steady state
condition. The steady state mass and energy balance equa-
tions are the same when the accumulation term is set to zero.
Mass and heat transfer coefficients are estimated by several
Hydrogen Rich Gas
Reformate to Storage
Screen z=0
Screen z=L1+L2
L1
L2
R
Z
tha reforming and (b) conceptual Flow pattern and
rming process.
where TR, Ed and Kd are the reference temperature, the acti-
formula of order two. It is noted that this method is well
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 5 ( 2 0 1 0 ) 1 2 7 8 4e1 2 7 9 9 12789auxiliary correlations. These auxiliary correlations are pre-
sented in Appendix B. The heat of reactions is reported as
follows (kJ/kmol of H2):
DH1 71;038:06DH2 36;953:33DH3 51;939:31DH4 56;597:54
5.2. Conventional tubular reactor model (CR model)
Themodeling assumptions of TR andAF-SPBR are similar. The
general fluid-phase balance is a model with the balances
typically accounting for accumulation, convection, and reac-
tion. The energy and mass balances for the gas phase can be
written as Eqs. (21) and (22):
Dejv2Cjvz2
vuCj
vz
rBaXmi1
nijri 3vCjvt
j 1;2;.;n
i 1;2;.;m 21
keffv2Tvz2
vvz
rucp
T Tref
rBaXmi1
DHiri 3 vvt
rcpT Tref
(22)
The boundary and initial conditions are as follows:
z 0 : Cj Cj0; T T0 (23)
Z L : vCjvz
0; vTvz
0 (24)
t 0 : Cj Cssj ; T Tss; a 1 (25)
Fz
dz
Fz+dz
Fig. 3 e Schematic for differential element along the flow
direction.5.3. Pressure drop (Ergun equation)
The pressure drop throughout the catalyst bed is calculated
based on the Ergun equation. This equation covers the entire
range of flow rates by assuming that the viscous losses and
the kinetic energy losses are additive [23]. This equation for
Cartesian systems is derived as below:
dPdz
150mf2s d
2p
1 3233
QAc
1:75rfsdp
1 333
Q2
Ac(26)
where dP is the pressure gradient,Q is the volumetric flow rate,
dp is the particle diameter, fs is the sphericity (for spherical
particles fs equals one), m is the fluid viscosity and r is the fluid
density.suited for the systems of stiff equations [34]. In addition,
Gears method can be used for solving the set of such stiff
ODEs.
8. Model validation
8.1. Model validation with the presence of catalystdeactivation
Model validation is carried out by comparing the TR results
[28] with the proposed configuration over 800 operating days.
The predicted results of the production rate, the correspond-vation energy and the deactivation constant of the catalyst,
respectively. The numerical values of TR, Ed and Kd, are 770 K,
1.642 105 J mol1 and 5.926 105 h1, respectively.
7. Numerical solution
In order to solve the set of coupled partial differential-
algebraic equations a two steps procedure is used. Firstly,
the steady state simulation is carried out to obtain the
initial conditions of the dynamic simulation. In the steady
state simulation all the time variations are considered to be
zero and activity will be considered to be one. Secondly,
the results of the steady state simulation are used as the
initial conditions for the time-integration of the dynamic
state equations in each node through the reactor. The
deactivation model and the conservation rules are ordinary
and partial differential equations, respectively. Moreover,
there would be algebraic equations due to the auxiliary
correlations, kinetics and thermodynamics of the reaction
system. These equations constitute a set of dynamic
equations.
The set of aforementioned equations of the model of
spherical and tubular reactors are solved by means of the
orthogonal collocation method [32,33]. Inner collocation
points are chosen as a root of a Jacobi polynomial. The
orthogonal collocation method is discussed further in
Appendix A. The system of PDEs is transformed into an
ordinary differential equation (ODE) system by means of this
numerical method. An energy balance is developed for each
collocation point, as well as a mass balance for each species.
The energy and mass balance equations of the spherical
reactor are systems of ODEs with initial conditions. The
system of ODEs is integrated by a modified Rosenbrock6. Catalyst deactivation model
The catalyst deactivation model is used from the previous
work which was presented by Rahimpour [31].
dadt
Kdexp Ed
R
1T 1TR
a7 (27)ing observed data and the residual error are presented in
Table 2. Good agreements between the daily observed plant
data and simulation results are achieved, so this model can
Table 2 e Comparison between predicted production rate and plant data.
Time (day) Naphtha feed (ton/h) Plant (kmol/h) AF-TPBR (kmol/h) AF-SPBR (kmol/h) Devi % (Tubular- Plant)
0 30.41 225.90 221.5802 221.4080 1.9134 30.41 224.25 222.5122 222.3432 0.7762 31.00 229.65 227.9313 227.7559 0.7597 30.78 229.65 226.7749 226.6038 1.25125 31.22 229.65 230.7985 230.6220 0.50160 31.22 229.65 231.2730 231.0971 0.71188 28.55 211.60 209.8377 209.6965 0.83223 30.33 222.75 224.7291 224.5558 0.88243 31.22 233.05 232.1821 232.0072 0.37298 30.67 228.65 228.1752 228.0081 0.21321 30.76 227.64 229.0932 228.9246 0.64
3
3
3
3
3
3
3
2
2
i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 5 ( 2 0 1 0 ) 1 2 7 8 4e1 2 7 9 912790satisfy successfully the industrial conditions. The related
deviations from the plant reported values are due to the fact
that the kinetics and models used for reaction system of
naphtha reforming underestimated the true reaction rate.
