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Modeling of an industrial fixed bed reactor based on lumped



Available online at www.sciencedirect.com

Journal of Industrial and Engineering Chemistry 14 (2008) 771–778 www.elsevier.com/locate/jiec

Modeling of an industrial ?xed b

ed reactor based on lumped kinetic models for hydrogenation of pyrolysis gasoline
Suthida Authayanun, Worasorn Pothong, Dang Saebea, Yaneeporn Patcharavorachot, Amornchai Arpornwichanop *
Department of Chemical Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok 10330, Thailand Received 28 January 2008; accepted 9 May 2008

Abstract In this work, a mathematical model of an industrial ?xed bed reactor for the catalytic hydrogenation of pyrolysis gasoline produced from ole?n production plant is developed based on a lumped kinetic model. A pseudo-homogeneous system for liquid and solid phases and three pseudocomponents: diole?ns, ole?ns, and parraf?ns, are taken into account in the development of the reactor model. Temperature pro?le and product distribution from real plant data on a gasoline hydrogenation reactor are used to estimate reaction kinetic parameters. The developed model is validated by comparing the results of simulation with those collected from the plant data. From simulation results, it is found that the prediction of signi?cant state variables agrees well with the actual plant data for a wide range of operating conditions; the developed model adequately represents the ?xed-bed reactor. # 2008 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved.
Keywords: Fixed-bed reactor; Hydrogenation; Pyrolysis gasoline; Mathematical model; Lumped kinetic model

1. Introduction A catalytic hydrogenation is an important industrial process involving many petroleum fractions in re?ning and petrochemical industries. The purpose of this process is to catalytically stabilize unsaturated and reactive hydrocarbon such as diole?ns, in order to avoid the formation of undesired products during downstream processing. In addition, the hydrogenation process can be used to remove sulphur content in petroleum products. Pyrolysis gasoline is one of the products obtained from a steam cracking process in an ole?n production. Typical pyrolysis gasoline has a boiling point in range of 40–120 8C and usually contains C5–C12 hydrocarbons [1]. Due to high contents of ole?ns and aromatics, the pyrolysis gasoline is suitable either as high-octane blending components for motor gasoline fuel or as high-aromatic feedstock for an aromatic extraction. However, a raw gasoline cut from the steam cracking process is unstable because of the presence of a large amount of unsaturated hydrocarbons, known as gum-forming

* Corresponding author. Tel.: +66 2 218 6878; fax: +66 2 218 6877. E-mail address: Amornchai.A@chula.ac.th (A. Arpornwichanop).

compounds, such as diole?n and styrene. To prevent gum formation during downstream processing or storage, the pyrolysis gasoline product is further stabilized by selective hydrogenation processes. The advantage of this process is that it can ef?ciently remove most of unstable compounds and convert them to desired ole?ns and aromatics, thus increasing overall yield [2]. Generally, the hydrogenation of pyrolysis gasoline can be classi?ed into two processes depending on the type of desired ?nal products. That is, if the purpose is in order to obtain a gasoline fuel blendstock, only the ?rst stage hydrogenation reactor where the selective hydrogenations of diole?ns and alkenylaromatics occur without saturating other unsaturated hydrocarbon, i.e., ole?ns and aromatics, is involved. On the other hand, if the process is aimed to obtain a product for further aromatics extraction, the second stage hydrogenation (total hydrogenation) reactor where the hydrogenations of ole?ns and hydrodesulphurization further occur without aromatics hydrogenation, is followed by the ?rst stage hydrogenation reactor [3]. In a hydrogenation reactor, pyrolysis gasoline in the liquid phase ?ows down over a ?xed bed of catalyst in the form of a thin liquid ?lm while hydrogen in the gas phase ?ows through the catalyst bed either cocurrently or countercurrently. This

1226-086X/$ – see front matter # 2008 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jiec.2008.05.007

