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Reactor modeling and simulation of moving-bed catalytic reforming process
Chemical Engineering Journal 176–177 (2011) 134–143
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Reactor modeling and simulation of moving-bed catalytic reforming process Maria S. Gyngazova ∗, Anatoliy V. Kravtsov, Emilia D. Ivanchina, Mikhail V. Korolenko, Nikita V. Chekantsev National Research Tomsk Polytechnic University, pr. Lenina 30, Tomsk 634050, Russia
a r t i c l e
i n f o
Article history: Received 20 December 2010 Received in revised form 25 August 2011 Accepted 16 September 2011 Keywords: Catalytic naphtha reforming Mathematical modeling Moving-bed reactor Simulation
a b s t r a c t Catalytic reforming of naphtha is one of the most important processes for high octane gasoline manufacture and aromatic hydrocarbons production. Mathematical modeling method can be used for optimization and prediction of operating parameters (octane number, reactors outlet temperature and yield) of the reforming process. In this paper the new approach for mathematical modeling of a continuous catalytic regenerative (CCR) reforming process is proposed. The approach is based on components aggregation into pseudo components according to their reactivity; creation and application of pseudo components reaction scheme; finding the dependence of the reactivity of the hydrocarbons from the same homological group on their octane numbers. The novelty of the presented mathematical model of a moving-bed catalytic reforming reactor is the account of the catalyst work instability, coking, activity and circulating factor of the catalyst. The reformate composition calculated with the proposed model agrees very well with experimental information. © 2011 Elsevier B.V. All rights reserved.
1. Introduction
presents a region-wise distribution of catalytic reforming capacity by process type [1]. The semi-regenerative scheme dominates the reforming capacity at about 57% of the total capacity followed by continuous regenerative at 27% [2]. More than 95% of the new catalytic reformers are designed with continuous catalyst regeneration (CCR). Moreover many units that were originally designed as SR have been revamped to CCR reforming units (Reformer Unit of Omsk Refinery, Russia, can be mentioned as an example of such a reconstruction). Although CCR plants have become increasingly important most published works regarding modeling and optimization of naphtha catalytic reforming process address SR processes [3–23]. Accurate mathematical description of CCR reforming process is of great importance for the reliable design and simulation of the reactors. Relatively few CCR reforming process models have been suggested in the literature pertaining to this field [24–27].
Catalytic reforming of naphtha is one of the most important processes for high octane gasoline manufacture and aromatic hydrocarbons production. The naphtha reformer is used to upgrade low octane heavy naphtha that is unsuitable for motor gasoline. Industrial catalysts used in catalytic reforming units consist of ␥Al2 O3 support, some metals such as Pt, Re, Ge, Ir, Sn and additive such as chlorine to increase isomerization reactions. There are several types of reactions taking place during the reforming process: dehydrogenation, isomerization, cyclization, aromatization, hydrocracking, hydrogenolisis and coke formation. Some of these reactions such as isomerization, cyclization, aromatization are desirable because of increasing the octane number. Other reactions causing the catalyst deactivation (such as coke formation and coke deposition) are undesirable. According to the strategy of catalyst regeneration the existing process technologies of catalytic naphtha reforming can be divided into semi-regenerative (SR), cyclic regenerative (CR) and continuous catalyst regenerative (CCR). Table 1
1.1. CCR reforming process description
Abbreviations: Ar, aromatic hydrocarbons; CCR reforming process, continuous catalytic regenerative reforming process; CR reforming process, cyclic regenerative reforming process; FBP, final boiling point, ◦ C; IBP, initial boiling point, ◦ C; N, cycloalkanes; N5 , cyclopentanes; N6 , cyclohexanes; Pn , normal paraffins; Pi , isoparaffins; RON, research octane number; SR reforming process, semi-regenerative reforming process; TBP, true boiling point, ◦ C. ∗ Corresponding author. Tel.: +7 9069551067; fax: +7 3822564320. E-mail addresses: [email protected], [email protected] (M.S. Gyngazova).
Since its introduction in the early 1970s, the CCR process has gained wide acceptance in refining and petrochemical industries worldwide. The process uses stacked radial-flow reactors and a CCR section to maintain a steady-state reforming operation at optimal process conditions: fresh catalyst performance, low reactor pressure and minimum recycled gas circulation [2]. A schematic flow diagram of CCR reforming process is shown in Fig. 1. The naphtha used as a catalytic reformer feedstock is combined with a recycle gas stream containing 60–90% (by mol) hydrogen.
1385-8947/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cej.2011.09.128
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Table 1 Worldwide distribution of naphtha reforming by capacity and process type.a Region
No. of refineries
Reforming as % crude capacity
Semiregenerative
Continuous
Other
N. America W. Europe Asia-Pacific E. Europe Middle East S. America Africa
159 104 161 93 45 67 46
20.5 14.6 9.3 14.9 10.2 6.5 14.8
46.4 54.0 42.4 86.4 63.0 80.4 81.9
26.8 31.5 44.8 11.0 23.1 9.3 0.0
26.8 14.5 12.8 2.6 13.9 10.3 18.1
Total
675
13.8
56.8
26.9
16.3
a
Share of reforming capacity by process type (%)
From Ref. [1].
The total reactor charge is heated and passes through the catalytic reformers. Catalyst flows vertically by gravity down the reactors, while the feed flows radially across the annular catalyst bed. Catalytic reforming is an endothermic process, hence an inter-stage furnace is used between each reactor in order to reheat the charge to the reaction temperature. The catalyst is continuously withdrawn from the last reactor and transferred to the regenerator. The withdrawn catalyst flows down through the regenerator where the accumulated carbon is burned off. Regenerated catalyst is purged and then lifted in hydrogen to the top of the reactor stack, maintaining nearly fresh catalyst quality [2]. The CCR process has enabled ultra-low pressure operations at 0.35 MPa and produced product octane levels as high as 108.
1.2. Catalytic reforming models Catalytic reforming has been studied extensively in order to understand the catalytic chemistry of the process. The first significant attempt at delumping naphtha into different constituents was made by Smith [3]. He considered naphtha to consist of three basic components: paraffins, naphthenes and aromatics. This model is still used due to its simplicity. The model derived by Krane [7] contained a reaction network of 20 pseudo components and recognized hydrocarbons from 6 to 10 carbon atoms. Kmak [16] proposed the first model incorporating the catalytic nature of the reactions by deriving a reaction scheme with Hougen–Watson–Langmuir–Hinshelwood-type kinetics. Rate equations derived from this type explicitly account for the interaction of chemical species with the catalyst [28]. The Kmak’s model was later refined by Marin and his colleagues [19–22], who presented the reaction network for the whole naphtha. Other models were proposed by Barreto et al. [5], Ansari and Tade [6], Aguilar
and Anchyeta [11,12], Burnett [13], Henningsen and BundgaardNielson [15] and other researchers. A process with continuous catalyst regeneration was modeled by Lee et al. [24] and good agreement with plant data was reported. Hou et al. [26] simulated a whole industrial CCR reforming process on Aspen Plus platform. Stijepovic et al. [25] proposed a model for a moving-bed reactor of CCR reforming unit. Lid and Skogestad [27] determined the optimal operating conditions for a CCR catalytic naphtha reformer utilizing the Smith’s model. But the mentioned above CCR reforming process models have some considerable drawbacks. Thus, the authors of [26] do not include isomerization reactions in their model, though the octane numbers of isomers can differ significantly (up to 30 points). The works [26,27] do not take into account the catalyst deactivation throughout the catalyst bed due to coking and the subsequent decrease of catalyst activity in the desired reactions. The impact of catalyst circulating factor on the catalyst coking is not considered in [25–27] also. As seen, most previous works on this subject were related to packed bed reactors (PBRs). In the present paper we create a CCR reforming model that reflects the influence of raw material composition on the reformate composition, take into account the kinetics of coke formation and the influence of catalyst circulating factor on catalyst deactivation. Consideration of all these factors significantly improves the model adequacy.
2. Kinetics of the reforming process The naphtha used as a catalytic reforming feed-stock is a complex mixture consisting of several hundred hydrocarbons with carbon atoms ranging from five to twelve, and each of the components undergoes various reactions: dehydrogenation, isomerization, dehydrocyclization, hydrocracking, hydrogenolisis and
Fig. 1. Flowsheet of a continuous catalytic reforming process [2].