Also using the average molecular weights and such other
physical properties for the three groups of pseudo compo-
nents (PNA), heat transfer coefficients maybe increase the
uncertainties.398 42.35 317.30
425 42.32 317.94
461 42.32 317.94
490 42.32 317.94
524 42.32 313.09
567 42.54 317.94
610 42.54 313.90
717 37.86 286.15
771 38.51 282.108.2. Steady state model validation
A comparison between the proposed model and TR has been
demonstrated at the steady state condition in Table 3. As seen,
there is a good agreement between the plant data and pre-
dicted mole fractions of components at the output of the
system. Analyses of components (paraffin, naphthene and
aromatic) are performed by PONA Test in Stan Hop Seta
apparatus. The aromatic is tested especially by ASTM 2159
equivalent to UOP 273 method [28].
Table 3 e Comparison between model prediction and plant da
Reactor number Inlet temperature (k) Inlet pressure (kPa)
1 777 3703
2 777 3537
3 775 3401
Reactor number Outlet temperature (k)
Plant NPBR SPFR
1 722 727.38 727.4
2 753 751.03 751.6
3 770 770.54 770.79. Results and discussion
In order to have a desirable prediction, the appropriate
number of interior collocation points has been evaluated.
According to Fig. 4, the aromatic molar flow rate is plotted
versus the mass of catalysts with different number of interior
collocation points. In Fig. 4(a) one, two and three and in Fig. 4
(b) one, five, and seven interior collocation points have been
used. As it is shown in Fig. 4(a), when the number of interior
collocation points is not enough, the diversity appears
24.5555 324.2907 2.2824.4826 324.2216 2.0524.6987 324.4426 2.1224.8622 324.6099 2.1725.0433 324.7952 3.8127.0586 326.8164 2.8627.2581 327.0210 4.2589.3742 289.1475 1.1294.9026 294.6767 4.53between the curves. But by increasing the number of interior
collocation points as shown in Fig. 4(b), the discrepancy
disappears between the curves. The curves with 5 and 7
interior points cover each other thoroughly. Therefore, the
N 5 is the most accurate choice.
Results of modeling involve the following main issues:
9.1 Changes of parameters along the spherical reactors.
9.2 Changes of parameters as a function of time.
ta for fresh catalyst.
Catalyst distribution (wt %) Input feedstock (mole %)
20 Paraffin 49.3
30 Naphthene 36.0
50 Aromatic 14.7
Aromatic in reformate (mole %)
Plant NPBR SPFR
5 e 34.78 34.77
6 e 47.28 47.12
5 57.7 56.26 56.18
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
3300
3350
3400
3450
3500
3550
3600
3650
3700
3750
Mass of catalyst (Dimensionless)
Pres
sure
(kPa
)
TR
SR
L=0.95R
L=0.70R
L=0.50R
L=0.90R
L=0.10R L=0.30R
Fig. 5 e Pressure profile along the mass of catalyst (solid
line: tubular reactor, dotted line: spherical reactor).
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 140
45
50
55
60
65
70
75
80
85
90
Mass of catalyst (Dimensionless)
Aro
matic
m
ola
r flo
w ra
te (k
mole
/hr)
one interior collocation pointNinterior=1
two interior collocation pointNinterior=2
three interior collocation pointNinterior=3
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 140
45
50
55
60
65
70
75
80
85
90
Mass of catalyst (Dimensionless)
Aro
ma
tic m
ola
r flo
w ra
te (k
mole
/hr)
One interior collocation pointNinterior=1
Five interior collocation pointNinterior=5
Seven interior collocation pointNinterior=7
a
b
Fig. 4 e Aromatic molar flow rate along themass of catalyst
(a) with1, 2 and 3 and (b) and 1, 5 and 7 interior orthogonal
collocation points.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
20
40
60
80
100
120
140
Mass of catalyst (Dimensionless)
Mola
r flo
w ra
te (k
mole
/hr)
800th
Day
1st
Day
Paraffin
Naphthene
Aromatic
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1250
1300
1350
1400
1450
1500
Mass of catalyst (Dimensionless)
Hyd
roge
n m
ola
r flo
w ra
te (k
mole
/hr)
800th
Day
1st
Day
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
720
730
740
750
760
770
780
Mass of catalyst (Dimensionless)
Tem
pera
ture
(K
)
TR
SR
a
b
C
Fig. 6 e (a) Production and consumption rates versus mass
of catalyst (solid line: the 1st day of production, dotted line:
the 800th day of production), (b) hydrogen molar flow rate
versus mass of catalyst (solid line: the 1st day of
production, dotted line: the 800th day of production) and (c)
the temperature profiles of TR and SR.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 5 ( 2 0 1 0 ) 1 2 7 8 4e1 2 7 9 9 12791
9.3 Effect of operating conditions and a comparison between
tubular and spherical reactors in this regard.
The variables that affect the performance of the catalyst,
the yield and quality of reformate are time, feedstock prop-
erties, reaction temperature, space velocity, reaction pressure,
and hydrogen per hydrocarbon ratio [35].
0 100 200 300 400 500 600 700 800
0.7
0.75
0.8
0.85
0.9
0.95
1
Time (Day)
Catalyst activity
1st
reactor
2nd
reactor
3rd
reactor
Fig. 7 e (a) The catalyst activity during 800 days of
operation for the 1st, the 2nd and the 3rd reactors.