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Nomenclature ai catalyst surface area/volume ratio [m2/m3] A reactor cross sectional area [m2] Ci concentration of component i [kmol/m3] Cp speci?c heat capacity [J/(kg K)] dp catalyst diameter [m] D diffusivity [m2/s] Ea apparent activity energy [J/mol] g gravitational constant [m/s2] G mass velocity [kg/(h m2)] H Henry constant DH heat of reaction [J/kmol] kad adsorption constant k ga i gas phase mass transfer coef?cient [s?1] k0,1, k0,2 apparent pre-exponential factor k1, k2 speci?c reaction rate constant klai liquid phase mass transfer coef?cient [s?1] Q ?ow rate [m3/h] r1, r2 rate of reaction [kmol/(m3 h)] T reactor temperature [K] u super?cial velocity [m/h] z reactor length [m] Greek symbols e void fraction eg gas holdup el liquid holdup m viscosity [kg/(m h)] r density [kg/m3] Subscripts di diole?ns f feed stream g gas phase H2 hydrogen HC lumped hydrocarbon components (diole?ns, ole?ns and paraf?ns) i reaction index l liquid phase ole ole?ns para paraf?ns q quench stream Superscripts B2 bottom catalyst bed F feed stream Q quench stream type of the reactor is known as a trickle bed reactor, one of the widely used three-phase reactors in industrial chemical processes. For the common mode of the reactor operation in industrial practice, the gas and liquid phases ?ow cocurrently downward because of the absence of ?ooding and its relatively lower pressure drop, compared with other modes of operation (i.e., cocurrent up?ow or countercurrent ?ow) [4]. Generally, commercial trickle bed reactors are operated under plug ?ow

conditions and the catalysts are effectively wetted. These result in high conversion to be achieved in the reactor. In addition, the low-pressure drop allows for a uniform partial pressure of gaseous reactants (i.e., hydrogen in hydroprocessing) in the reactor. This would be important for ensuring hydrogen-rich condition at catalyst surface along the entire length of the reactor [5]. Owing to the signi?cance of trickle bed reactors to the petroleum, petrochemical, chemical and other industries, numerous review papers have appeared in the literature, emphasizing on the development of various empirical correlations to describe hydrodynamics and transport phenomena within the reactor. Among of these are contributions by Satter?eld [4], Hofman [6], Herskowitz and Smith [7], Ng and Chu [8], Zhukova et al. [9], Gianetto and Specchia [10], and Dudukovi et al. [11]. The current status of trickle bed reactors with respect to hydrodynamics and its effect on process intensi?cation is recently discussed by Nigam and Larachi [12]. Since the two ?owing phases in a trickle bed reactor make the reactor behavior complex, involving mass and heat transfer processes between gas and liquid and between liquid and catalyst particle, a number of research efforts have been carried out on the development of mathematical models to describe such a complicated behavior. Nijhuis et al. [13], for example, investigated the performance of a trickle bed reactor for the hydrogenation of styrene using a mass transfer model in which catalyst particles are assumed to be surrounded by a dynamic liquid zone, a static liquid zone, and a dry zone and the results obtained was compared with a monolithic reactor. Mostou? et al. [14] proposed a simple model for the process of pyrolysis gasoline hydrogenation. The proposed model integrates hydrodynamic parameters and kinetic models necessary to simulate such a process. However, most previous investigations were focused on the simulation of trickle bed reactors using steady-state models derived from experimental data. It is known that these models do not provide any information on the dynamics of the reactor which is an important issue for controlling the reactor during startup and shutdown period. In general, the mathematical models developed for describing the reactor with ?xed-bed catalyst can be classi?ed into two groups: pseudo-homogeneous and heterogeneous models. In the pseudo-homogeneous model, mass and heat transfers between the ?uid and solid phases are negligible. Thus, the concentration of reactants and temperatures at catalyst surface are assumed to be the same as those in bulk phase whereas in the heterogeneous model, the difference of such state variables between different phases is taken into account. Although, the heterogeneous model has been reported to be good accuracy, it is very complicated with too many unknown/uncertain parameters involved. The aim of this work is to develop a simpli?ed dynamic model of an industrial ?rst-stage hydrogenation reactor in which hydrogenation reactions of a pyrolysis gasoline in an ole?n plant occur. A pseudo-homogeneous system for the liquid and solid phases is assumed in order to simplify the complexity involving multi-phases in the trickle bed reactor. Furthermore, hydrocarbon components in the system are lumped into three