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Fig. 2. The example of differences in isomers research octane numbers (RON).
hydrodealkilation. Thus a detailed kinetic model considering all the components and reactions would be too complicated. To overcome this problem reactants in the mixture are classified in certain and limited groups called pseudo components. The number of selected pseudo components in the mixture is a determinating factor for model design. Obviously, the more the number of specified pseudo components are the higher the accuracy of the model will be, but at the same time this leads to more complicated mathematical formulation. There is a need to develop a universal mathematical model that could balance these contradictions and that could be used for different raw material compositions. Accurate kinetic equations are of great importance for the reliable design and simulation of the reactors. Here we formalized the reactions mechanism taking into account components reactivity, but without sensitivity loss to change of initial hydrocarbons raw material composition. To aggregate the components we combine hydrocarbons into pseudo components on the basis of affinity of their reactivity expressed for this process in magnitude of antiknock value. Components having not more than 7 carbon atoms are considered as individual hydrocarbons in the formalized scheme, because their reactivity and octane numbers differ a lot (Fig. 2). Hydrocarbons C8 –C12 are aggregated according to their homological groups. Unlike aggregation of the whole mixture according to homological groups, the basic characteristic of gasoline – octane number – is considered. For example, octane numbers of 2-methylpentane and 2,3-dimethylbutane differ in 30 points
although these hydrocarbons belong to one homological group (isoparaffin hydrocarbons C6 ). The scheme of reactions between pseudo-components accepted on such basis has been used at construction of mathematical model of catalytic reforming of hydrocarbons on Pt-containing catalysts. This has allowed foreseeing the consequences of raw material structure change. The researches executed on the basis of experimental data, received at the industrial unit, have allowed accepting the following formalized scheme of the mechanism of catalytic reforming process in moving-bed reactors (Fig. 3). According to the chemical reaction rate law elementary reaction rate at the set temperature is proportional to concentration of reacting substances in the degrees showing number of particles entering interaction: r = k · f (C)
(1)
f (C) = C1v1 · C2v2 · · ·Cnvn
(2)
where r is the reaction rate; k is the rate constant; Ci is initial components concentration and vi is the stoichiometric coefficient in gross-equation of chemical reaction. The given equation is true for elementary reactions. Complex reactions can have a fractional order.
Fig. 3. Formalized reaction scheme for naphtha reforming.
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Table 2 Estimated values of the rate constants at T = 520 ◦ C and p = 0.7 MPa for Pt–Sn reforming catalyst, s−1 . No.
Chemical reaction
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Hydrocracking of Pn Isomerization Pn → Pi Isomerization Pi → Pn Dehydrocyclization of Pn to N6 Hydrocracking of Pi Dehydrocyclization of Pi to N6 Hydrogenation of N5 to Pi Isomerization N5 → N6 Dehydrogenation of N6 to Ar Hydrogenation of Ar to N6 Dehydrocyclization of Pn to N5 Dehydrocyclization of Pi to N5 Isomerization N6 → N5 Coking
Number of carbon atoms in the molecule C4
C5
C6
C7
C8
C9
C10
C11
C12
0.041 0.065 0.005 0.000 0.012 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.00000
0.050 0.107 0.009 0.000 0.036 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.00000
0.060 0.128 0.016 0.001 0.046 0.000 0.176 0.275 0.157 0.085 0.006 0.002 0.056 0.00017
0.089 0.218 0.018 0.003 0.059 0.001 0.261 0.707 0.182 0.124 0.009 0.002 0.074 0.00021
0.122 0.263 0.021 0.005 0.073 0.004 0.449 1.314 0.181 0.147 0.010 0.003 0.075 0.00029
0.155 0.261 0.024 0.006 0.099 0.004 0.444 1.569 0.174 0.152 0.010 0.004 0.081 0.00032
0.214 0.272 0.024 0.006 0.115 0.004 0.470 1.961 0.174 0.152 0.009 0.005 0.084 0.00034
0.338 0.261 0.025 0.012 0.138 0.004 0.496 2.222 0.174 0.152 0.009 0.007 0.090 0.00038
0.468 0.258 0.024 0.006 0.144 0.004 0.514 2.222 0.174 0.152 0.009 0.008 0.090 0.00041
Where Pn is for normal paraffins, Pi is for isoparaffins, N6 is for cyclohexanes, N5 is for cyclopentanes, Ar is for aromatic hydrocarbons.
Having such level of mechanism specification the change of concentration of i – component in reversible j – reaction of the first order can be written as a system of the material balance equations: dCi = dt
lj kj (x)Ci (x)CH
2
(3)
j
where j = 1, . . ., m is a number of chemical reaction; Ci (x) and kj (x) are respectively distributions of hydrocarbons concentration and rate constants on number of carbon atoms in a molecule x; lj is a reaction order on hydrogen; t is space time. For the naphthenes dehydrogenation and aromatics hydrogenation reactions lj = 3, for the dehydrocyclization, hydrocracking and hydrodealkylation reactions lj = 1, for the isomerization reactions lj = 0. All the reactions are listed in Table 2. Practically kinetic parameters can be obtained experimentally measuring the reagents concentration change with time. From the kinetic curves it is possible to estimate the rate constants. The Arrhenius plot let us determine pre-exponential factors and activation energies. However the same parameters estimation can be done mathematically. The procedure of parameters estimation is carried out by minimization of the sum of the squares of the deviations between the plant and the calculated values of the key variables such as the composition of effluent from the last reactor and the outlet temperatures of the four reactors. In this paper kinetic parameters were defined mathematically. Having the reactants concentrations as the input data, the reactions rates as the responses and an initial guess of unknown parameters the least square parameters estimate was found. The optimization method based on the determination of the fixed points of the rate constants admitted region was applied. According to the Scarf’s theorem [29] a completely-labelled simplex (all vertices have different labels) is to be found. The fixed point is situated inside the simplex. The results of the rate constants estimation are given in Table 2. As seen from Table 2, for Pt–Sn catalyst rate constants of isomerization of N5 to N6 with the subsequent dehydrogenation of cycloalkanes to aromatic hydrocarbons have the largest values. Also the process of normal paraffins isomerization goes with a high rate. Binding energy decreases with the increase of hydrocarbons molecular weight and the rate constants increase in proportion to the hydrocarbon number in the homologous series. Hydrocracking rate constants of lighter hydrocarbons are approximately the same for normal paraffins and isoparaffins. Hydrocracking rate constants of heavy hydrocarbons differ a lot, and the rate constants of normal paraffins hydrocracking have much higher values than that of isoparaffins. Rate constants of dehydrocyclization of Pn and Pi to N5 and N6 are practically the same.
3. Reactor model Each reactor consists of two perforated coaxial cylinders between which the catalyst moves slowly downwards under the gravity force (Fig. 4). The catalyst is progressively coked as it moves through the reactors. The catalyst passes through all the reactors and after leaving the last reactor it is sent to the continuous catalyst regeneration unit. The coked catalyst undergoes a sequence of steps involving controlled coke combustion, oxychlorination, and calcinations to restore catalyst activity and metal redispersion [25]. For describing the process in moving-bed reactor we consider the two-phase flow. The passive phase is the gas flow, the active phase is the gas in the pores of the solid catalyst particles. According to the calculation of Reynolds (Re = 4.5, laminar flow) and Peclet numbers (Pe = 702) we can assume that diffusion plays insignificant role in the process of mass transfer which occurs by means of convection. For the industrial CCR reforming process the reaction limited regime is observed (Thiele modulus ˚j < 1, internal effectiveness factor j = 0.9–1). For the mathematical description of hydrodynamic and heat model of catalytic reforming reactor some assumptions are accepted:
Fig. 4. Schematic representation of a radial moving-bed reactor.
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Fig. 5. Comparison of RON between actual data and simulation results.