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1000
1500
2000
2500
3000
L/R
Pressu
re (kP
a) FR=1.0
FR=2.0
FR=2.5
FR=3.0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.29
0.3
0.31
0.32
0.33
0.34
0.35
0.36
L/R
Aro
matic yield
FR=1.0
FR=2.0
FR=2.5
FR=3.0
b
c
0.85
0.86
0.87
0.88
i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 5 ( 2 0 1 0 ) 1 2 7 8 4e1 2 7 9 912792Fig. 8 e (a) Aromatic and paraffin and (b) light end and
hydrogen mole productions during 800 days of operation.3500
4000a9.1. Changes of parameters along the spherical reactors
The changes of parameters along the length of the spherical
reactors in the 1st and the 800th days of operation will be
investigated in the first section.
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.78
0.79
0.8
0.81
0.82
0.83
0.84
L/R
Hyd
ro
gen
yield
FR=1.0
FR=2.0
FR=2.5
FR=3.0
Fig. 9 e The effect of different FR ratios on (a) the pressure
versus L/R, (b) the aromatic yield versus L/R and (c) the
hydrogen yield versus L/R.
2000 2200 2400 2600 2800 3000 3200 3400 3600 3800 4000
1480
1485
1490
1495
1500
1505
Operating pressure (kPa)
Hyd
ro
gen
p
ro
du
ctio
n (km
ole/h
r)
TR
SR
P=3070 kPa
(B)(A)
Fig. 11 e Hydrogen production versus operating pressure
for spherical and tubular reactor.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 5 ( 2 0 1 0 ) 1 2 7 8 4e1 2 7 9 9 127930.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
0.26
0.27
0.28
0.29
0.3
0.31
0.32
0.33
0.34
0.35
0.36
Mass of catalyst (Dimensionless)
Aro
ma
tic yi
eld
TR
SR
P=1703 kPa
P=2703 kPa
0.36
0.37
a
bAs shown in Fig. 5, the pressure is depicted versus the
dimensionless mass of catalysts of three reactors for various
L/Rs. it can be seen, by increasing L/Rs the pressure drop
increases. Thus, for L/R 0.95 the greatest pressure drop isachieved. At higher L/Rs, a huge bulk of feed encounters less
empty zones at the inlet and the outlet of the reactor. As
a result, a sudden pressure drop happens in the pressure
profile. The steps indicate the pressure drop in each reactor.
The dimensionless mass of catalyst for the 1st, the 2nd and
the 3rd reactors is in the range of 0e0.2, 0.2e0.5 and 0.5e1,
respectively. The dimensionless mass of catalyst 0 showsthe inlet of the 1st spherical reactor and the dimensionless
mass of catalyst 1 implies the outlet of the 3rd reactor. Onthe other hand, if L/R decreases to lower than 0.7, the pressure
drop would decrease too. However, working with the L/R 0.5is useless because most of the reactor space is empty without
any catalyst. Thus, the L/R 0.7 is chosen not only to reducethe useless fabrication of materials for free zone but also to
have a little pressure drop. The reason which makes this ratio
a proper choice will be discussed later.
In previous works, the total molar flow rate was assumed
to be constant while it increases throughout the reactor in
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
0.29
0.3
0.31
0.32
0.33
0.34
0.35
Mass of catalyst (Dimensionless)
Aro
ma
tic yi
eld
TR
SR
P=3703 kPa
P=4703 kPa
Fig. 10 e Aromatic yield versus mass of catalyst in third
reactor (a) for operating pressures 1703 and 2703 kPa and
(b) for operating pressures 3703 and 4703.
0 1 2 3 4 5 6 7
0
500
1000
1500
2000
2500
3000
3500
4000
Feed flow rate scale up ratio
Pressu
re (kP
a)
SR
TR
0 1 2 3 4 5 6 7
0.2
0.22
0.24
0.26
0.28
0.3
0.32
0.34
0.36
0.38
0.4
Feed flow rate scale up ratio
Aro
matic yield
SR
TR
a
b
Fig. 12 e (a) Pressure versus feed flow rate scale up ratio
and (b) aromatic yield versus feed flow rate scale up ratio at
3703 kPa for tubular and spherical reactors(solid line:
tubular reactor, dotted line: spherical reactor).
i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 5 ( 2 0 1 0 ) 1 2 7 8 4e1 2 7 9 9127941
2
3
4
5
6
0
5
10
15
1500
2000
2500
3000
3500
4000
Flow scale up ratioCatalyst scale up ratio
Pre
ss
ure
(k
Pa
)
0.8
0.9
ie
ld
a
cplants. In this study, the total molar flow and also all physical
properties such as heat capacity and thermal conductivity are
assumed to be variable along the reactors.
A scheme of components molar flow rates versus the
mass of catalyst along the reactor for the 1st and the 800th
days of operation is depicted in Fig. 6(a). As seen, the aim of
naphtha reforming is satisfied, because the molar flow rate
of aromatics increases along the reactor and fortunately
the molar flow rates of naphtha and paraffin decrease.
Each break point in this figure indicates the inlet temper-
ature of the following reactor. Because the temperature
increases by using pre heaters at the inlet of each reactor,
the reaction rates change and discontinuities appear in the
figure.
Also, Fig. 6(b) illustrates hydrogen molar flow rate versus
the mass of catalyst along the reactor. Fig. 6(c) presents
the temperature distribution through the TR and SR. As the
naphtha reforming is predominantly endothermic, the
temperature decreases in the reactors.
