This document summarizes a study on dynamic modeling and simulation of catalytic naphtha reforming. The dynamic model developed includes reaction kinetics, heat exchanger models, and furnace models. Kinetic modeling of the fixed bed reactors connected in series forms the core of the simulation. Reaction rates are represented using Hougen-Watson Langmuir-Hinshelwood expressions. Simulation results using MATLAB show fair agreement with plant data. The model can capture major dynamics in the reforming process system.

1. International Journal of Chemical Engineering and Applications, Vol. 1, No. 2, August 2010
ISSN: 2010-0221
Dynamic Modeling and Simulation of Catalytic
Naphtha Reforming
H.M.Arani1, S.Shokri2, M.Shirvani3
surface.
Abstract—In this paper, according to the recent progresses in More recently Jorge [5] presented a twenty-four lumps
naphtha reforming technology, dynamic modeling of catalytic model with 71 reactions and Taskar [6] proposed a more
naphtha reforming process is studied. The dynamic model is detailed thirty-five lumps model used for the optimization of
composed of the reforming reaction model, the heat exchanger
model, furnace model, which together, are capable to capture
semi-regenerative naphtha catalytic reformers. Generally
the major dynamics that occur in this process system. Kinetic speaking, detailed models are theoretically sound but quite
modeling of the reactions of the fixed bed reactors connected in complicated, consequently difficult for application because
series form the most significant part of the overall simulation of very complex lumping scheme and parameter estimation to
effort. MATLAB software in SIMULINK mode is used for maintain a good balance between kinetics, simplicity and
dynamic simulation. Hougen-Watson Langmuir-Hinshelwood applicability of the model [7].
type reaction rate expressions are used to represent rate of each
reaction.The results show models are in fair agreement with the
On the other hand, dynamic modeling was performed by
actual operating data. Yongyou et al. [15] by a 17 lumps kinetic model and solution
was performed after linearization. Actually, very limited
Index Terms—Catalytic reforming, Dynamic modeling, attempt on dynamic simulation of this process have been
Simulation, Naphtha appeared in the literature. A modeling and dynamic
simulation on the catalytic reforming process was carried out
by Ansari [16] using Smith's kinetic scheme.
I. INTRODUCTION
A. Process Description
Catalytic naphtha reforming is an important process for
producing high octane gasoline, aromatic feedstock and Catalytic naphtha reforming contains three reactors in
hydrogen in petroleum-refining and petrochemical series, as shown in Fig. 1. It is generally carried out in
industries. three/four fixed or moving bed reformers. The catalyst used
Advanced process control and process optimization in reformer is commonly a bifunctional bimetallic catalyst
strategies are important to be considered in catalytic such as Pt-Re/Al2O3, providing the metal function and the
reforming of naphtha due to its impacts on refineries profit. acid function. The product stream from the first reactor after
These are achieved mostly via a reliable mathematical preheating enters the second reactor and similarly the product
dynamic model. stream from the second reactor after preheating enters the
The catalytic reforming process came into operation in third one. Thus, the reactor feeds are raised to the proper
refineries in the late 1940s. The reforming of naphtha feed temperature by heaters located before the reactors, since the
stocks over platinum catalysts was pioneered by Universal reactions are endothermic. The product stream from the final
Oil Products (UOP), with the plat forming process introduced reactor enters a separator wherein hydrogen rich gas stream is
in 1947. separated from the products which is then recycled back and
Concerning the kinetic modeling of the naphtha processes mixed with the first reactor fresh feed. Reactors are of
Smith [1] firstly proposed a four lumps model by considering different sizes, with the smallest one located in the first stage
naphtha as being composed of naphthenes, paraffins, and the largest one in the last. Temperature profile of the
aromatics and light hydrocarbons (<C5), lumps with average reactors is shown in Fig. 2.
carbon number properties in 1959. However, it is not much
precise because of its limited lumps. Kmak [2] developed a
detailed model (Exxon model) including twenty-two lumps,
which was refined by Froment [3] who developed a more
detailed twenty-eight lumps model with 81 reactions.