• mass and heat transport occurs by means of convection; • adiabatic operation; • the formalized mechanism of hydrocarbons transformation (Fig. 3). The model of moving-bed catalytic reforming reactor, presented by a system of equations of material balance for components and the equation of heat balance is the following:
⎧ l ⎪ ⎪ ∂C ∂C 1 ∂C ⎪ i i i ⎪G· = −u · −ϕ· + · rj (l)aj (l)dl ⎪ ⎪ l ∂z ∂R ∂l ⎨
the heat capacity of mixture and catalyst respectively, J/(kg K); Qj is jth reaction heat, J/mol, Qj is assumed to be constant within each homological group (normal alkanes, isoalkanes, aromatic hydrocarbons, cyclopentanes, cyclohexanes); T is temperature, K; rj is jth reaction rate, mol/(m3 h). The parameter z is used in Eq. (4) instead of t because G is not a fixed value and changes in the range of 130–170 m3 /h. The term of equation ∂Ci /∂z shows the change of ith component concentration against the catalyst deactivation
0
l ⎪ ⎪ ⎪ 1 m · C m · G · ∂T = −u · m · C m · ∂T − ϕ · cat · C cat · ∂T + ⎪ Q · rj (l)aj (l)dl · ⎪ j p p p ⎪ l ∂z ∂R ∂l ⎩
(4)
0
The conditions are: at z = 0, Ci = Ci,0 ; T = Ten ; at l = 0, Ci = Ci,0 (at the reactor entrance); T = Ten ; at r = 0, Ci = Ci,0 ; T = Ten . where z is a volume of raw material processed from the moment when the fresh catalyst (new catalyst, no regenerations were done) was loaded, m3 ; G is a raw material flow rate, m3 /h; z = G·t (t is a time of catalyst work from the new catalyst load, h); Ci is a concentration of ith component, mol/m3 ; u is a flow rate, m/h; R is a radius of the catalyst layer, m; l is a catalyst layer length in the reactor, m; ϕ is a catalyst flow rate, m/h; r is an integral reactions rate for component i, mol/(m3 h); a(l) is a catalyst activity distribution through the catalyst layer length in the reactor with a moving bed; m , cat are the density of mixture and catalyst respectively, kg/m3 ; Cpm , Cpcat are
because of aging (it depends on the number of regenerations i.e., on the catalyst circulating factor). Components concentrations depend on u – the rate of flow motion along the catalyst bed radius (raw material is radially input). Components concentrations change also with a change of ϕ – the catalyst flow rate along the height of the reactor. This happens because the catalyst flow rate influences the coke concentration in different layers of the catalyst, and thus catalyst activity changes in a different manner along the reactor height because of the coking. The reactions rate rj for component i (according to the reactions mechanism – Fig. 3) depends on the catalyst motion coordinate l and the catalyst activity a. In the model the catalyst deactivation is considered. In movingbed reactors catalyst activity changes through the radius and height of catalyst layer and with time. In our formalized reaction scheme (Fig. 3) coke is one of the reactions components. The coke
Fig. 6. Comparison of reformate yield between actual data and simulation results.
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Fig. 7. Change in catalyst activity with time (simulation results).
concentration can be calculated according to the kinetics of coke formation (according to Fig. 3 and Eq. (4)). Coking rate constants for hydrocarbons with different numbers of carbon atoms are given in Table 2. The catalyst activity will decrease with the coke concentration increase. It was found that the catalyst activity depends on the catalyst circulating factor (hcir ) the following way: aj = A0 · e−˛j ·Ccoke /hcir
(5)
where Ccoke is a mass fraction of coke on the catalyst; a is a catalyst activity; hcir = u · m /(ϕ · cat ); A0 is a linear component determining the number of catalyst active centres; ˛ is a coefficient of catalyst poisoning – nonlinear component that determines different extent of angle and edge atoms deactivation due to coking. The rate of catalyst metal sites deactivation has considerably greater magnitude than the rate of catalyst acid sites deactivation. Calculations show that 3 ≤ ˛ ≤ 5.9 – for reactions on metal sites of catalyst; 0.3≤ ˛ ≤ 0.52 – for reactions on acid sites of catalyst. Dehydrogenation reaction takes place on the metal sites. The rate of catalyst deactivation in cycloalkanes dehydrogenation reactions has the largest values. Therefore coefficient of catalyst poisoning ˛ for this type of reactions is maximum. Hydrocracking reactions occur on the acid sites and the catalyst deactivation against this type of reactions is insignificant. For other reactions realized via bifunctional mechanism coefficient ˛ is between these limits. The values of experimentally defined A0 and ˛ for the main types of reactions are given in Table 3. Another important problem is the calculation of reformate octane number according to the catalysate composition obtained as a result of modeling. Octane number (ON) is one of the most important properties of gasoline and is a measure of its antiknock property. Octane blending is known to exhibit nonlinear interactions (both synergetic and antogonistic) among the various constituent hydrocarbon molecular classes (paraffins, olefins, aromatics, etc.) [30]. Early a mathematical model for gasoline octane number calculation was elaborated on the basis of experimental data [31,32]. The model is based on physicochemical nature of blending process and takes into account non-additivity of gasoline properties. Thus the blending octane number model taking into account the deviation from additivity is written as: ONmix =
m
(ONi · Ci ) + B
(6)
i=1
Table 3 The values of experimentally defined A0 and ˛ for the main types of reactions. Reactions
˛
A0
Cycloalkanes dehydrogenation Alkanes hydrocracking Alkanes isomerization Alkanes dehydrocyclization
5.7 0.3 0.4 0.8
59.77 3.14 3.69 21.84
1 Bi Bj Ci Cj 100 m−1 m
B=
(7)
i=1 j=2
D n i
Bi = ˛
(8)
Dmax
where ONmix denotes the gasoline octane number; ONi represents the pure-component octane number for each molecule i in the fuel; Ci is the concentration of hydrocarbons in the mixture; B is a total deviation of hydrocarbons octane number from additivity; Bi , Bj denote parameters showing the tendency of ith molecule to intermolecular interaction with jth molecule; Di is a dipole moment of molecule i, debye; Dmax is the maximum possible dipole moment of the hydrocarbons mixture, debye; ˛ and n denote the kinetic coefficients defining the intensity of intermolecular interactions from dipole moment D. All the octane numbers calculations at the present paper were done with the help of the model described above (Eq. (6)–(8)). 4. Results and discussion The example of calculation of CCR reforming process is given in Tables 5 and 6, Figs. 5 and 6. The experimental data were obtained from the industrial CCR reforming unit of Russian refinery. Table 4 Specifications of reactors, feed and product, operating conditions and catalyst properties. Parameter
Numerical value
Unit
Naphtha feed stock Catalyst mass flow rate Pressure Reactors inlet temperature Diameter and length of Reactor 1 Diameter and length of Reactor 2 Diameter and length of Reactor 3 Diameter and length of Reactor 4 Catalyst load Reactor 1 Reactor 2 Reactor 3 Reactor 4 Properties of the catalyst Particle diameter Pt Sn Reactor bulk density
160 745 0.7 520 2.20, 11.18 2.40, 10.50 2.70, 11.65 3.20, 13.45
m3 /h kg/h MPa ◦ C m m m m
8950 13,425 22,375 44,750
kg kg kg kg
1.6 0.29 0.29 560
mm wt. % wt. % kg/m3
Distillation fraction of naphtha feed and reformate TBP IBP 10% 50% 90% FBP
Naphtha feed [◦ C] 60.26 90.05 125.68 165.10 195.90
Reformate [◦ C] −0.50 68.73 138.26 182.01 241.05
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Fig. 8. Hydrocarbons concentration change throughout the catalyst bed (model calculation results). *The calculations were done for the same conditions as at the industrial unit: T = 520 ◦ C; p = 0.7 MPa; Pt–Sn/␥-Al2 O3 catalyst, hcir = 0.008 m3 /m3 .
Specifications of reactors, feed and product, operating conditions and catalyst properties are presented in Table 4. Comparing the values presented in Table 5, we can see, that reformate composition calculated on model coincides with experimental data from the industrial unit with the set accuracy (in our case the calculation error should not exceed an error of chromatographic analysis). The same can be said about the coke concentration calculated on the mathematical model (Table 6). Calculated values agree very well with the experimental data from the industrial unit. Table 5 Results of calculation of catalytic reforming process in moving-bed reactor with the mathematical model.a Group composition, % mas.
Calculation
Experiment
n-Alkanes i-Alkanes Naphthenes-5 Naphthenes-6 Aromatic hydrocarbons Catalysate octane number Product yield
6.78 14.19 0.57 0.78 77.67
6.84 14.35 0.34 0.23 77.16
While using CCR reforming mathematical model it is also possible to compare the different catalytic reforming units work efficiency and choose more suitable variant of process optimization for given raw material. The simulation results delivered by our model are compared to values from the industrial CCR plant (Figs. 5 and 6). The obtained simulation results of reformate octane number and product yield are in very good agreement with the actual data from the industrial unit. Also with the help of the model we calculated the catalyst integral activity change (Fig. 7). These simulation results practically coincide with the real situation on the plant. At the beginning of the time period under consideration the catalyst was incorrectly regenerated and lost its activity dramatically due to its structure changes. Than the catalyst was gradually replaced in the system and the integral catalyst activity increased up to some stationary value. So the model allows considering the real catalyst activity during the operation of the industrial unit.
102.5 89.2
a The calculations were done for the same conditions as the experiment at the industrial unit: T = 520 ◦ C; p = 0.7 MPa; Pt–Sn/␥-Al2 O3 catalyst; raw material composition was characterized by chromatographic analysis.
Table 6 Comparison between experimental and calculated concentrations of coke on the surface of Pt-Sn/␥-Al2 O3 catalyst at the reactor outlet.a Pt–Sn/␥-Al2 O3 catalyst
Sample 1 Sample 2
Coke, wt. % Experiment
Calculation
5.54 4.13
5.63 4.03
a The calculations were done for the same conditions as the experiment at the industrial unit: T = 520 ◦ C; p = 0.7 MPa; Pt–Sn/␥-Al2 O3 catalyst; coke concentration was characterized by thermogravimetric analysis.
Fig. 9. Coke distributions in axial and radial directions for the reactor system (model calculation results).