9.2. Changes of parameters as a function of time
In the second part, the variation of parameters as a function of
time will be discussed. Fig. 7 reveals the average catalyst
10
5
10
15
0.4
0.5
0.6
0.7
Catalyst scale up ratio
Hy
dro
ge
n y
Fig. 13 e 3-D figure which shows the effect of flow scale up ratio
yield.1
2
3
4
5
6
0
5
10
15
0.2
0.25
0.3
0.35
0.4
0.45
Flow scale up ratioCatalyst scale up ratio
Aro
ma
tic
y
ie
ld
bactivity as a function of time in three reactors. As the reactions
proceed, the catalyst activity decreases. The catalyst activity
has an inverse relationship with the temperature, in other
words, as the temperature decreases the catalyst activity
increases.
Fig. 8(a) illustrates the effect of catalyst deactivation on the
product and reactant production rates. By decreasing the
catalyst activity, the aromatic production rate decreases and
hence the amount of unreacted paraffin increases due to
lower reaction rate. As a result of catalyst deactivation, both
the reaction rate and the production rate decrease. The light
end (off gas) production rate as a function of time is depicted
in Fig. 8(b). As seen, this product also decreases in the course
of time due to the catalyst deactivation. An unpredictable
behavior is observed in Fig. 8(b) for hydrogen production. The
catalyst aging acts in away that hydrogen producesmore after
the 800th day of operation compared with the 1st day.
9.3. Effect of operating conditions and a comparisonbetween tubular and spherical reactors in this regard
The effect of operating conditions such as flow scale up ratio
(FR), operating pressures and other parameters are studied in
the following section.
2
3
4
5
6
Flow scale up ratio
and catalyst scale up ratio on (a) pressure and (b) aromatic
and high catalyst loading, the sufficient time exists for con-
verting the feed to aromatics. Therefore the peak is seen in
low feed flow rates (less than 1). When the feed flow rate scale
up ratio equals to 1, the aromatic yield in the tubular reactor is
slightly higher than the yield in the spherical reactor. By
increasing the scale up ratio in two reactors the aromatic yield
decreases in both reactors but the slope is sharper in TR. The
pressure drop has a strongly negative effect on the aromatic
production in tubular reactors due to the FR. It should be
mentioned that Fig. 12(a, b) are depicted in the constant inlet
pressure of 3070 kPa for tubular and spherical reactors.
The simultaneous effect of catalyst and FRs on pressure,
aromatic and hydrogen yields is investigated in the following
3-D plots. The various catalyst distributions in SR in compar-
ison with the TR are identified by catalyst scale up ratio.
Fig. 13(a) illustrates the simultaneous effect of catalyst and
FR on pressure. For all catalyst scale up ratios the pressure
decreases by increasing the FR. Especially for lower catalyst
scale up ratios, the pressure drop is higher due to lower
reactor diameter and high viscose loss in higher velocities.
When, the catalyst scale up ratio increases to 5, the flux
decreases due to the increase in the reactor diameter. There-
fore the pressure becomes approximately constant. In low
0.3
0.338
0.35
0.4
0.45
Aro
matic yield
CMR=1
CMR=2
CMR=3
CMR=4
a
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 5 ( 2 0 1 0 ) 1 2 7 8 4e1 2 7 9 9 127959.3.1. The effect of flow scale up ratio (FR)The effect of FR on pressure is illustrated first. The pressure
versus L/R for different FRs is shown in Fig. 9(a). FR indicates
that the flow rate of fresh naphtha feed in spherical reactor is
more compared with the feed stream in TR. As seen,
increasing the FR increases the pressure drop and this will be
more significant for higher L/Rs. The slope of curves starts to
change at the L/R 0.7 and the variation of pressure dropexperiences a new trend in spherical reactors. At the L/R 0.7,the pressure drop increases by increasing the FR. But, the
pressure drop augmentation at this ratio is approximately less
than higher values of L/Rs. Therefore, the L/R 0.7 is anappropriate choice, due to observation of considerable pres-
sure drop after this point. This is an evidence to show that the
L/R 0.7 is a proper choice. The aromatic yield versus L/R fordifferent FRs is illustrated in Fig. 9(b). According to the Le
Chateliers principle, for FRs equal to 1e2 the pressure drop at
L/R 0.7e0.9 shifts the reaction to the aromatics andhydrogen production. The residence time decreases in higher
FRs owing to providing a larger quantity of reactants per unit
of catalyst. Consequently, it decreases the products yield (see
Fig. 9(b)e(c)). Higher pressure drop at FRs of 2.5e3 reduces the
reactants partial pressures and this affects the reaction rates.
It should bementioned that all the previous results in this part
have been achieved at the constant inlet compressor pressure
of 3703 kPa.
9.3.2. Effect of operating pressureFig. 10(a, b) shows the aromatic production in spherical
reactor (SR) and tubular reactor (TR) based on the dimen-
sionless mass of catalyst for various operation pressures. As
seen from Fig. 10(a), when the operating pressure equals
1703 kPa, the aromatic yield in the SR is considerably higher
than the TR. As the operating pressure increases, the differ-
ence between the aromatic yields in two reactor configura-
tions decreases (see the graph for Pressure of 2703 kPa). The
intersection of tubular and spherical curves is named
the turning junction point. However, the arrangement of the
curves will change at the turning junction point and the
aromatic yield in TR becomes more than the one in SR (see
Fig. 10(b)). In other words, the TR unlike the SR is incapable of
operating satisfactorily at low pressures. In spite of SR
advantages (lower pressure drop, lower constructionmaterial,
lower surface area and lower related maintenance costs), the
operating pressure should be wisely determined when
compared with the TR. The same trend is observed for
hydrogen production rate versus the operating pressure for SR
and TR configurations in Fig. 11.