Ramage [4] developed the Mobile thirteen lumps model that
considered the adsorption of chemical lumps on the catalyst
1,2
Research Institute of Petroleum Industry (RIPI), West Blvd. Azadi
Sport Complex, Tehran, Iran
3
Assistant Professor, School of Chem. Eng., Iran Univ. Sci. Tehran., Iran
Corresponding author: Tel.:+982148252503; fax: +982144739713 Figure 1. Process flow scheme of the catalytic naphtha reformer
E-mail address: Shokris@ripi.ir
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2. International Journal of Chemical Engineering and Applications, Vol. 1, No. 2, August 2010
ISSN: 2010-0221
Where, Pi in the above equations is the partial pressure of the
components and T is the temperature. As done by Hu et al.
(2003) [9] and Taskar (1996) [6], all constants of adsorption
terms were obtained by studying the reforming of C7
hydrocarbons. Thermodynamics of reactions are considered
in another work [10].
B. Reactors Dynamic Model
Figure 2.Temperature distribution in reactors length
A dynamic mathematical model with the kinetics
described above is developed by assembling the mass and
energy balance on the system of reforming reactions. The
II. DYNAMIC MODEL
mass balance provides the variation of the concentrations of
There are a number of different methods for modeling the the components along the reactors, and the energy balance
catalytic reforming process, and the main idea behind all of gives the variation of temperature. Mass and energy balances
them is to determine the operating conditions of the for each reformer are both nonlinear partial differential
reforming unit and to predict the yield of reformate and the equations in space and time. By taking component material
temperature profile accurately. balances as well as energy balanc on a differential element
A model must predict the behavior not only within the “dw” of catalyst bed the following system of differential
reactor, but in the auxiliary areas of the unit as well. It should equations can be obtained.
also consider the complex nature of the process and the Mass balance equations for an element of catalyst weight in
reactions which take place during the process of reforming. a plug flow reactor (proved in appendix A) are:
A. Reaction Kinetic Model
Reactions of catalytic naphtha reforming are elementary dFi nr ε d ( ci )
− + ∑ γ i , j rj =
and Hougen-Watson Langmuir- Hinshelwood type of dw j =1 ρ b dt
reaction rate expressions are used to describe the rate of each (1)
reaction.
Rate expressions of this type explicitly account for the Where:
interaction of chemical species with catalyst and contain ci Fi
yi = nc
= nc
(2)
denominators in which characteristic terms of adsorption of
reacting species are presented. The reaction rate coefficients ∑c
i =1
i ∑F
i =1
i
obey the Arrhenius law. All reaction rate equations are
shown in Table 1. m
Ft = (3)
M av
TABLE 1: REACTION RATE EQUATIONS
nc
M av = ∑ yi M i (4)
i =1
Fi = yi Ft (5)
The energy balance equation for the reactor shown in
Fig. 1 can be written (proved in appendix B) as:
nc nc
dT nr
− ( ∑ Fi C pi ) − ∑ rj ( ∑ H iγ i , j )
dT i =1 dw j =1 i =1 (6)
=
dt ε nc
( C pcata + ∑ ci C pi )
ρb i =1
Where, ni is the number of moles of ith lump for element
with dw of catalyst weight.
Where,
In the above table, adsorption terms for the metal function T
(θ), and for the acid function (Γ), are defined as follows (Van. H i = H 0 + ∫ C pi dT (7)
Trimpont, Marin and Froment, 1988 ) T0
In Hu et al. [9] catalyst heat capacity in the denominator of
energy equation was ignored, while this has great influence
on dynamic response of reactors.