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pseudo-components: diole?ns, ole?ns, and parraf?ns. A parameter optimization problem is formulated and solved to ?nd kinetic reaction parameters based on actual plant data of temperature pro?le and product distribution. 2. Description of the ?rst stage hydrogenation of pyrolysis gasoline Fig. 1 illustrates the simpli?ed schematic diagram of an industrial ?rst stage hydrogenation reactor studied in this work. First, the raw pyrolysis gasoline (C5+) from an ethylene production process is mixed with makeup and recycle hydrogen, and diluent (hydrogenated gasoline product). After heating against the reactor ef?uent, the mixed stream of gasoline (raw gasoline, hydrogen and diluent) is delivered to the ?rst stage reactor in which liquid phase hydrogenations of diole?ns and alkenylaromatics occur in the presence of Ni or Pd supported catalyst. The inlet temperature varies between 60 and 120 8C and the reactor is approximately operated at the pressure of 30 atm. It is noted that operating the reactor at low temperatures and high pressures for maintaining the hydrocarbon stream in the liquid phase is preferable choice since it is bene?cial not only to reduce pressure drop through the catalyst bed but also to wash high molecular weight species, i.e., polymer, which otherwise deposit on the catalyst surface, thereby accelerating the loss of its activity. Since hydrogenations are exothermic reaction causing an increase in the reactor temperature, some hydrogenated gasoline (quench stream) is added directly to the reactor between two catalyst beds in order to maintain the reactor temperature at suitable level. The reactor ef?uent is passed to a heat exchange to heat up the gasoline feed and then is ?ashed in a hot separator. The vapor from the separator is sent to further process in order to make recycle hydrogen whereas the bottom liquid hydrogenated gasoline is passed through the second stage reactor. However, a portion of the hydrogenated gasoline is recycled to the ?rst stage reactor and used as the diluent and quench streams.

As mentioned earlier, the typical pyrolysis gasoline is a complex mixture of diole?ns, alkenylaromatics, ole?ns, aromatics, paraf?ns and naphthenes, mostly within C5 and C10. It has been known that the stabilization of the pyrolysis gasoline involves the elimination of unstable compounds, i.e., diole?ns and alkenylaromatics. Nevertheless, other unsaturated hydrocarbons, i.e., ole?ns, may also be hydrogenated. It is noted that chemical reactions in the reactor primarily involve the consecutive hydrogenations of diole?ns to ole?ns and then to paraf?ns within the same carbon number group. 3. Model of hydrogenation ?xed bed reactors The aim of this work is to develop a dynamic model for the ?rst stage hydrogenation reactor in which hydrogen and raw pyrolysis gasoline cocurrently ?ow through a ?xed bed of catalyst. This type of reactor is also known as a trickle bed reactor (TBR). Table 1 shows the speci?cation of the trickle bed reactor studied in this work as well as the properties of catalyst particles. To develop the dynamic model of the trickle bed reactor for the hydrogenation of pyrolysis gasoline, the following assumptions have been made [15,16]: (1) the reactor operates at transient condition under adiabatic and isobaric conditions, (2) the gas and liquid phases are supposed to be in a plug ?ow condition, (3) axial dispersion in both the gas and liquid phases is negligible, (4) the gas–liquid mass transfer resistance is considered whereas the mass transfer resistance at the liquid– solid interface and the resistance to pore diffusion are included in the effective kinetic expressions, (5) the catalyst particles are assumed to be completely wetted with the liquid, (6) all the reactions are assumed to take place in the liquid phase, and (7) the interphase and intraparticle heat transfer limitations are assumed to be negligible and the heat generated from the reactions is assumed to be carried away by the ?owing liquid. Furthermore, since a large number of reactions and components take part in the reaction system, the model is usually complex. To reduce the complexity of the model, all hydrocarbon components in the system are re?ned into three hydrocarbon classes based on the lumping criteria discussed by Somer et al. [17], Cheng et al. [1], and Chen et al. [18]. It is noted that each class represents a single compound. The classi?cation of hydrocarbons from C4 to C9 of pyrolysis
Table 1 The speci?cation of a gasoline hydrogenation reactor and the properties of catalyst particles. Reactor Height of top catalyst bed Height of bottom catalyst bed Diameter Catalyst particles (Ni/Al2O3) Shape Diameter Void fraction Volume of top catalyst bed Volume of bottom catalyst bed 7.9 m 15.75 m 1.8 m Sphere 3 mm 0.4 20 m 3 40 m 3