9.3.3. The effect of feed flow rate scale up ratioThe capability of spherical reactors in using higher flow rates
in comparison with the tubular ones is clearly represented by
Fig. 12(a). If the feed flow ratio in TR is doubled, the pressure
decreases drastically. On the other hand if the feed flow ratio
in spherical reactor equals to 7, the pressure declines.
Therefore, if the feed flow ratio in spherical reactor increases
more products would be achieved. The effect of flow rate
augmentation on quality is investigated by considering theproduct yields. According to Fig. 12(b), the peak is observed for
low feed flow rate in both reactors. Due to low feed flow rate0 1 2 3 4 5 6
0.2
0.25
Flow scale up ratio
0 1 2 3 4 5 6 7
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.876
0.9
1
Flow scale up ratio
Hyd
ro
gen
yield
CMR=1
CMR=2
CMR=3
CMR=4
bFig. 14 e The effect of CMR and the flow scale up ratio on (a)
aromatic yield and (b) hydrogen yield.
catalyst scale up ratios, the pressure drop increases by
increasing the FR. Fig. 13(b) illustrates the simultaneous effect
of catalyst and FRs on the aromatic yield. In each FR, if the
catalyst scale up ratio increases, the aromatic yield will
increase. In general, the catalyst scale up ratio causes higher
aromatic yield for each FR. However, increasing FR decreases
the aromatic yield in each catalyst scale up ratio. The simul-
taneous effect of catalyst and FR is considered on hydrogen
yield in Fig. 13(c).
The effect of FR on aromatic yield for different catalyst
mass ratios (CMRs) is depicted in Fig. 14(a) for SR. The
aromatic yield is considered to be 0.338 in industry and the
industry data for CMR 1 is depicted as solid line. If the FRequals 2, in order to achieve the same (0.338) aromatic yield
the CMR should be a little less than 2 (1.9 times). Similarly, if
the FR equals 3, the CMR should be a little less than 3(2.85
times) in fixed aromatic yield. In high CMRs, as FR increases,
the difference between the fixed aromatic yield (0.338) and the
obtained aromatic yield increases. In general, in order to have
a specific flow (FR) a little less than the specified value is
needed for catalyst loading. The difference between these two
values is larger for higher FRs. The effect of FR on hydrogen
yield in different CMRs is depicted in Fig. 14(b). In CMR 1, as
changes to examine the effect of temperature. Fig.15(a, b)
finite difference method. Results show that the AF-SPBR can
be properly applied instead of TR. This study shows that for
0.6
0.65
0.7
0.75
0.8
0.85
0.9
Hyd
roge
n yi
eld
T1=777, T
2=777
T1=777, T
3=775
T2=777, T
3=775
a
i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 5 ( 2 0 1 0 ) 1 2 7 8 4e1 2 7 9 912796650 700 750 800 850
0.45
0.5
0.55
Inlet temperature (K)
650 700 750 800 850
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Inlet temperature (K)
Aro
mat
ic y
ield
T1=777, T
2=777
T1=777, T
3=775
T2=777, T
3=775
b
Fig. 15 e The effect of inlet temperatures on (a) hydrogenand (b) aromatic yields.naphtha reforming process the AF-SPBR configuration is more
efficient than the previous ones. The practical operating
conditions data together with the mathematical model can be
used to develop the AF-SPBR model for new plant setups and
revamps of process in future.
Acknowledgement
The authors would like to thanks gratefully to Samira Hafe-
ziyeh for her helpful recommendation to improve the English
language of the manuscript.
Appendix A. Orthogonal Collocation method
Jacobi polynomials
a;billustrates the effect of temperature on hydrogen and
aromatic yield, respectively. As the temperature exceeds,
hydrogen is consumed and the yield decreases. The results
show that increasing the 1st reactor temperature (dotted lines
in Fig.15(a, (b)) is more efficient in order to hydrogen and
aromatic production.
10. Conclusion
In any process, a significant incentive to minimize the pres-
sure drop has led to developing a number of alternatives on
the flow configurations. According to this concept, one
potentially interesting idea for catalytic naphtha reforming
process is the application of AF-SPBR. The pressure drop
problem is successfully overcome in this new configuration. In
this study, the AF-SPBR is proposed for catalytic naphtha
reforming process. The effect of several parameters on
aromatic and hydrogen yields is investigated. Most of the
parameters of the systemare considered to be variable such as
heat capacity, viscosity, molecular weight, pressure, density
and the total molar flow. Optimum pressure and L/R are
determined. The dynamic model is solved by the orthogonal
collocation method and the results are much better in
comparison with the other conventional methods such asFR increases hydrogen yield decreases and a peak is observed
in the figure. Hydrogen yield becomes constant for the CMRs
higher than 3. If higher FRs is desired, the CMR should bemore
than 3. In order to achieve the fixed hydrogen yield (0.87),
when the FR is less than 3, it is satisfactory to work with
minimum CMR which equals to 2.
9.3.4. The effect of temperature on the products yieldsIn order to consider the effect of temperature, the inlet
temperatures of two reactors out of three is considered to be
constant and the inlet temperature of the other reactorThe Jacobi function, JN x, is a polynomial of degreeN that is,orthogonal with respect to the weighting function xb1 xa.
2C
32 2C
32
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 5 ( 2 0 1 0 ) 1 2 7 8 4e1 2 7 9 9 12797The Jacobi polynomial of degree N has the power series as
follow:
Ja;bN x XNi0
1NigN;ixi (A e1)
The domain of x is in the range [0, 1].
