Developing of the mathematical model for controlling the operation of alkane dehydrogenation catalyst in production of linear alkyl benzene

Chemical Engineering Journal 238 (2014) 129–139

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Chemical Engineering Journal journal homepage: www.elsevier.com/locate/cej

Developing of the mathematical model for controlling the operation of alkane dehydrogenation catalyst in production of linear alkyl benzene E.V. Frantsina ⇑, E.N. Ivashkina, E.D. Ivanchina, R.V. Romanovskii National Research Tomsk Polytechnic University, pr. Lenina 30, Tomsk 634050, Russia

h i g h l i g h t s  Process model dehydrogenation of alkanes is predicting the deactivation of catalyst.  The influence of raw material for the catalyst lifetime was obtained.  The optimum working parameters for different Pt-catalysts were determined.  The optimum flow rate of water in the reactor has been found.

a r t i c l e

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Article history: Available online 15 October 2013 Keywords: Dehydrogenation Pt-catalyst Linear alkyl benzene Deactivation Optimal activity Mathematical model

a b s t r a c t The main results are presented on the modeling of the industrial process of catalytic dehydrogenation of C9–C14 n-alkanes which is one of the technological stages in the production of linear alkyl benzene used in the synthesis of synthetic detergents. Application of the developed mathematical model in evaluating the influence of the raw material composition on the target product yield is considered. The calculation results are given for the optimal technological modes with different dehydrogenation Pt-catalysts and also for prediction of catalysts lifetime duration. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction The dehydrogenation of hydrocarbons is one of the most important processes in the organic synthesis. The process of dehydrogenation of C9–C14 n-alkanes into alkenes is used in the production of linear alkyl benzene (LAB) that are the intermediate products in the synthesis of synthetic detergents and surfactants [1]. In an industrial reactor, this process is usually performed at the pressure of 0.2 MPa, and the temperature of 465–495 °C. Different catalysts are used, usually containing platinum deposited on alumina or zeolite. A rather high selectivity of 90% is obtained at a relatively low conversion of approx. 10–11%. The average catalyst operating cycle duration is 5–8 months. Even a slight increase in the selectivity, activity or stability of Pt-catalysts used in the alkane dehydrogenation can substantially influence the cost and the quality of the LAB produced [2–5]. Thus, the urgency of solving the problems related to the abovementioned changes is obvious. The modernization of this technology is not limited to the development and the improvement of Pt-catalysts. The computer assistance for industrial processes aimed at optimizing the ⇑ Corresponding author. Tel.: +7 9050897129. E-mail address: [email protected] (E.V. Frantsina). 1385-8947/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cej.2013.09.049

operating modes is also of a great importance [6,7]. The application of the process simulation systems determines a new level of operational efficiency of processes related, and allows optimizing the operating modes of catalysts. Therefore, our aim was to develop an intelligent system controlling the operation of the alkane dehydrogenation catalyst in the LAB production, and allowing the increase in the operational efficiency of an industrial unit. 2. Brief description of the technology The LAB production complex includes five interconnected units: PAREX unit, preliminary fractionation facility, dehydrogenation plant for converting alkanes into alkenes, unit for selective hydrogenation of side products of dehydrogenation, and the alkylation plant, where the LAB is produced from the alkenes and benzene (Fig. 1). 3. The mathematical model The system for controlling the operation of gasoline reforming Pt catalysts was recently developed, based on the hierarchical

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Symbols H S Ci

e ri wj T DHj Cp

q

enthalpy (kJ/mol) entropy (J/mol K) concentration of ith hydrocarbon (mol/m3) pore volume of catalyst layer rate of reaction (mol/m3 h) rate of jth component in ith reaction transformation (mol/m3 h) temperature of the process (K) thermal effect of reaction (J/mol) thermal capacity of a mixture (J/mol K) density of a mixture (kg/m3)

approach, at the Department of Chemistry of Fuels and Chemical Cybernetics in Tomsk Polytechnic University. It was then successfully applied in the industry [8,9]. The mathematical formulation of the process of C9–C14 alkane dehydrogenation is based on the same approach. The mixture of n-alkanes with the difference of 1–4 carbon atoms in their carbon chains, e.g. C10–C13 or C11–C14, is used as a raw material for dehydrogenation. In this case, the C10–C14 fraction is unsuitable. The restriction is dictated by the necessity to convert the light n-alkanes without boosting the cracking of the heavier alkanes. Results of studies of the reactivity of the given homologous group show that these hydrocarbons have substantially different relative rates of dehydrogenation [10]: the lighter hydrocarbons are much more slowly dehydrogenated than the heavier ones. Thus, in order to avoid a high yield of gases in the cracking of heavier hydrocarbons and high losses of the target product, it is necessary to provide the required number of carbon atoms. Nevertheless, the raw material contains C9 and C14