Fig. 1. Schematic diagram of the ?rst stage gasoline hydrogenation process studied in this work.

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gasoline in each pseudo-component consists of diole?ns, ole?ns and paraf?ns. The following lumped kinetic model scheme is considered to represent the hydrogenation reaction process in the present study: Diolefins ! Olefins ! Paraffins The concentration dependence of each pseudo-component on the rate expression is based on that proposed in the literature for the selective hydrogenation of pyrolysis gasoline [17]. It was observed that the hydrogenation showed irreversible reaction and ?rst order with respect to hydrogen and unsaturated reactant concentration. In addition, from experimental results, it was noticed that the disappearance of ole?ns is in?uenced from a number of diole?ns in the reaction system; hydrogenation of ole?ns occurs after the diole?ns are completely hydrogenated. This indicates that the diole?ns are strongly absorbed on the catalyst surface. Hence, the rate of ole?ns hydrogenation contains the adsorption term [16,17]. Based on the available information, the rate expressions based on lumped kinetic models as given below are employed. r 1 ? k1 C di;l CH2 ;l r2 ? k2 C ole;l C H2 ;l 1 ? kad Cdi;l (1) (2)

The overall external mass transfer resistance between the gas and liquid phases can be written as: 1 1 1 ? ? K l ai Hkg ai kl ai (7)

For slightly solution gases, such as hydrogen, the value of the Herry’s constant (H) exceeds unity and the gas ?lm mass transfer resistance can be negligible [9]. Therefore, the total mass transfer is approximately equal to the liquid phase mass transfer coef?cient as: 1 1 ? K l ai k l ai (8)

The liquid ?lm mass transfer coef?cient (klai) for H2 is calculated using the correlation reported by Korsten and Hoffmann [20]:  7  1=2 kl;H2 ai Gl ml ? 0:4 (9) Dl;H2 ml rl Dl;H2 Energy balance: @T ??ug C p;g rg ? ul C p;l rl ??@T=@z? ? ??DH??1 ? e??r 1 ? r 2 ? ? @t eg rg C p;g ? el rl C p;l (10) where DH is the heat of hydrogenation reaction which is approximated to ?30 kcal/mol for each double bond reaction [21]. 3.2. Quench section Within the trickle bed reactor, a ?xed-bed catalyst is divided into two beds between which a quench stream is added directly. The ?uid ?owing through the top catalyst bed and the quench stream are mixed and then enter the bottom catalyst bed. Here, the space between successive beds is treated as a quench section which is assumed to be a perfectly stirred tank as demonstrated in Fig. 2. It is further assumed that the mixing process reaches the steady-state condition instantaneously due to fast dynamic response. Therefore, the steady-state model of the stirred tank (Eqs. (11)–(15)) is employed to compute initial inlet conditions of reactant concentrations and temperature for the bottom catalyst bed.
Q B2 F ?Q f ? Qq ?CH2 ;l ? Q f CH2 ;l ? Qq CH2 ;l

where r1 and r2 are the hydrogenation rates of diole?ns and ole?ns, respectively, k1 and k2 are the speci?c effective reaction rate constants, kad is the adsorption constant. The temperature dependence of these kinetic and adsorption parameters is described by the Arrhenius correlation. 3.1. Reactor models Based on the assumptions stated above, mass and energy balances are performed and the following equations are obtained: Mass balance: @C H2 ;g ug @CH2 ;g K l;H2 ai ?? ? ?CH2 ;g ? C H2 ;l ? @t eg @z eg @C H2 ;l ul @CH2 ;l K l;H2 ai ?? ? ?C H2 ;g ? C H2 ;l ? @t el @z el 1?e ?r 1 ? r 2 ? ? el @C HC;l ul @C HC;l 1 ? e ?? ? ?r HC ? el @t el @z (3)