The evaluation of coefficients is done by using the
following recurrence formula
gN; i
gN; i1 N i 1
i$N i a b
i b (A e2)
Starting with
gN;0 1 (A e3)
gN,i are constant coefficients, and a and b are parameters
characterizing the polynomials.
Lagrange Interpolation Polynomials
For a given set of data points (x1, y1), (x2, y2),.,(xN, yN) and
(xN1, yN1) an interpolation formula passing through all(N 1) points is an Nth degree polynomial. A suitable inter-polation polynomial for the orthogonal collocation method is
Lagrange interpolation polynomial, which passes through the
interior collocation points, roots of Jacobi polynomials, and it
is expressed as
yNx XN1j1
yjljx (A e4)
where yN is the Nth degree polynomial, yi is the value of y at
the point xi, and li(x) is defined as
lix YN1j 1jsi
x xj
xi xj
(A e5)
Furthermore,
lixj 0 isj
1 i j (A e6)
The first and second derivative at the interpolation points
are:
dyNxidx
XN1j1
dljxidx
yj (A e7)
d2yNxidx2
XN1j1
d2ljxidx2
yj (A e8)
For i 1;2.;N;N 1:The first derivative vector, composed of (N 1) first deriv-
atives at the (N 1) interpolation points is:
y0N dyNx1
dx;dyNx2
dx;.;
dyNxNdx
;dyNxN1
dx
T(A e9)
Similarly, the second derivative vector is defined as
y00N "d2yNx1
dx2;d2yNx2
dx2;.;
d2yNxNdx2
;d2yNxN1
dx2
#T(A e10)The function vector is defined as values of y at (N 1)collocation points asCp C1 C26664
3
T
sin h
C3T
7775 C46664
5
T
cos h
C5T
7775 (B e2)
where cp is in J/(kmol K) and T is in K [37].
To complete the simulation, extra correlations should be
added to the model. In the case of heterogeneous model,
because of transfer phenomena, the correlations for estima-
tion of heat and mass transfer between two phases should be
considered. It isbecauseof theconcentrationandheatgradient
betweenbulkof thegasphaseandthefilmofgasonthecatalyst
surface, which caused by the resistance of the film layer.
B.3. Mass transfer correlations
To flow through a packed bed, the correlation is given by the
following equation [38]:
kcidpDim
3
1 31g
um1 3g
1=2m
rDim
(B e3)y y1; y2; y3;.; yN; yN1T (A e11)By means of these definitions of vectors y and derivative
vectors, the first and second derivative vectors can be written
in terms of the function vector y using matrix notation
y0 A$yy00 B$y (A e12)
Where the matrices A and B are defined as
A aij
dljxidx
; i; j 1; 2;.;N;N 1
(A e13)
B (bij
d2ljxidx2
; i; j 1;2;.;N; N 1)
(A e14)
The matrices A and B are (N 1, N 1) square matrices.Once the (N 1) interpolation points are chosen, then all theLagrangian building blocks, li(xi), are completely known, and
thus the matrices A and B are also known [36].
Appendix B. Auxiliary Correlations
B.1. Gas phase viscosity
Viscosity of reactants and products is obtained from the
following formula:
m C1TC2
1 C3T C4T2
(B e1)
where m is the viscosity in Pa.s and T is the temperature in K.
Viscosities are at 1 atm [37].
B.2. Gas phase Heat capacity
Heat Capacity of reactants and products at Constant Pressure
is obtained from the following formula:where dp is particle diameter (m), 3b is void fraction of packed
bed, is shape factor of pellet, u is superficial velocity through
i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 5 ( 2 0 1 0 ) 1 2 7 8 4e1 2 7 9 912798packed bed (m/s), is viscosity of gas fluid phase (kg/m s) and is
fluid density (kg/m3).
Diffusivity of component i in the gas mixture is given by
Ref. [39].
Dim 1 yi
P
yi=Dij (B e4)
The binary diffusivities are calculated using the Fullere
SchetterGiddins equation which is reported by Reid et al.[40]. In the following FullerSchetterGiddins correlation, vci,Mi are the critical volume andmolecular weight of component
i which are reported in.
Dij 107T3=2
1=Mi 1=Mj
1=2Ptv3=2ci v3=2cj
2 (B e5)
B.4. Heat transfer correlation
The heat transfer coefficient between the gas phase and solid
phase is obtained by the following correlation [41]:
hfcprm
cpmK
2=3 0:458
3b
rudpm
0:407(B e6)
where in the above equation, u is superficial velocity of gas
and the other parameters are those of bulk gas phase, dp is the
equivalent catalyst diameter, K is the thermal conductivity of
gas, r, m are density and viscosity of gas, respectively and 3 is
void fraction of catalyst bed. To see the constants which are
used in these equations please see reference [22].