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3. International Journal of Chemical Engineering and Applications, Vol. 1, No. 2, August 2010
ISSN: 2010-0221
C. Furnace ِ Model: Assuming perfect mixing results in achieving a lumped
Simple model of fired heater furnaces are used here. parameter model for the heat exchanger, as bellow:
In the mathematical model of this system the following
assumptions are used: d (C p , cold M cold Tcold , o )
1) Outlet gas temperature from the furnace is equal to tube dt (12)
wall temperature = Fcold ( H cold ,i − H cold , o ) − q
2) The temperature of the tube wall is equivalent over the
length of tube d (C p , hot M hotThot , o )
3) Variation of gas temperature inside tube is linear (13)
dt
We consider the tubes for heat transfer according to fig.3
= Fhot ( H hot ,i − H hot , o ) − q
The heat transferred q is:
(14)
q = F U A Δ Tm
Where, ΔTm is logarithm of mean temperature difference.
(Thot ,i − Tcold ,o ) − (Thot ,o − Tcold ,i ) (15)
ΔTm =
Figure 3. Furnace tube.
Thot ,i − Tcold ,o
Unsteady state energy balance with the considered ln( )
assumptions is as: Thot ,o − Tcold ,i
d (mwC p wTw + m f C p f T f , m )
E. Octane Number:
dt (8)
Octane number of the product from naphtha reforming unit
.
= q − (T f , out − T f , in )C p f m f can be expressed by concentrations as follows [14]:
n
(16)
Where, RON = b W ∑ r r
(T f , in + T f , out ) r =1
T f ,m = (9) Where, br are coefficients and Wr are weight concentrations.
2 TABLE 2: GROUP DEFINITION AND REGRESSION COEFFICIENTS OF LINEAR
Supposing linear variation of gas temperature, tube exit RON MODEL DEVELOPED BY WALSH AND
temperature is equal to Tf,out and Tf,m. Substituting equation (9) COWORKERS.
into (8) results in:
•
m f C p f d (T f ,in )
d (T f ,out ) q − (T f ,out − T f ,in )C p f m f − (10)
= 2 dt
dt mf Cp f
(mwC p w + )
2
In the above equations q is the amount of heat absorbed
by tubes. If the amount of heat generated by fuel is denoted
by Q and the efficiency of the furnace by η, then:
q =η Q (11)
D. Heat Exchanger Model:
Low order lumped parameter model of heat exchangers
were used. Mathematical modeling plays an important role
not only in designing and optimizing chemical engineering
processes but also in studying the dynamic characteristics
and controllability of existing equipment.
Fig. 4 depicts the thermal shell balance scheme on heat
exchanger for developing the required model.
III. SIMULATION
Level-1 M-files of S-function in MATLAB software are
used in this paper for simulating the above equations.
Distribution of nodes in the space of reactor plays an
important role in converging to the solution when solving the
equations. Nodes in beginning of reactor are very close
together according to Fig. 5.
Figure 4. Heat Exchanger.
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4. International Journal of Chemical Engineering and Applications, Vol. 1, No. 2, August 2010
ISSN: 2010-0221
714.5
Output temp. of first reactor
714
713.5
713
Figure 5. Node distribution in reactor length.
712.5
0 2000 4000 6000 8000 10000 12000
time (sec)
Derivative terms in the right hand side of partial Figure 7. Comparison of plant data with simulated model for 3 o C
differential equations are fitted by second order polynomial. temperature rise in reactor 1.
744.7
y = cx 2 + bx + a (17)
744.6
Output temp. of second reactor
744.5
Slope is calculated from the equation: 744.4
744.3
dy (18)
= 2cx + b 744.2
dx
744.1
Constants b and c can be calculated using the values of 744
three consecutive nodes. 743.9
0 2000 4000 6000 8000 10000 12000
Fig. 6 shows a flow diagram of the system simulated via time (sec)
MATLAB SIMULINK. Figure 8. Comparison of plant data with simulated model for 3 o C
temperature rise in reactor 2.
763.8
763.7
Output temp. of third reactor
763.6
763.5
763.4
763.3
763.2
763.1
Figure 6. Dynamic model and simulation of model by MATLAB software. 763
0 2000 4000 6000 8000 10000 12000
time (sec)
Figure 9. Comparison of plant data with simulated model for 3 o C
In the SIMULINK mode all variables can be plotted versus temperature rise in reactor 3.
time. The Solver type used in simulation is ode23tb with SATISFACTORY FITTING between PLANT AND MODEL IS
variable steps. DETECTED FROM THE FIGURES.