(11) (12) (13) (14) (15)

(4) (5)

Q B2 F ?Q f ? Qq ?Cdi;l ? Q f Cdi;l ? Qq Cdi;l Q B2 F ?Q f ? Qq ?Cole;l ? Q f Cole;l ? Qq Cole;l Q ?Q f ? Qq ?CB2 ? Q f C F para;l para;l ? Qq C para;l

The correlations used for the evaluation of hydrodynamics and mass transfer parameters for the trickle bed reactor were taken from the literature. The liquid hold up in the catalyst bed was calculated by the following correlation [19]: !?1=3   Gl d p 1=3 d3 gr2 p l el ? 9:9 (6) ml m2 l

T B2 ?

ug Arg C p;g T F ? rl C p ?Q f T F ? Qq T Q ? ug Arg C p;g ? ?Q f ? Qq ?rl C p;l

It is noted that Eqs. (3)–(5) and (10) is used to explain the dynamic response of the reactor for both the top and bottom catalyst sections. The inlet condition of the top reactor section

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4. Kinetic parameter identi?cation Before performing the solution of the models developed in the previous section, the speci?c reaction rate constants (k1, k2) and the adsorption constant (kad) in the rate expression, Eqs. (1) and (2), for hydrogenation of diole?ns and ole?ns have to be determined. These variables are dependent on the temperature according to the Arrhenius relation as follows:   ?Ea1 k1 ? k0;1 exp (17) RT k2 ? k0;2 exp   ?Ea2 RT  kad ? k0;ad exp ?Eaad RT  (19) (18)

Fig. 2. Schematic diagram of a quench section in the gasoline hydrogenation reactor.

is determined following the condition of raw pyrolysis gasoline feed whereas that of the bottom section is derived from the outlet of the top catalyst section and the inlet condition of quench stream feed. 3.3. Numerical solution The dynamic model of a trickle bed reactor developed in the earlier section results in a set of partial differential equations (PDEs) describing the mass and energy balances. In this work, the partial differential equations are solved numerically using a method of lines technique. Based on this approach, the spatial derivative terms in Eqs. (3)–(5) and (10) are discretized by an orthogonal collocation method on ?nite elements. The following equation is used to approximate the spatial derivative term:
NP dyi 1X ? Ai j y j dz hk j?1

where k0 is the apparent pre-exponential factor and Ea is the apparent activity energy. It is noted that Eqs. (17)–(19) is used to explain the temperature dependence of kinetic and adsorption parameters which are proposed by Somer et al. [17]. Therefore, the unknown kinetic parameters consist of k0,1, k0,2, k0,ad, Ea1, Ea2 and Eaad. The estimation of these parameters is carried out based on the industrial plant data on the gasoline hydrogenation unit (GHU) of an ole?n plant. It should be noted that under normal operation, the reactor is usually operated within a narrow region in which the reactor operating condition was smooth and has a slight variation with time, so the plant data observed are assumed to be at a quasisteady-state condition. 4.1. Formulation of parameter identi?cation problem The following optimization problem is solved as to ?nd the kinetic parameters which minimize the sum of residual squares between the prediction taken from the models and the plant data of the temperature pro?le within the reactor and the concentration of hydrocarbon components at the outlet of the reactor. The objective function to be optimized is as follows: min J k0;1 ; k0;2 ; k0;3 Ea1 ; Ea2 ; Eaad ?
N X i?1

(16)

where yi represents a vector of state variables at position i in each element, hk is the length of element k, NP is the number of collocation points in each element (k), and A is the weighting matrix for the ?rst order derivative. Here, each ?xed bed of catalyst in the reactor is divided into 10 elements with an equal space and 2 internal collocation points are used for each ?nite element. Collocation points and weighting coef?cients are determined using the algorithms of Villadsen and Michelsen [22]. An approximation of the spatial derivative terms in Eqs. (3)– (5) and (10) makes the partial differential equations reduce to a system of differential and/or algebraic equations (DAEs). In this work, the resulting DAEs are solved by means of the backward difference method using the well-known differential equation solver, DASSL [23].