T0 Tin Cin V G t z

x x Mr

start temperature (temperature of an environment) (K) temperature of an input in a reactor (K) entrance concentration of hydrocarbon (mol/m3) volume of catalyst (m3) hour expenditure of raw material (m3/h) time (h) total volume of the processed raw material (m3) mass concentration of substance in hydrocarbons (mass%) molar fraction of substance in hydrocarbons (mol/l) molar weight (kg/mol).

n-alkanes (0.01–0.50 wt.%) that are taken into account in the mathematical formulation of the process. The mathematical model we developed for the n-alkane dehydrogenation on Pt-catalysts is sensitive to the changes in the chemical composition of raw materials [11]. For the ith component, the material balance can be written with the differential equation:

G

N X @C i @C i þG ¼ ð1  eÞ r j ; @z @V j¼1

i ¼ 1 . . . M;

j ¼ 1 . . . N;

ð1Þ

where G is the raw material flow rate, m3/h; Ci is the ith hydrocarbon concentration, mol/m3; V is the catalyst volume, m3; e = 0–1 is the catalyst layer porosity; rj is the jth reaction rate, mol/(m3 h); z = G  t is the total volume of raw material processed after catalyst regeneration, m3; t is the time, h; M is the number of components, and N is the number of reactions. The heat balance can also be written with the differential equation:

G

@T @T þG ¼ ð1  eÞ @z @V

PN

j¼1 ðDH j r j Þ

Cp

;

ð2Þ

where T is the process temperature, K; DHj is the reaction heat, J/mol; C is the heat capacity of the mixture, J/(kg K); q is the raw material density, kg/m3. The initial and boundary conditions are the following:

z ¼ 0 : C i ¼ 0; T ¼ T 0 ; V ¼ 0 : C i ¼ C i;in ; T ¼ T in :

Fig. 1. LAB production flow chart: (I) n-alkanes from Parex unit; (II) n-alkanes C10– C13; (III) n-alkanes C14–C17; (IV) n-alkanes C18 and higher; (V) hydrogenous gas; (VI) mixture of n-alkanes and monoalkenes; (VII) recycling n-alkanes; (VIII) benzene from benzene reforming installation; (IX) alkylate bottom; (X) alkyl benzene; (XI) sulfur from the elemental sulfur installation; (XII) LAB sulfonate; (XIII) alkali; and (XIV) sodium LAB sulfonate.

The basis for the considered mathematical model is the formalized hydrocarbon conversion scheme that takes the hydrocarbon reaction abilities under dehydrogenation conditions into account (Fig. 2). Known conceptions [12] of the dehydrogenation mechanism allowed forming the presumable transformation scheme of the process. We used the Gaussian program package with PM3 procedure of NDDO (Neglect of Diatomic Differential Overlap) method based on quantum-chemistry modeling to calculate the electron molecule structures, and to estimate the thermodynamic characteristics (DGr, DHr, DS) for the reactions conducted under 753 K and 0.2 MPa. The method under consideration takes into account oscillatory and rotator movements of atoms, electron orbit patterns, effects of double bonds conjugation, and reproduces the structure and energy hyper valence compounds with high validity, providing adequate accuracy for high-quality reproduction of molecule physiochemical characteristics [13,14]. The results are illustrated in Table 1. The calculated data on the component structures involved in the dehydrogenation process is compared with the experimental data [15]. In the absence of extensive information on higher alkanes, the comparison is made on the basis of entropy and heat

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Fig. 2. The formalized reaction network of the dehydrogenation process.