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Fig. 10. Catalyst activity distributions in axial and radial directions for the reactor system (model calculation results).
Mathematical modeling is a powerful tool for the analysis of a complex multicomponent catalytic process. Fig. 8 shows hydrocarbons concentration change throughout the catalyst bed (model calculation results). Hydrocarbons concentration is plotted as a function of dimensionless radial (radial distance/reactor radius) and axial (axial distance/reactor length) distances. At the entrance of the reaction mixture the temperature has its maximum value
Fig. 11. Temperature profiles in reactors (model calculation results).
and the rate of reactions and conversion is high. Along the axial direction the loss of catalyst activity due to coking causes the subsequent decrease in reaction rates. Figs. 9 and 10 illustrate distributions of the coke and the catalyst activity, respectively. As
Fig. 12. Coke accumulation on the catalyst with time for different values of catalyst circulating factor: hcir1 = 0.008 m3 /m3 , hcir2 = 0.010 m3 /m3 , hcir3 = 0.016 m3 /m3 (model calculation results).
Fig. 13. Coke content as a function of catalyst circulating factor (model calculation results).
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expected, the largest coke content and the minimal catalyst activity occur at the entrance of the reaction mixture into the reaction zone because of the intensive cycloalkanes dehydrogenation reactions. And cycloalcanes and aromatic hydrocarbons are supposed to be coke precursors. Along the reactor length (axial direction) the coke cumulation takes place. Fig. 11 presents temperature distribution through the reactors. As the naphtha reforming is predominantly endothermic the temperature decreases in the reactors. The largest temperature drop can be observed in the first reactor where the main reaction is the conversion of naphthenes to aromatics (this reaction is highly endothermic and requires a large amount of heat). In the last reactors isomerization, dehydrocyclization and hydrocracking reactions play an important role. Catalyst circulating factor is one of the important parameters that influence the coke content and catalyst activity. Fig. 12 illustrates coke distribution versus residence time for different values of catalyst circulating factor. Also coke content versus catalyst circulating factor is depicted in Fig. 13. As seen, the amount of coke on the catalyst decreases with the catalyst circulating factor increase. For higher numbers of catalyst circulating factor the catalyst flow rate has greater values, catalyst spends less time in the reactor. Less coke content on the catalyst causes higher catalyst activity that in turn lets reactions go with higher rates. The catalyst circulating factor values of 0.008–0.010 m3 /m3 are common for the industrial operation of CCR reformers.
Cpm Cpcat Di Dmax G hcir i j k lj l n ONmix ONi Pe Qj r R Re t T Ten u
vi 5. Conclusion This paper has introduced a new approach for mathematical modeling of multicomponent process of CCR reforming. The approach is based on: • components aggregation into pseudo components according to their reactivity; • creation and application of pseudo components reaction scheme; • finding the dependence of the reactivity of the hydrocarbons from the same homological group on their octane numbers. In this work we have presented a mathematical model for a moving-bed catalytic reforming reactor that takes into account the catalyst work instability, activity and circulating factor of the catalyst. The model allows monitoring the process and can help to find optimal operation regimes. The mathematical model allows solving successfully the problem of product quality and quantity rising in operating manufacture conditions and also improving technical and economical values of industrial process. Also, in this model the peculiarities of raw material composition as well as the technological peculiarities have been considered. Appendix A. Nomenclature
Parameter Description catalyst activity a A0 experimentally defined coefficient, a linear component determining the number of catalyst active centres B total deviation of hydrocarbons octane number from additivity parameters showing the tendency of ith molecule to Bi , Bj intermolecular interaction with jth molecule mass fraction of coke on the catalyst Ccoke Ci concentration of component i, mol/m3 Ci,0 inlet concentration of component i, mol/m3
x z
heat capacity of hydrocarbons mixture, J/(kg K) heat capacity of catalyst, J/(kg K) dipole moment of molecule i, debye maximum possible dipole moment of the hydrocarbons mixture, debye raw material flow rate, m3 /h catalyst circulating factor, m3 /m3 numerator numerator rate constant, h−1 reaction order on hydrogen length of reactor, m kinetic coefficient defining the intensity of intermolecular interactions from dipole moment D gasoline octane number pure-component octane number for each molecule i in the fuel of transport by convection Peclet number, Pe = rate ofrate transport by diffusion or dispertion jth reaction heat, J/mol reaction rate, mol/(m3 h) radius of the catalyst layer, m Reynolds number time, h temperature, K inlet temperature, K hydrocarbons flow rate, m/h stoichiometric coefficient in gross-equation of chemical reaction, numerator volume of raw material processed from the moment when the fresh catalyst (new catalyst, no regenerations were done) was loaded, m3 , z = G·t (t is a time of catalyst work from the new catalyst load, h)
Greek letters kinetic coefficient defining the intensity of intermolecular ˛ interactions from dipole moment D ˛j experimentally defined coefficient of catalyst poisoning – nonlinear component that determines different extent of angle and edge atoms deactivation due to coking internal effectiveness factor j m density of hydrocarbons mixture, kg/m3 cat density of catalyst, kg/m3 ϕ catalyst flow rate, m/h ˚j Thiele modulus References [1] D. Nakamura, Worldwide refining capacity creeps ahead in 2004, Oil Gas J. (Decemeber) (2004) 40. [2] A. Aitani, Catalytic naphtha reforming, in: Encyclopedia of Chemical Processing, 2006, pp. 397–406. [3] R.B. Smith, Kinetic analysis of naphtha reforming with platinum catalyst, Chem. Eng. Prog. 55 (6) (1959) 76–80. [4] D. Bommannan, R.D. Strivastava, D.N. Saraf, Modeling of catalytic naphtha reformers, Can. J. Chem. Eng. 67 (1989) 405–411. ˜ M.G. Gonzalez, Lat. Am. Appl. Res. 26 (1) (1996) 21–34. [5] G.F. Barreto, J.M. Vinas, [6] R.M. Ansari, M.O. Tade, Saudi Aramco J. Technol. Spring (1988) 13–18. [7] H.G. Krane, A.B. Groh, B.L. Shulman, J.H. Sinfelt, Reactions in Catalytic Reforming of Naphthas, World Petroleum Congress, 1960, pp. 39–53. [8] Y.M. Zhorov, Mathematical description of platforming for optimization of a process (I), Kinetika i Kataliz 6 (6) (1965) 1092–1098. [9] U. Taskar, J.B. Riggs, Modeling and optimization of a semiregenerative catalytic naphtha reformer, AIChE J. 3 (№43) (1997) 740–753. [10] Yu.V. Sharikov, P.A. Petrov, Universal model for catalytic reforming, Chem. Petrol. Eng. 43 (2007) 580–584. [11] R. Aguilar, J. Anchyeta, Oil Gas J. (July) (1994) 80–83. [12] R. Aguilar, J. Anchyeta, Oil Gas J. (January) (1994) 93–95. [13] R.L. Burnett, H.L. Steinmetz, E.M. Blue, E.M. Noble, Petrol Chem. Am. Chem. Soc., Detroit Meeting, April, 1965. [14] J.H. Jenkins, T.W. Stephens, Hydrocarbon Process. (November) (1980) 163–167.
M.S. Gyngazova et al. / Chemical Engineering Journal 176–177 (2011) 134–143 [15] J. Henningsen, M. Bundgaard-Nielson, Catalytic reforming, Br. Chem. Eng. 15 (11) (1970) 1433–1436. [16] W.S. Kmak, A Kinetic Simulation Model of the Power Forming Process AICHE Meeting, Houston, 1972. [17] M.P. Ramage, K.P. Graziani, F.J. Krambeck, Chem. Eng. Sci. 35 (1980) 41–48. [18] M.P. Ramage, K.R. Graziani, P.H. Shipper, F.J. Krambeck, B.C Choi, Adv. Chem. Eng. 13 (1987) 193. [19] G.B. Marin, G.F. Froment, J.J. Lerou, W. De Backer, EFCE 2 (27) (1983) C117, Paris. [20] G.B. Marin, G.F. Froment, Reforming of C6 hydrocarbons on a Pt-Al2 O3 catalyst, Chem. Eng. Sci. 37 (5) (1982) 759–773. [21] P.A. Van Trimpont, G.B. Marin, G.F. Froment, Ind. Eng. Chem. Res. 27 (1988) 1. [22] G.B. Marin, G.F. Froment, The development and use of rate equations for catalytic refinery process, in: Proceedings of the 1st Kuwait Conference on Hydrotreating Processes, Kuwait, March 5–9, 1989. [23] M.O. Coppens, G.F. Froment, Fractal aspects in the catalytic reforming of naphtha, Chem. Eng. Sci. 51 (1996) 2283–2292. [24] J.W. Lee, K.Y. Ko, Y.K. Jung, K.S. Lee, A modeling and simulation study on a naphtha reforming unit with catalyst circulation and regeneration system, Comput. Chem. Eng. 21 (1997) 1105–1110.