?Tiactual ? Timodel ? ?

2

k X j?1

?Cactual ? C model ? j;out j

2

(20)

subject to the reactor model at steady-state condition: ug ul ul dC H2 ;g ? ?kl;H2 ai ?CH2 ;g ? C H2 ;l ? dz dCH2 ;l ? kl;H2 ai ?C H2 ;g ? C H2 ;l ? ? ?1 ? e??r 1 ? r 2 ? dz dCdi;l ? ??1 ? e??r 1 ? dz (21) (22) (23)

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ul ul

dC ole;l ? ??1 ? e???r 1 ? r 2 ? dz dC para;l ? ?1 ? e??r 2 ? dz

(24) (25) (26) (27) (28)

Table 3 Comparison of the reactor temperature and diole?ns concentration obtained from model prediction and real plant production data. Case study Outlet temperature from the top catalyst bed (8C) Plant 1 2 3 4 5 173.11 184.99 181.61 175.04 179.86 Calculated 175.97 181.66 180.18 176.78 183.86 Outlet temperature from the bottom catalyst bed (8C) Plant 182.07 193.09 186.98 191.07 192.1 Calculated 190.91 194.49 191.26 195.68 201.75 Diole?ns concentration (kmol/m3) Plant <0.01 <0.01 <0.01 <0.01 <0.01 Calculated 0.0027 0.0029 0.0027 0.0034 0.0038

dT ??DH??1 ? e??r 1 ? r 2 ? ? dz ug C p;g rg ? ul C p;l rl   ?Ea1 r 1 ? k0;1 exp Cdi;l C H2 ;l RT r2 ? k0;2 exp??Ea2 =RT?Cole;l CH2 ;l 1 ? k0;ad exp??Eaad =RT?Cdi;l

where i is a number of available temperature measurements within the reactor. It is noted that the reactor temperatures are on-line measured at the location of z = 0, 0.5, 1.9, 3.3, 4.7, 6.1, 7.5, 7.9, 8.9, 11.7, 14.5, 17.3, 20.1, 22.9, 23.65 m from the reactor inlet (N = 15). The formulated optimization problem is solved using a simultaneous model solution and optimization approach. Following this approach, the derivative term appeared in Eqs. (21)–(26) is discretized using an orthogonal collocation method; ordinary differential equations are approximated by algebraic equations which are posted as nonlinear constraints. The resulting constrained optimization program is solved by the SNOPT solver [24,25] which is based on a sparse sequential quadratic programming technique. More detail of the solution method can be found in Arpornwichanop and Kittisupakorn [26]. Table 2 shows the values of the estimate kinetic and adsorption parameters obtained from the solution of the parameter optimization problem. 5. Simulation results The applicability of the developed reactor model incorporated the lumped kinetic models with the estimate parameter is evaluated against the plant production data at different process conditions. Table 3 shows the calculated outlet temperature of the top and bottom catalyst beds and the concentration of diole?ns at the reactor outlet for ?ve case studies, compared with the plant data. It is noted that in each case study, the composition of the raw pyrolysis gasoline fed into the gasoline hydrogenation reactor is different. This results from the use of different feedstocks, e.g., light naphtha and liquid natural gas, for a steam cracking process in an ole?n production plant. It is indicated from Table 3 that the predictions of outlet temperature from the top and bottom catalyst bed give a good agreement with the plant data; small relative differences between the actual and predicted value of the outlet temperature of the top
Table 2 The value of the estimate kinetic parameters. Reaction rate constants and adsorption constant k1 k0 Ea (J/mol) 7,345 22,500 k2 7,839 35,370 kad 2.057 14,907