IV. RESULTS AND DISCUSSION
Results of simulated model are compared with V. CONCLUSION
experimental data obtained from the operation data sheets of In this paper, simulation of the dynamic model of the
a refinery plant in Iran and are shown in Fig. 7. In order to catalytic naphtha reformer process by MATLAB software is
validate the dynamic model, output temperatures of the presented. The kinetic parameters of model are based on the
reactors for input temperatures of three degrees centigrade steady state condition and are obtained from a commercial
are compared with the data of a refinery in Iran. Plant data are plant data furnished by a domestic petroleum refinery. This
collected at every 600 seconds. The results of simulation and dynamic model is in form of partial deferential equations.
comparison are shown in figures 7, 8 and 9. The nonlinear model of the system was solved numerically
by MATLAB software.
The simulation results reveals of satisfactory fitness
between data and the model.
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5. International Journal of Chemical Engineering and Applications, Vol. 1, No. 2, August 2010
ISSN: 2010-0221
NOMENCLATURE nc
d (∑ Fi H i ) nc
dH i
− i =1
dw = −(∑ Fi )dw (24)
Ac Catalyst bed area dw i =1 dw
ci (kmol / m3 ) Particle i mole concentration nc
dFi
Catalyst diameter
− (∑ H i )dw
d p( m ) i =1 dw
E Aj Activation energy
G( kg / m 2 .s ) Total mass flux Internal energy is related to enthalpy and by expansion of
ε Porosity of catalyst bed
the right hand side of equation (20) we have:
nc
μ( pa.s ) Viscosity d ( Ecata + ∑ ni ( H i − PVi ))
dEsys
ri (kmol / kg cat.s) Reaction Rate = i =1
dt dt
R Gas constant dEcata nc
dH i
= dw + ∑ ni
ρ s ( kg / m 3 ) Density of catalyst particle dt i =1 dt (25)
nc
ρ f ( kg / m )3 dn d ( PV )
Fluid Density + ∑ Hi i −
i =1 dt dt
Ω( m2 ) Catalyst bed Area
=
dEcata nc
dw + ∑ ni
dH i
dt i =1 dt
Mav (kg / kmol) Average molecular weight
nc
εdw dci d ( PV )
+ ∑ Hi ( ) −
i =1 ρ b dt dt
APPENDIX A
Where V is the volume of catalyst element upon which the
Mass balance equation for element of catalyst weight in a
balance is performed.
plug flow reactor is:
ε
V = dw (26)
nr ρb
Fi.w − Fi , w + dw + ∑ γ i , j rj dw ni is the number of i'th lump mole in the element with dw
j =1
(19) of catalyst weight.
d (ni ) d (ci ) ε By equations (19) and (23) the following equation is
= = dw
dt dt ρb obtained:
dE sys dE cata nc
dH i
dt
=
dt
dw + ∑n i
dt
+
(27)
In the above equation ni is as bellow: i =1
nc
dFi nr
d (P) ε
ε ∑H i (− + ∑γ i, j jr ) dw −
dt ρ b
dw
ni = ci dw (20) i =1 dw j =1
ρb By equation (7), (20), (23), (25) and (27), and by ignoring
And in final step the following equation is attained: pressure effects, we reach to the following equation:
nc
dT dT ε nc
dT
dFi nr ε d (ci ) − (∑ Fi C pi ) = C pcata + ∑c C
− + ∑ γ i , j rj = (21) dw dt ρ b
i pi
dt (28)
ρb dt
i =1 i =1
dw j =1 nr nc
+ ∑ r j (∑ H i γ i , j )
j =1 i =1
APPENDIX B
Energy balance equation for an element of catalyst weight And the resulted final equation is:
in a plug flow reactor is: nc nc
dT nr
− ( ∑ Fi C pi ) − ∑ rj ( ∑ H iγ i , j )
dT i =1 dw j =1 i =1 (29)
nc nc
dEsys =
∑ FH − ∑ Fi H i ε nc
= dt
i =1
i i
w i =1 w + dw
dt
(22) ( C pcata +
ρb
∑c C
i =1
i pi )
Differential form of the above equation is in the form:
nc REFERENCES
d (∑ Fi H i ) [1] Smith, R.B. (1959). Kinetic analysis of naphtha reforming
dEsys
− i =1
dw = (23) withplatinum catalyst. Chem. Eng. Pm~ e s s5,5 . 6,76.