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[25] M.Z. Stijepovic, P. Linke, M. Kijevcanin, Optimization approach for continuous catalytic regenerative reformer process, Energy Fuels 24 (2010) 1908–1916. [26] W. Hou, H. Su, Y. Hu, J. Chu, Modeling, Simulation and Optimization of a whole industrial catalytic naphtha reforming process on Aspen Plus platform, Chin. J. Chem. Eng. 14 (5) (2006) 584–591. [27] T. Lid, S. Skogestad, Data reconciliation and optimal operation of a catalytic naphtha reformer, J. Process Control 18 (2008) 320–331. [28] G.J. Antos, A.M. Aitani, Catalytic Naphtha Reforming, Marcel Dekker, 2004, p. 602. [29] H. Scarf, The approximation of fixed points of a continuous mapping, SIAM J. Appl. Math. 15 (5) (1967) 1328–1343. [30] P. Ghosh, K.J. Hickey, S.B. Jaffe, Development of detailed gasoline compositionbased octane model, Ind. Eng. Chem. Res. (45) (2006) 337–345. [31] J.A. Smyslyaeva, E.D. Ivanchina, A.V. Kravtsov, Ch.T. Duong, Accounting the intensity of intermolecular interactions of mixed components in mathematical modelling of commodity gasolines blending process, Oil Refining Petrol. Chem. (9.) (2010) 9–14 (in Russian). [32] J.A. Smyslyaeva, Ch.T. Duong, Development of a detailed model for calculating the octane numbers of gasoline blends, IFOST-2010 (2010) 448–450.
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Chemical Engineering Journal journal homepage: www.elsevier.com/locate/cej
Reactor modeling and simulation of moving-bed catalytic reforming process Maria S. Gyngazova ∗, Anatoliy V. Kravtsov, Emilia D. Ivanchina, Mikhail V. Korolenko, Nikita V. Chekantsev National Research Tomsk Polytechnic University, pr. Lenina 30, Tomsk 634050, Russia
a r t i c l e
i n f o
Article history: Received 20 December 2010 Received in revised form 25 August 2011 Accepted 16 September 2011 Keywords: Catalytic naphtha reforming Mathematical modeling Moving-bed reactor Simulation
a b s t r a c t Catalytic reforming of naphtha is one of the most important processes for high octane gasoline manufacture and aromatic hydrocarbons production. Mathematical modeling method can be used for optimization and prediction of operating parameters (octane number, reactors outlet temperature and yield) of the reforming process. In this paper the new approach for mathematical modeling of a continuous catalytic regenerative (CCR) reforming process is proposed. The approach is based on components aggregation into pseudo components according to their reactivity; creation and application of pseudo components reaction scheme; finding the dependence of the reactivity of the hydrocarbons from the same homological group on their octane numbers. The novelty of the presented mathematical model of a moving-bed catalytic reforming reactor is the account of the catalyst work instability, coking, activity and circulating factor of the catalyst. The reformate composition calculated with the proposed model agrees very well with experimental information. © 2011 Elsevier B.V. All rights reserved.
1. Introduction
presents a region-wise distribution of catalytic reforming capacity by process type [1]. The semi-regenerative scheme dominates the reforming capacity at about 57% of the total capacity followed by continuous regenerative at 27% [2]. More than 95% of the new catalytic reformers are designed with continuous catalyst regeneration (CCR). Moreover many units that were originally designed as SR have been revamped to CCR reforming units (Reformer Unit of Omsk Refinery, Russia, can be mentioned as an example of such a reconstruction). Although CCR plants have become increasingly important most published works regarding modeling and optimization of naphtha catalytic reforming process address SR processes [3–23]. Accurate mathematical description of CCR reforming process is of great importance for the reliable design and simulation of the reactors. Relatively few CCR reforming process models have been suggested in the literature pertaining to this field [24–27].
Catalytic reforming of naphtha is one of the most important processes for high octane gasoline manufacture and aromatic hydrocarbons production. The naphtha reformer is used to upgrade low octane heavy naphtha that is unsuitable for motor gasoline. Industrial catalysts used in catalytic reforming units consist of ␥Al2 O3 support, some metals such as Pt, Re, Ge, Ir, Sn and additive such as chlorine to increase isomerization reactions. There are several types of reactions taking place during the reforming process: dehydrogenation, isomerization, cyclization, aromatization, hydrocracking, hydrogenolisis and coke formation. Some of these reactions such as isomerization, cyclization, aromatization are desirable because of increasing the octane number. Other reactions causing the catalyst deactivation (such as coke formation and coke deposition) are undesirable. According to the strategy of catalyst regeneration the existing process technologies of catalytic naphtha reforming can be divided into semi-regenerative (SR), cyclic regenerative (CR) and continuous catalyst regenerative (CCR). Table 1
1.1. CCR reforming process description
Abbreviations: Ar, aromatic hydrocarbons; CCR reforming process, continuous catalytic regenerative reforming process; CR reforming process, cyclic regenerative reforming process; FBP, final boiling point, ◦ C; IBP, initial boiling point, ◦ C; N, cycloalkanes; N5 , cyclopentanes; N6 , cyclohexanes; Pn , normal paraffins; Pi , isoparaffins; RON, research octane number; SR reforming process, semi-regenerative reforming process; TBP, true boiling point, ◦ C. ∗ Corresponding author. Tel.: +7 9069551067; fax: +7 3822564320. E-mail addresses: [email protected], [email protected] (M.S. Gyngazova).
Since its introduction in the early 1970s, the CCR process has gained wide acceptance in refining and petrochemical industries worldwide. The process uses stacked radial-flow reactors and a CCR section to maintain a steady-state reforming operation at optimal process conditions: fresh catalyst performance, low reactor pressure and minimum recycled gas circulation [2]. A schematic flow diagram of CCR reforming process is shown in Fig. 1. The naphtha used as a catalytic reformer feedstock is combined with a recycle gas stream containing 60–90% (by mol) hydrogen.
1385-8947/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cej.2011.09.128
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135
Table 1 Worldwide distribution of naphtha reforming by capacity and process type.a Region
No. of refineries
Reforming as % crude capacity
Semiregenerative
Continuous
Other
N. America W. Europe Asia-Pacific E. Europe Middle East S. America Africa
159 104 161 93 45 67 46
20.5 14.6 9.3 14.9 10.2 6.5 14.8
46.4 54.0 42.4 86.4 63.0 80.4 81.9
26.8 31.5 44.8 11.0 23.1 9.3 0.0
26.8 14.5 12.8 2.6 13.9 10.3 18.1
Total
675
13.8
56.8
26.9
16.3
a
Share of reforming capacity by process type (%)
From Ref. [1].
The total reactor charge is heated and passes through the catalytic reformers. Catalyst flows vertically by gravity down the reactors, while the feed flows radially across the annular catalyst bed. Catalytic reforming is an endothermic process, hence an inter-stage furnace is used between each reactor in order to reheat the charge to the reaction temperature. The catalyst is continuously withdrawn from the last reactor and transferred to the regenerator. The withdrawn catalyst flows down through the regenerator where the accumulated carbon is burned off. Regenerated catalyst is purged and then lifted in hydrogen to the top of the reactor stack, maintaining nearly fresh catalyst quality [2]. The CCR process has enabled ultra-low pressure operations at 0.35 MPa and produced product octane levels as high as 108.
1.2. Catalytic reforming models Catalytic reforming has been studied extensively in order to understand the catalytic chemistry of the process. The first significant attempt at delumping naphtha into different constituents was made by Smith [3]. He considered naphtha to consist of three basic components: paraffins, naphthenes and aromatics. This model is still used due to its simplicity. The model derived by Krane [7] contained a reaction network of 20 pseudo components and recognized hydrocarbons from 6 to 10 carbon atoms. Kmak [16] proposed the first model incorporating the catalytic nature of the reactions by deriving a reaction scheme with Hougen–Watson–Langmuir–Hinshelwood-type kinetics. Rate equations derived from this type explicitly account for the interaction of chemical species with the catalyst [28]. The Kmak’s model was later refined by Marin and his colleagues [19–22], who presented the reaction network for the whole naphtha. Other models were proposed by Barreto et al. [5], Ansari and Tade [6], Aguilar
and Anchyeta [11,12], Burnett [13], Henningsen and BundgaardNielson [15] and other researchers. A process with continuous catalyst regeneration was modeled by Lee et al. [24] and good agreement with plant data was reported. Hou et al. [26] simulated a whole industrial CCR reforming process on Aspen Plus platform. Stijepovic et al. [25] proposed a model for a moving-bed reactor of CCR reforming unit. Lid and Skogestad [27] determined the optimal operating conditions for a CCR catalytic naphtha reformer utilizing the Smith’s model. But the mentioned above CCR reforming process models have some considerable drawbacks. Thus, the authors of [26] do not include isomerization reactions in their model, though the octane numbers of isomers can differ significantly (up to 30 points). The works [26,27] do not take into account the catalyst deactivation throughout the catalyst bed due to coking and the subsequent decrease of catalyst activity in the desired reactions. The impact of catalyst circulating factor on the catalyst coking is not considered in [25–27] also. As seen, most previous works on this subject were related to packed bed reactors (PBRs). In the present paper we create a CCR reforming model that reflects the influence of raw material composition on the reformate composition, take into account the kinetics of coke formation and the influence of catalyst circulating factor on catalyst deactivation. Consideration of all these factors significantly improves the model adequacy.