Appendix C. Nomenclature
Parameter description
a catalyst activity, e
aij element of matrix A, e
A moles of aromatic formed, kmol h1
A matrix defined in Eq. (Ae12), e
Ac cross-section area of reactor, m2
B matrix is defined in Eq. (Ae12), e
bij element of matrix B, e
C concentration, kmol m3
Ci coefficient of Eqs. (B-1) to (B-2), e
Cj0 inlet concentration of component j, kmol m3
cp specific heat capacity, kJ kmol1 K1
dp particle diameter, m
De effective diffusivity, m2s1
Dim diffusivity of component i in the gas mixture, m2 s1
Ed activation energy of catalyst, J mol1
Ei activation energy for ith reaction, kJ kmol1
hf heat transfer coefficient, W m2 K1
HC hydrocarbon, kmol h1
H2 hydrogen, kmol h1
J jacobi function, e
keff effective thermal conductivity, W m1 s1
kci mass transfer coefficient for component i, m h1kf1 forward rate constant for reaction (1), kmol h1
kg cat1 M Pa1kf2 forward rate constant for reaction (2), kmol h1
kgcat1 MPa2
kf3 forward rate constant for reactions (3), kmol h1
kg cat1
kf4 forward rate constant for reactions (4), kmol h1
kg cat1
Ke1 equilibrium constant, MPa3
Ke2 equilibrium constant, MPa1
Kd deactivation constant of the catalyst, h1
L length of reactor, m
lj building block of jacobi polynomial, e
m number of data sets used, e
m number of reaction, e
mc mass of catalyst, kg
Mi molecular weight of component i, kg kmol1
Mw average molecular weight of the feedstock, kg kmol1
n average carbon number for naphtha, e
n number of component, e
N degree of Jacobi function, e
NA molar flow rate of aromatic, kmol h1
Ni molar flow rate of component i, kmol h1
p moles of paraffin formed, kmol h1
Pi partial pressure of ith component, kPa
P total pressure, kPa
Q volumetric flow rate, m3 s1
r radius, m
ri rate of reaction for ith reaction, kmol kg cat1 h1
R gas constant, kJ kmol1 K1
Ri inner radius of spherical reactor, m
Ro outer radius of spherical reactor, m
sa specific surface area of catalyst pellet, m2 kg1
t time, h
T temperature of gas phase, KTref reference temperature, KTR reference temperature, Kur radial velocity, m s
1
x variable represent length of reactor, m
yN jacobi polynomial of degree N, e
yi mole fraction for ith component in gas phase, e
yis mole fraction for ith component on solid phase, e
vc critical volume, cm3 kmol1
y0N first derivative of jacobi Equation, ey00N second derivative of jacobi Equation, ea characteristic parameter of Jacobin equation, e
b characteristic parameter of Jacobin equation, e
g coefficient of equation (Ae1), e
3 void fraction of catalyst bed, e
m viscosity of gas phase, kg m1 s1
vij stoichiometric coefficient of component i in
reaction j, e
r density of gas phase, kg m3
rB reactor bulk density, kg m3
s tensile stress, Nm2
fs sphericity, e
DH heat of reaction, kJ kmol1
a aromatic, e
cal calculated, e
h hydrogen, ei numerator for reaction, e
j numerator for component, e
naphtha reforming process on Aspen Plus platform. Chin J
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 5 ( 2 0 1 0 ) 1 2 7 8 4e1 2 7 9 9 12799Chem Eng 2006;14(5):584e91.[7] Smith RB. Kinetic analysis of naphtha reforming with
platinum catalyst. Chem Eng Prog 1959;55(6):76e80.[8] Weifeng H, Hongye S, Yongyou H, Jian C. Lumped kinetics
model and its on-line application to commercial catalyticnaphtha reforming process. J Chem Ind Eng 2006;57(7).
[9] Boyas RS, Froment GF. Fundamental kinetic modeling ofcatalytic reformer. Ind Eng Chem Res 2009;48:1107e19.
[10] Stijepovic MZ, Ostojic AV, Milenkovic I, Linke P.Development of a kinetic model for catalytic reforming ofnaphtha and parameter estimation using industrial plantdata. Energy Fuels 2009;23:979e83.
[11] Ramage MP, Graziani KP, Krambeck FJ. 6 Development ofMobils kinetic reforming model. Chem Eng Sci 1980;35:41e8.
[12] Ramage MP, Graziani KR, Schipper PH, Krambeck FJ, Choi BC.A review of Mobils industrial process modeling philosophy.Adv Chem Eng 1987;13:193e266.
[13] Krane HG, Groh AB, Schuhnan BL, Sinfeh JH. Reactions incatalytic reforming of naphthas, Paper presented in FifthWorld Petroleum Congress; 1960.
[14] Kmak WS. A kinetic simulation model of the powerformmgprocess. AIChE Natl Meet; 1972.
[15] Marin GB, Froment GF, Lerou JJ, De Backer W. Simulation ofa catalytic naphtha reforming unit. W Eur Fed Chem Engn naphthene, e
out outlet, e
p paraffin, e
ss steady state, e
T transpose, e
AF-SPBR axial-flow spherical packed-bed reactor, e
AF-TPBR axial-flow tubular packed-bed reactor, e
FBP final boiling pint, CIBP initial boiling pint, CLHSV liquid hourly space velocity, hr1
OF objective function, e
Pt platinum, e
RF-SPBR radial flow spherical packed-bed reactor, e
RF-TPBR radial flow tubular packed-bed reactor, e
Re rhenium, e
RON research octane number, e
Sph. spherical reactor, e
tub tubular reactor, e
TBP true boiling point, K
WHSV weight hourly space velocity, h1
r e f e r e n c e s
[1] Aitani AM. Catalytic naphtha reforming, Encyclopedia ofChemical Processing. 10.1081/E-ECHP-120039766; 2005.
[2] Antos GJ, Aitani AM. Catalytic naphtha reforming. 2nd ed.New York: Marcel Dekker Inc; 1995.
[3] Juarez JA, Macias EV. Kinetic modeling of naphtha catalyticreforming reactions. Energy Fuels 2000;14:1032e7.
[4] MostafazadehAKhosravanipour, RahimpourMR.Amembranecatalytic bed concept for naphtha reforming in the presence ofcatalyst deactivation. Chem Eng Process 2009;48:683e94.