dw dt [2] Kmak, W.S., Stuckey, A.N. (1973). Powerforming process studies with
a kinetic simulation model. AlChE National Meetmg, New Orleans,
The following equation is attained by expansion of the left March, PaperNo.56a.
hand side of the above equation: [3] Froment, GF.(IY87). Thc Kinetic of Complex Catalytic Reactions.
Chem. Eng. Sci., 42,5, 1073.
163

6. International Journal of Chemical Engineering and Applications, Vol. 1, No. 2, August 2010
ISSN: 2010-0221
[4] Ramagc, M.P., Graiani, K.R.,K rambeck, F.l.(1980). Developmcnt of
Mobil's kinetic reforming model. Chem. Eng. Sci., 35, I, 41
[5] lorge Ancheyta~luarezE, duardo Villafuene-Macias. (2000). Kinetic
Modeling of Naphtha Catalytic Reforming Reactions. Energy & Fuels,
14, 5, 1032.
[6] Taskar, U,, Riggs, J.B. (1997). Modeling and optimization of
asemiregenerative catalytic naphtharefarmer. AIChEf., 43, 3, 740.
[7] Hu. Y., Su, H., Chu, 1. (2003). Modeling. Simulation andOptimization
of Commercial Naphtha Catalytic Reforming Process. Pmceedinxs
"/the 42"* IEEE Cofifwmce on Decaion and Coniml, 6206-6211,Dec.
9~12,Hawuii,USA.
[8] Rahimpour, M.R., Esmaili, S., Bagheri, GN.A., “Kinetic and
deactivation model for industrial catalytic naphtha reforming”, Iran. J.
Sci. Tech., Trans. B: Tech., 27, 279- 290(2003).
[9] Hu, Y.Y., Su, H.Y., Chu, J., “The research summarize of catalytic
reforming unit simulation”, Contr. Instrum. Chem. Id.2,9 (2),
19-23(2002). (In Chinese)
[10] H. M. Arani, M. Shirvani2, K. Safdarian and E. Dorostkar," Lumping
procedure for a kinetic model of catalytic naphtha reforming" Braz. J.
Chem. Eng. vol.26 no.4 Oct./Dec. 2009
[11] HOU Weifen, SU Hongye, H, U Yongyou, CHU Jian, Zhejiang
University, "Modeling, Simulation and Optimization of a Whole
Industrial Catalytic Naphtha Reforming Process on Aspen Plus
Platform", Chinese J. Chem. Eng., 14(5) 584-591 (2006).
[12] M. R. Rahimpour, "Operability of an Industrial Catalytic Naphtha
Reformer in the Presence of Catalyst Deactivation",Chem. Eng.
Technol., 29, No. 5,(2006).
[13] Yongyou Hu, Weihua Xu, Hongye Su, Jian Chu, Zhejiang
university,"Modeling, Simulation and Optimization of Commercial
Naphtha Catalytic Reforming Process", IEEE, (2004).
[14] George J. fintos, abdullah M. aitan,"Catalytic naphtha reforming,
second edition, revised an expanded", MARCELD EKKER, INC,
(2004).
[15] Yongyou Hu, Weihua Xu, Hongye Su, Jian Chu, Zhejiang university, "
A Dynamic Model for Naphtha Catalytic Reformers", IEEE, Taiwan,
September 2-4,2004
[16] R.M. Ansari, M.O. Tade, "Constrained nonlinear multivariable control
of a catalytic reforming process", Control Engineering Practice 6 (1998)
695-706.
[17] Anderson, P.C.; Sharkey, J.M.; Walsh, R.P. J. Inst. Petr. 1972, 58 (560),
83.
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