2. Kinetics of the reforming process The naphtha used as a catalytic reforming feed-stock is a complex mixture consisting of several hundred hydrocarbons with carbon atoms ranging from five to twelve, and each of the components undergoes various reactions: dehydrogenation, isomerization, dehydrocyclization, hydrocracking, hydrogenolisis and
Fig. 1. Flowsheet of a continuous catalytic reforming process [2].
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Fig. 2. The example of differences in isomers research octane numbers (RON).
hydrodealkilation. Thus a detailed kinetic model considering all the components and reactions would be too complicated. To overcome this problem reactants in the mixture are classified in certain and limited groups called pseudo components. The number of selected pseudo components in the mixture is a determinating factor for model design. Obviously, the more the number of specified pseudo components are the higher the accuracy of the model will be, but at the same time this leads to more complicated mathematical formulation. There is a need to develop a universal mathematical model that could balance these contradictions and that could be used for different raw material compositions. Accurate kinetic equations are of great importance for the reliable design and simulation of the reactors. Here we formalized the reactions mechanism taking into account components reactivity, but without sensitivity loss to change of initial hydrocarbons raw material composition. To aggregate the components we combine hydrocarbons into pseudo components on the basis of affinity of their reactivity expressed for this process in magnitude of antiknock value. Components having not more than 7 carbon atoms are considered as individual hydrocarbons in the formalized scheme, because their reactivity and octane numbers differ a lot (Fig. 2). Hydrocarbons C8 –C12 are aggregated according to their homological groups. Unlike aggregation of the whole mixture according to homological groups, the basic characteristic of gasoline – octane number – is considered. For example, octane numbers of 2-methylpentane and 2,3-dimethylbutane differ in 30 points
although these hydrocarbons belong to one homological group (isoparaffin hydrocarbons C6 ). The scheme of reactions between pseudo-components accepted on such basis has been used at construction of mathematical model of catalytic reforming of hydrocarbons on Pt-containing catalysts. This has allowed foreseeing the consequences of raw material structure change. The researches executed on the basis of experimental data, received at the industrial unit, have allowed accepting the following formalized scheme of the mechanism of catalytic reforming process in moving-bed reactors (Fig. 3). According to the chemical reaction rate law elementary reaction rate at the set temperature is proportional to concentration of reacting substances in the degrees showing number of particles entering interaction: r = k · f (C)
(1)
f (C) = C1v1 · C2v2 · · ·Cnvn
(2)
where r is the reaction rate; k is the rate constant; Ci is initial components concentration and vi is the stoichiometric coefficient in gross-equation of chemical reaction. The given equation is true for elementary reactions. Complex reactions can have a fractional order.
Fig. 3. Formalized reaction scheme for naphtha reforming.
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Table 2 Estimated values of the rate constants at T = 520 ◦ C and p = 0.7 MPa for Pt–Sn reforming catalyst, s−1 . No.
Chemical reaction
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Hydrocracking of Pn Isomerization Pn → Pi Isomerization Pi → Pn Dehydrocyclization of Pn to N6 Hydrocracking of Pi Dehydrocyclization of Pi to N6 Hydrogenation of N5 to Pi Isomerization N5 → N6 Dehydrogenation of N6 to Ar Hydrogenation of Ar to N6 Dehydrocyclization of Pn to N5 Dehydrocyclization of Pi to N5 Isomerization N6 → N5 Coking
Number of carbon atoms in the molecule C4
C5
C6
C7
C8
C9
C10
C11
C12
0.041 0.065 0.005 0.000 0.012 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.00000
0.050 0.107 0.009 0.000 0.036 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.00000
0.060 0.128 0.016 0.001 0.046 0.000 0.176 0.275 0.157 0.085 0.006 0.002 0.056 0.00017
0.089 0.218 0.018 0.003 0.059 0.001 0.261 0.707 0.182 0.124 0.009 0.002 0.074 0.00021
0.122 0.263 0.021 0.005 0.073 0.004 0.449 1.314 0.181 0.147 0.010 0.003 0.075 0.00029
0.155 0.261 0.024 0.006 0.099 0.004 0.444 1.569 0.174 0.152 0.010 0.004 0.081 0.00032
0.214 0.272 0.024 0.006 0.115 0.004 0.470 1.961 0.174 0.152 0.009 0.005 0.084 0.00034
0.338 0.261 0.025 0.012 0.138 0.004 0.496 2.222 0.174 0.152 0.009 0.007 0.090 0.00038
0.468 0.258 0.024 0.006 0.144 0.004 0.514 2.222 0.174 0.152 0.009 0.008 0.090 0.00041
Where Pn is for normal paraffins, Pi is for isoparaffins, N6 is for cyclohexanes, N5 is for cyclopentanes, Ar is for aromatic hydrocarbons.
Having such level of mechanism specification the change of concentration of i – component in reversible j – reaction of the first order can be written as a system of the material balance equations: dCi = dt
lj kj (x)Ci (x)CH
2
(3)
j
where j = 1, . . ., m is a number of chemical reaction; Ci (x) and kj (x) are respectively distributions of hydrocarbons concentration and rate constants on number of carbon atoms in a molecule x; lj is a reaction order on hydrogen; t is space time. For the naphthenes dehydrogenation and aromatics hydrogenation reactions lj = 3, for the dehydrocyclization, hydrocracking and hydrodealkylation reactions lj = 1, for the isomerization reactions lj = 0. All the reactions are listed in Table 2. Practically kinetic parameters can be obtained experimentally measuring the reagents concentration change with time. From the kinetic curves it is possible to estimate the rate constants. The Arrhenius plot let us determine pre-exponential factors and activation energies. However the same parameters estimation can be done mathematically. The procedure of parameters estimation is carried out by minimization of the sum of the squares of the deviations between the plant and the calculated values of the key variables such as the composition of effluent from the last reactor and the outlet temperatures of the four reactors. In this paper kinetic parameters were defined mathematically. Having the reactants concentrations as the input data, the reactions rates as the responses and an initial guess of unknown parameters the least square parameters estimate was found. The optimization method based on the determination of the fixed points of the rate constants admitted region was applied. According to the Scarf’s theorem [29] a completely-labelled simplex (all vertices have different labels) is to be found. The fixed point is situated inside the simplex. The results of the rate constants estimation are given in Table 2. As seen from Table 2, for Pt–Sn catalyst rate constants of isomerization of N5 to N6 with the subsequent dehydrogenation of cycloalkanes to aromatic hydrocarbons have the largest values. Also the process of normal paraffins isomerization goes with a high rate. Binding energy decreases with the increase of hydrocarbons molecular weight and the rate constants increase in proportion to the hydrocarbon number in the homologous series. Hydrocracking rate constants of lighter hydrocarbons are approximately the same for normal paraffins and isoparaffins. Hydrocracking rate constants of heavy hydrocarbons differ a lot, and the rate constants of normal paraffins hydrocracking have much higher values than that of isoparaffins. Rate constants of dehydrocyclization of Pn and Pi to N5 and N6 are practically the same.
3. Reactor model Each reactor consists of two perforated coaxial cylinders between which the catalyst moves slowly downwards under the gravity force (Fig. 4). The catalyst is progressively coked as it moves through the reactors. The catalyst passes through all the reactors and after leaving the last reactor it is sent to the continuous catalyst regeneration unit. The coked catalyst undergoes a sequence of steps involving controlled coke combustion, oxychlorination, and calcinations to restore catalyst activity and metal redispersion [25]. For describing the process in moving-bed reactor we consider the two-phase flow. The passive phase is the gas flow, the active phase is the gas in the pores of the solid catalyst particles. According to the calculation of Reynolds (Re = 4.5, laminar flow) and Peclet numbers (Pe = 702) we can assume that diffusion plays insignificant role in the process of mass transfer which occurs by means of convection. For the industrial CCR reforming process the reaction limited regime is observed (Thiele modulus ˚j < 1, internal effectiveness factor j = 0.9–1). For the mathematical description of hydrodynamic and heat model of catalytic reforming reactor some assumptions are accepted:
Fig. 4. Schematic representation of a radial moving-bed reactor.