[5] Hu Y, Xu W, Jian Chu HS. A dynamic model for naphthacatalytic reformers, International conference on controlapplications; 2004.
[6] Weifeng H, Hongye S, Yongyou H, Jian C. Modeling,simulation and optimization of a whole industrial catalytic1983;2(27):1e7.[16] Li J, Tan Y, Liao L. Modeling and optimization of a semi-regenerative catalytic naphtha reformer, conference oncontrol application; 2005.
[17] Taskar U, Riggs JB. Modeling and optimization ofa Semiregenerative catalytic naphtha reformer. AIChE J 1997;43(3):740e53.
[18] Juarez JA, Macias EV, Garcia LD, Arredondo EG. Modeling andsimulation of four catalytic reactors in series for naphthareforming. Energy Fuels 2001;15:887e93.
[19] Stijepovic MZ, Linke P, Kijevcanin M. Optimization approachfor continuous catalytic regenerative reformer process.Energy Fuels 2010;24:1908e16.
[20] Weifeng H, Hongye S, Shengjing M, Jian C. Multiobjectiveoptimization of the industrial naphtha catalytic reformingprocess. Chin J Chem Eng 2007;15(1):75e80.
[21] Rahimpour MR. Enhancement of hydrogen production ina novel fluidized-bed membrane reactor for naphthareforming. Int J Hydrogen Energy 2009;34:2235e51.
[22] Iranshahi D, Rahimpour MR, Asgari A. A novel dynamicradial-flow, spherical-bed reactor concept for naphthareforming in the presence of catalyst deactivation. Int JHydrogen Energy 2010;35:6261e75.
[23] Fogler HS. Elements of chemical reaction engineering.2nd ed. NJ: Prentice-Hall Englewood Cliffs; 1992.
[24] Zardi F, Bonvin D. Modeling, simulation and modelvalidation for an axial-radial ammonia synthesis reactor.Chem Eng Sci 1992;47(9e11):2523e8.
[25] Brumbaugh AK. Modified spherical reactor, U.S. Patent No.2,996,361; 1961.
[26] Streeter VL, Wylie EB, Bedford KW. Fluid mechanics. 9th ed.Boston: WCB McGraw-Hill, Inc; 1998.
[27] Rase HF. Chemical reactor design for process plants, vol. 2.John Wiley & Sons, Inc.; 1977.
[28] OperatingDataofcatalytic reformerunit,Domesticrefinery,2005.[29] Rahimpour MR, Ghader S, Baniadam M, Fathi Kalajahi J.
Incorporation of flexibility in the design of a methanolsynthesis loop in the presence of catalyst deactivation. ChemEng Technol 2003;26(6):672.
[30] Rahimpour MR, Abbasloo A, Sayyad Amin J. A novel radialflow, spherical-bed reactor concept for methanol synthesisin the presence of catalyst deactivation. Chem Eng Technol2008;31(11):1615e29.
[31] Rahimpour MR. Operability of an industrial catalytic naphthareformer in the presence of catalyst deactivation. Chem EngTechnol 2006;5:29.
[32] Balakotaiah V, Luae D. Effect of flow direction onconversion in isothermal radial flow fixed-bed reactors.AIChE J 1981;27(3):442.
[33] Hlavkek V, Kubicek M. Modeling of chemical reactors-XXV,cylindrical and spherical reactor with radial flow. Chem EngSci 1972;27:177.
[34] Shampine LF, Reichelt MW. The MATLAB ode suite. SIAM JSci Comput 1977;18(1):1e22.
[35] Pisyorius JT. Analysis improves catalytic reformertroubleshooting. Oil Gas J; 1985:146e51.
[36] Rice RG, Do D. Applied mathematics and modeling forchemical engineers. New York: John Wiley & Sons; 1995.
[37] Perry RH, Green DW, Maloney JO. Perrys chemical engineershandbook. 7th ed. McGraw-Hill; 1997.
[38] Thoenes Jr D, Kramers H. Mass transfer from spheres invarious regular packing to a flowing fluid. Chem Eng Sci1958;8:271.
[39] Wilke CR. Estimation of liquid diffusion coefficients. ChemEng Prog 1949;45(3):218e24.
[40] Reid RC, Sherwood TK, Prausnitz J. The properties of gasesand Liquids. 3rd ed. New York: McGraw-Hill; 1977.
[41] Smith JM. Chemical engineering kinetics. New York:
McGraw-Hill; 1980.
Modeling of an axial flow, spherical packed-bed reactor for naphtha reforming process in the presence of the catalyst deact ...IntroductionLiterature reviewReaction scheme and kineticsProcess descriptionConventional configurationSpherical reactor setup
Reactor modelingAxial- flow spherical packed-bed reactor model (AF-SPBR model)Conventional tubular reactor model (CR model)Pressure drop (Ergun equation)
Catalyst deactivation modelNumerical solutionModel validationModel validation with the presence of catalyst deactivationSteady state model validation
Results and discussionChanges of parameters along the spherical reactorsChanges of parameters as a function of timeEffect of operating conditions and a comparison between tubular and spherical reactors in this regardThe effect of flow scale up ratio (FR)Effect of operating pressureThe effect of feed flow rate scale up ratioThe effect of temperature on the products yields
ConclusionAcknowledgementOrthogonal Collocation methodJacobi polynomialsLagrange Interpolation Polynomials
Auxiliary CorrelationsGas phase viscosityGas phase Heat capacityMass transfer correlationsHeat transfer correlation
NomenclatureReferences
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