and bottom catalyst beds with less than 5% are observed. Furthermore, the concentration of diole?ns at the reactor outlet calculated from the developed reactor model agrees with the plant values. It should be noted here that since the available plant data do not provide information on the concentrations of other hydrocarbon components such as ole?ns and paraf?ns, a comparison of these components is not given. Fig. 3(a)–(d) demonstrates, respectively, the typical dynamic response of the concentration pro?les of diole?ns, ole?ns and paraf?ns, and the reactor temperature pro?le during a startup operation for the case study 1. Table 4 gives the operating conditions for the case study 1 as an example. It can be seen from Fig. 3(a) that the concentration of diole?ns sharply decreases at the top catalyst bed (z < 7.9 m) due to the hydrogenation reaction rate of diole?ns and therefore, leading to a high increase in ole?ns (Fig. 3(b)). As ole?ns consecutively react with hydrogen, the concentration of paraf?ns is increased as shown in Fig. 3(c). The exothermic hydrogenation reactions result in the increased reactor temperature (Fig. 3(d)). However, it is noticed that the reactor temperature in the bottom catalyst bed is initially decreased. This is because of a lower temperature of the quench stream introduced to the reactor.
Table 4 Operating and initial conditions for case study 1. P Dl;H2 DH Hydrogen gas feed Q T(0) C H2 ?0? Pyrolysis gasoline feed Q T(0) r Cdi(0) Cole(0) Cpara(0) Quench Q T(0) Cole(0) Cpara(0) C H2 ?0? 30 atm 10?5 cm2/s ?30 kcal/mol 8350 kg/h 392 K 0.93 kmol/h 69 m3/h 392 K 820 kg/m3 1.48 kmol/m3 1.23 kmol/m3 2.97 kmol/m3 15 m3/h 310 K 2.20 kmol/m3 3.11 kmol/m3 0.25 kmol/m3

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Fig. 3. Dynamic responses of the reactor for case study 1: (a) diole?ns, (b) ole?ns, (c) paraf?ns, and (d) temperature.

Simulation results demonstrate that the reactor takes approximately 15 min from initial condition to reach a steady-state condition and the dynamic responses of the reactor display a reasonable path to steady-state conditions. Fig. 4 shows the concentration pro?les along the reactor length at steady-state condition based on information from case study 1. It can be seen from the ?gure that the hydrogenation of diole?ns results in an increase in the ole?n concentration. However, the concentration of ole?ns at the bottom catalyst bed trends to decrease slowly due to the disappearance of the diole?n in the reactor and the hydrogenation of ole?ns to paraf?ns. There is an insigni?cant increase in paraf?ns concentration in both the top and bottom catalyst beds.

The steady-state temperature pro?le under the same case study is illustrated in Fig. 5. It can be seen that the temperature pro?le computed from the model agrees quite well with that obtained from the plant data. The reaction heat from the hydrogenations of diole?ns and ole?ns causes an increase in the reactor temperature along the length of reactor. However, after the reaction mixture is added with a quench stream at the quench section, the reactor temperature drops at the entrance of the bottom catalyst bed. It is also observed that the increased temperature in the top bed of catalyst is steeper than that in the bottom bed. This can be explained by a decrease in the concentration of diole?ns.

Fig. 4. Steady-state concentration pro?les for case study 1.

Fig. 5. Steady-state temperature pro?le for case study 1.

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6. Conclusions In this work, a dynamic model for an industrial ?xed bed reactor in which the catalytic hydrogenations of a pyrolysis gasoline obtained from an ole?n production plant occur, was developed. All hydrocarbon components in the system were lumped into three pseudo-components: diole?ns, ole?ns and paraf?ns. The dynamic modeling resulted in a system of partial differential equations which was solved numerically by the method of lines. Kinetic parameters were estimate based on industrial plant data using optimization technique. The reactor model with the estimate kinetic parameters was validated with actual plant data. It was observed that although the model contains some simplifying assumptions, it was found to be good agreement with plant data; the model gave a good prediction of temperature and lumped components in the reactor. This shows that the model adequately approximates the real system and can be used as a useful tool to further study on the design, optimization and control of the reactor. Acknowledgements The authors would like to acknowledge kind supports from Dr. Kongkrapan Intarajang and Thai Ole?n Company (TOC). References
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