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Fig. 5. Comparison of RON between actual data and simulation results.
• mass and heat transport occurs by means of convection; • adiabatic operation; • the formalized mechanism of hydrocarbons transformation (Fig. 3). The model of moving-bed catalytic reforming reactor, presented by a system of equations of material balance for components and the equation of heat balance is the following:
⎧ l ⎪ ⎪ ∂C ∂C 1 ∂C ⎪ i i i ⎪G· = −u · −ϕ· + · rj (l)aj (l)dl ⎪ ⎪ l ∂z ∂R ∂l ⎨
the heat capacity of mixture and catalyst respectively, J/(kg K); Qj is jth reaction heat, J/mol, Qj is assumed to be constant within each homological group (normal alkanes, isoalkanes, aromatic hydrocarbons, cyclopentanes, cyclohexanes); T is temperature, K; rj is jth reaction rate, mol/(m3 h). The parameter z is used in Eq. (4) instead of t because G is not a fixed value and changes in the range of 130–170 m3 /h. The term of equation ∂Ci /∂z shows the change of ith component concentration against the catalyst deactivation
0
l ⎪ ⎪ ⎪ 1 m · C m · G · ∂T = −u · m · C m · ∂T − ϕ · cat · C cat · ∂T + ⎪ Q · rj (l)aj (l)dl · ⎪ j p p p ⎪ l ∂z ∂R ∂l ⎩
(4)
0
The conditions are: at z = 0, Ci = Ci,0 ; T = Ten ; at l = 0, Ci = Ci,0 (at the reactor entrance); T = Ten ; at r = 0, Ci = Ci,0 ; T = Ten . where z is a volume of raw material processed from the moment when the fresh catalyst (new catalyst, no regenerations were done) was loaded, m3 ; G is a raw material flow rate, m3 /h; z = G·t (t is a time of catalyst work from the new catalyst load, h); Ci is a concentration of ith component, mol/m3 ; u is a flow rate, m/h; R is a radius of the catalyst layer, m; l is a catalyst layer length in the reactor, m; ϕ is a catalyst flow rate, m/h; r is an integral reactions rate for component i, mol/(m3 h); a(l) is a catalyst activity distribution through the catalyst layer length in the reactor with a moving bed; m , cat are the density of mixture and catalyst respectively, kg/m3 ; Cpm , Cpcat are
because of aging (it depends on the number of regenerations i.e., on the catalyst circulating factor). Components concentrations depend on u – the rate of flow motion along the catalyst bed radius (raw material is radially input). Components concentrations change also with a change of ϕ – the catalyst flow rate along the height of the reactor. This happens because the catalyst flow rate influences the coke concentration in different layers of the catalyst, and thus catalyst activity changes in a different manner along the reactor height because of the coking. The reactions rate rj for component i (according to the reactions mechanism – Fig. 3) depends on the catalyst motion coordinate l and the catalyst activity a. In the model the catalyst deactivation is considered. In movingbed reactors catalyst activity changes through the radius and height of catalyst layer and with time. In our formalized reaction scheme (Fig. 3) coke is one of the reactions components. The coke
Fig. 6. Comparison of reformate yield between actual data and simulation results.
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139
Fig. 7. Change in catalyst activity with time (simulation results).
concentration can be calculated according to the kinetics of coke formation (according to Fig. 3 and Eq. (4)). Coking rate constants for hydrocarbons with different numbers of carbon atoms are given in Table 2. The catalyst activity will decrease with the coke concentration increase. It was found that the catalyst activity depends on the catalyst circulating factor (hcir ) the following way: aj = A0 · e−˛j ·Ccoke /hcir
(5)
where Ccoke is a mass fraction of coke on the catalyst; a is a catalyst activity; hcir = u · m /(ϕ · cat ); A0 is a linear component determining the number of catalyst active centres; ˛ is a coefficient of catalyst poisoning – nonlinear component that determines different extent of angle and edge atoms deactivation due to coking. The rate of catalyst metal sites deactivation has considerably greater magnitude than the rate of catalyst acid sites deactivation. Calculations show that 3 ≤ ˛ ≤ 5.9 – for reactions on metal sites of catalyst; 0.3≤ ˛ ≤ 0.52 – for reactions on acid sites of catalyst. Dehydrogenation reaction takes place on the metal sites. The rate of catalyst deactivation in cycloalkanes dehydrogenation reactions has the largest values. Therefore coefficient of catalyst poisoning ˛ for this type of reactions is maximum. Hydrocracking reactions occur on the acid sites and the catalyst deactivation against this type of reactions is insignificant. For other reactions realized via bifunctional mechanism coefficient ˛ is between these limits. The values of experimentally defined A0 and ˛ for the main types of reactions are given in Table 3. Another important problem is the calculation of reformate octane number according to the catalysate composition obtained as a result of modeling. Octane number (ON) is one of the most important properties of gasoline and is a measure of its antiknock property. Octane blending is known to exhibit nonlinear interactions (both synergetic and antogonistic) among the various constituent hydrocarbon molecular classes (paraffins, olefins, aromatics, etc.) [30]. Early a mathematical model for gasoline octane number calculation was elaborated on the basis of experimental data [31,32]. The model is based on physicochemical nature of blending process and takes into account non-additivity of gasoline properties. Thus the blending octane number model taking into account the deviation from additivity is written as: ONmix =
m
(ONi · Ci ) + B
(6)
i=1
Table 3 The values of experimentally defined A0 and ˛ for the main types of reactions. Reactions
˛
A0
Cycloalkanes dehydrogenation Alkanes hydrocracking Alkanes isomerization Alkanes dehydrocyclization
5.7 0.3 0.4 0.8
59.77 3.14 3.69 21.84
1 Bi Bj Ci Cj 100 m−1 m
B=
(7)
i=1 j=2
D n i
Bi = ˛
(8)
Dmax
where ONmix denotes the gasoline octane number; ONi represents the pure-component octane number for each molecule i in the fuel; Ci is the concentration of hydrocarbons in the mixture; B is a total deviation of hydrocarbons octane number from additivity; Bi , Bj denote parameters showing the tendency of ith molecule to intermolecular interaction with jth molecule; Di is a dipole moment of molecule i, debye; Dmax is the maximum possible dipole moment of the hydrocarbons mixture, debye; ˛ and n denote the kinetic coefficients defining the intensity of intermolecular interactions from dipole moment D. All the octane numbers calculations at the present paper were done with the help of the model described above (Eq. (6)–(8)). 4. Results and discussion The example of calculation of CCR reforming process is given in Tables 5 and 6, Figs. 5 and 6. The experimental data were obtained from the industrial CCR reforming unit of Russian refinery. Table 4 Specifications of reactors, feed and product, operating conditions and catalyst properties. Parameter
Numerical value
Unit
Naphtha feed stock Catalyst mass flow rate Pressure Reactors inlet temperature Diameter and length of Reactor 1 Diameter and length of Reactor 2 Diameter and length of Reactor 3 Diameter and length of Reactor 4 Catalyst load Reactor 1 Reactor 2 Reactor 3 Reactor 4 Properties of the catalyst Particle diameter Pt Sn Reactor bulk density
160 745 0.7 520 2.20, 11.18 2.40, 10.50 2.70, 11.65 3.20, 13.45
m3 /h kg/h MPa ◦ C m m m m
8950 13,425 22,375 44,750
kg kg kg kg
1.6 0.29 0.29 560
mm wt. % wt. % kg/m3
Distillation fraction of naphtha feed and reformate TBP IBP 10% 50% 90% FBP
Naphtha feed [◦ C] 60.26 90.05 125.68 165.10 195.90
Reformate [◦ C] −0.50 68.73 138.26 182.01 241.05
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Fig. 8. Hydrocarbons concentration change throughout the catalyst bed (model calculation results). *The calculations were done for the same conditions as at the industrial unit: T = 520 ◦ C; p = 0.7 MPa; Pt–Sn/␥-Al2 O3 catalyst, hcir = 0.008 m3 /m3 .
Specifications of reactors, feed and product, operating conditions and catalyst properties are presented in Table 4. Comparing the values presented in Table 5, we can see, that reformate composition calculated on model coincides with experimental data from the industrial unit with the set accuracy (in our case the calculation error should not exceed an error of chromatographic analysis). The same can be said about the coke concentration calculated on the mathematical model (Table 6). Calculated values agree very well with the experimental data from the industrial unit. Table 5 Results of calculation of catalytic reforming process in moving-bed reactor with the mathematical model.a Group composition, % mas.
Calculation
Experiment
n-Alkanes i-Alkanes Naphthenes-5 Naphthenes-6 Aromatic hydrocarbons Catalysate octane number Product yield
6.78 14.19 0.57 0.78 77.67
6.84 14.35 0.34 0.23 77.16
While using CCR reforming mathematical model it is also possible to compare the different catalytic reforming units work efficiency and choose more suitable variant of process optimization for given raw material. The simulation results delivered by our model are compared to values from the industrial CCR plant (Figs. 5 and 6). The obtained simulation results of reformate octane number and product yield are in very good agreement with the actual data from the industrial unit. Also with the help of the model we calculated the catalyst integral activity change (Fig. 7). These simulation results practically coincide with the real situation on the plant. At the beginning of the time period under consideration the catalyst was incorrectly regenerated and lost its activity dramatically due to its structure changes. Than the catalyst was gradually replaced in the system and the integral catalyst activity increased up to some stationary value. So the model allows considering the real catalyst activity during the operation of the industrial unit.
102.5 89.2
a The calculations were done for the same conditions as the experiment at the industrial unit: T = 520 ◦ C; p = 0.7 MPa; Pt–Sn/␥-Al2 O3 catalyst; raw material composition was characterized by chromatographic analysis.
Table 6 Comparison between experimental and calculated concentrations of coke on the surface of Pt-Sn/␥-Al2 O3 catalyst at the reactor outlet.a Pt–Sn/␥-Al2 O3 catalyst
Sample 1 Sample 2
Coke, wt. % Experiment
Calculation
5.54 4.13
5.63 4.03
a The calculations were done for the same conditions as the experiment at the industrial unit: T = 520 ◦ C; p = 0.7 MPa; Pt–Sn/␥-Al2 O3 catalyst; coke concentration was characterized by thermogravimetric analysis.
Fig. 9. Coke distributions in axial and radial directions for the reactor system (model calculation results).
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Fig. 10. Catalyst activity distributions in axial and radial directions for the reactor system (model calculation results).
Mathematical modeling is a powerful tool for the analysis of a complex multicomponent catalytic process. Fig. 8 shows hydrocarbons concentration change throughout the catalyst bed (model calculation results). Hydrocarbons concentration is plotted as a function of dimensionless radial (radial distance/reactor radius) and axial (axial distance/reactor length) distances. At the entrance of the reaction mixture the temperature has its maximum value
Fig. 11. Temperature profiles in reactors (model calculation results).
and the rate of reactions and conversion is high. Along the axial direction the loss of catalyst activity due to coking causes the subsequent decrease in reaction rates. Figs. 9 and 10 illustrate distributions of the coke and the catalyst activity, respectively. As
Fig. 12. Coke accumulation on the catalyst with time for different values of catalyst circulating factor: hcir1 = 0.008 m3 /m3 , hcir2 = 0.010 m3 /m3 , hcir3 = 0.016 m3 /m3 (model calculation results).
Fig. 13. Coke content as a function of catalyst circulating factor (model calculation results).
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expected, the largest coke content and the minimal catalyst activity occur at the entrance of the reaction mixture into the reaction zone because of the intensive cycloalkanes dehydrogenation reactions. And cycloalcanes and aromatic hydrocarbons are supposed to be coke precursors. Along the reactor length (axial direction) the coke cumulation takes place. Fig. 11 presents temperature distribution through the reactors. As the naphtha reforming is predominantly endothermic the temperature decreases in the reactors. The largest temperature drop can be observed in the first reactor where the main reaction is the conversion of naphthenes to aromatics (this reaction is highly endothermic and requires a large amount of heat). In the last reactors isomerization, dehydrocyclization and hydrocracking reactions play an important role. Catalyst circulating factor is one of the important parameters that influence the coke content and catalyst activity. Fig. 12 illustrates coke distribution versus residence time for different values of catalyst circulating factor. Also coke content versus catalyst circulating factor is depicted in Fig. 13. As seen, the amount of coke on the catalyst decreases with the catalyst circulating factor increase. For higher numbers of catalyst circulating factor the catalyst flow rate has greater values, catalyst spends less time in the reactor. Less coke content on the catalyst causes higher catalyst activity that in turn lets reactions go with higher rates. The catalyst circulating factor values of 0.008–0.010 m3 /m3 are common for the industrial operation of CCR reformers.
Cpm Cpcat Di Dmax G hcir i j k lj l n ONmix ONi Pe Qj r R Re t T Ten u
vi 5. Conclusion This paper has introduced a new approach for mathematical modeling of multicomponent process of CCR reforming. The approach is based on: • components aggregation into pseudo components according to their reactivity; • creation and application of pseudo components reaction scheme; • finding the dependence of the reactivity of the hydrocarbons from the same homological group on their octane numbers. In this work we have presented a mathematical model for a moving-bed catalytic reforming reactor that takes into account the catalyst work instability, activity and circulating factor of the catalyst. The model allows monitoring the process and can help to find optimal operation regimes. The mathematical model allows solving successfully the problem of product quality and quantity rising in operating manufacture conditions and also improving technical and economical values of industrial process. Also, in this model the peculiarities of raw material composition as well as the technological peculiarities have been considered. Appendix A. Nomenclature
Parameter Description catalyst activity a A0 experimentally defined coefficient, a linear component determining the number of catalyst active centres B total deviation of hydrocarbons octane number from additivity parameters showing the tendency of ith molecule to Bi , Bj intermolecular interaction with jth molecule mass fraction of coke on the catalyst Ccoke Ci concentration of component i, mol/m3 Ci,0 inlet concentration of component i, mol/m3
x z
heat capacity of hydrocarbons mixture, J/(kg K) heat capacity of catalyst, J/(kg K) dipole moment of molecule i, debye maximum possible dipole moment of the hydrocarbons mixture, debye raw material flow rate, m3 /h catalyst circulating factor, m3 /m3 numerator numerator rate constant, h−1 reaction order on hydrogen length of reactor, m kinetic coefficient defining the intensity of intermolecular interactions from dipole moment D gasoline octane number pure-component octane number for each molecule i in the fuel of transport by convection Peclet number, Pe = rate ofrate transport by diffusion or dispertion jth reaction heat, J/mol reaction rate, mol/(m3 h) radius of the catalyst layer, m Reynolds number time, h temperature, K inlet temperature, K hydrocarbons flow rate, m/h stoichiometric coefficient in gross-equation of chemical reaction, numerator volume of raw material processed from the moment when the fresh catalyst (new catalyst, no regenerations were done) was loaded, m3 , z = G·t (t is a time of catalyst work from the new catalyst load, h)
Greek letters kinetic coefficient defining the intensity of intermolecular ˛ interactions from dipole moment D ˛j experimentally defined coefficient of catalyst poisoning – nonlinear component that determines different extent of angle and edge atoms deactivation due to coking internal effectiveness factor j m density of hydrocarbons mixture, kg/m3 cat density of catalyst, kg/m3 ϕ catalyst flow rate, m/h ˚j Thiele modulus References [1] D. Nakamura, Worldwide refining capacity creeps ahead in 2004, Oil Gas J. (Decemeber) (2004) 40. [2] A. Aitani, Catalytic naphtha reforming, in: Encyclopedia of Chemical Processing, 2006, pp. 397–406. [3] R.B. Smith, Kinetic analysis of naphtha reforming with platinum catalyst, Chem. Eng. Prog. 55 (6) (1959) 76–80. [4] D. Bommannan, R.D. Strivastava, D.N. Saraf, Modeling of catalytic naphtha reformers, Can. J. Chem. Eng. 67 (1989) 405–411. ˜ M.G. Gonzalez, Lat. Am. Appl. Res. 26 (1) (1996) 21–34. [5] G.F. Barreto, J.M. Vinas, [6] R.M. Ansari, M.O. Tade, Saudi Aramco J. Technol. Spring (1988) 13–18. [7] H.G. Krane, A.B. Groh, B.L. Shulman, J.H. Sinfelt, Reactions in Catalytic Reforming of Naphthas, World Petroleum Congress, 1960, pp. 39–53. [8] Y.M. Zhorov, Mathematical description of platforming for optimization of a process (I), Kinetika i Kataliz 6 (6) (1965) 1092–1098. [9] U. Taskar, J.B. Riggs, Modeling and optimization of a semiregenerative catalytic naphtha reformer, AIChE J. 3 (№43) (1997) 740–753. [10] Yu.V. Sharikov, P.A. Petrov, Universal model for catalytic reforming, Chem. Petrol. Eng. 43 (2007) 580–584. [11] R. Aguilar, J. Anchyeta, Oil Gas J. (July) (1994) 80–83. [12] R. Aguilar, J. Anchyeta, Oil Gas J. (January) (1994) 93–95. [13] R.L. Burnett, H.L. Steinmetz, E.M. Blue, E.M. Noble, Petrol Chem. Am. Chem. Soc., Detroit Meeting, April, 1965. [14] J.H. Jenkins, T.W. Stephens, Hydrocarbon Process. (November) (1980) 163–167.
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