Table 1 The mean values of reaction thermodynamic characteristics in dehydrogenation process (753 K, 0.20 MPa). Reaction

DGr (kJ/mol)

DHr (kJ/mol)

DS (kJ/(mol K))

1. Alkane ? Alken-1 + H2 2. Alkane ? Alken-2(n) + H2 3. Alkene-2(n) ? Alkadiene (cumul) + H2 4. Alkene-2(n) ? Alkadiene (conn) + H2 5. Alkene-2(n) ? Alkadiene (sec) + H2 6. Alkene-1 ? Alkadiene (cumul) + H2 7. Alkene-1 ? Alkadiene (conn) + H2 8. Alkene-1 ? Alkadiene (sec) + H2 9. Isoalkane ? Isoalken + H2 10. Isoalkene ? Isoalkadiene + H2 11. Alkene ? Isoalkene 12. Alkane ? Isoalkane 13. Alkane ? Cycloalkane + H2 14. Alkane ? Arene + 4H2 15. Alkene ? Cycloalkane 16. Alkene ? Arene + 3H2 17. Cycloalkane ? Arene + 3H2 18. Alkadiene ? Arene + 2H2 19. Isoalkane ? Cycloalkane + H2 20. Isoalkane ? Arene + 4H2 21. Isoalkene ? Arene + 3H2 22. Isoalkene ? Cycloalkane 23. Alkane ? Cracking product 24. Alkane ? Cracking product 25. Alkadiene ? Cracking product 26. Isoalkane ? Cracking product 27. Isoalkene ? Cracking product 28. Isoalkadiene ? Cracking product 29. Arene ? Coke formation product 30. Alkene ? Coke formation product 31. Alkadiene ? Coke formation product

47.94 70.34 5.44 –69.26 –47.69 –8.28 –67.49 –47.29 –81.14 –67.91 –2.27 3.06 –64.21 –331.21 –7.86 –289.29 –333.12 –251.07 –76.48 –353.60 –289.56 –12.44 –137.77 –137.76 –137.22 –138.74 –140.03 –137.75 –510.66 –508.64 –509.35

49.89 33.04 90.37 32.49 49.89 78.56 29.59 49.92 24.50 33.38 0.94 2.51 –33.12 –58.68 –64.51 –90.07 –25.52 –137.45 –37.15 –49.66 –67.64 –55.13 84.03 84.05 83.26 84.39 81.69 98.31 –425.15 –423.12 –424.17

0.13 0.14 0.13 0.14 0.13 0.13 0.13 0.13 0.14 0.14 0.00 0.00 0.04 0.36 –0.07 0.27 0.36 0.15 0.05 0.40 0.30 –2.04 1.05 0.14 0.17 0.16 0.16 0.16 0.56 0.56 0.56

capacity. Under average conditions of the process (733 K and 2 atm), the mean relative error of the entropy component does not exceed 5%. Under standard conditions (298 K and 1 atm), the relative error in calculating the entropy does not exceed 5%, the heat capacities – 7%. The results of the calculation show that aromatization reaction appears to be the most thermodynamically probable ðDG0r  300 kJ=molÞ. Isomerization reactions of alkanes and alkenes do not run in the process. Also, the formation of dienes with

cumulative double bonds is not allowed thermodynamically ðDG0r  5 kJ=molÞ. The presence of isomeric alkanes in the product is determined by the dehydrogenation processes of iso-alkanes which are present in raw materials. All other possible reactions are thermodynamically probable and have approximately the same values of isobaric-isothermal potential ðDG0r  70 kJ=molÞ. Dienes with conjugate and secured double bonds are produced in the process, whereas the formation of dienes with cumulative double bonds is not thermodynamically allowed under these

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conditions. Cracking ðDG0r  140 kJ=molÞ and coke formation ðDG0r  510 kJ=molÞ are the main by-reactions. Based on these results, the formalized scheme of higher alkanes C9–C14 dehydrogenation process was formed (Fig. 2). Substances are combined into several groups of pseudo components according to their reactionary ability evaluated according to isobaric–isothermal potential DGr. Thus, 11 groups of pseudo components take part in 22 types of chemical reactions (see Fig. 3). This level of mechanism formalization allows cutting the mathematical description of passing reactions and time solution of material and thermal balance equations down, as well as keeping the sensitivity concerning raw feed components, and the selfdescriptiveness concerning products of passing reactions. The target reactions (dehydrogenation of alkanes into alkenes) and the side reactions (dehydrogenation of alkanes into dienes, dehydrocyclization, coking) pass on the surface of a dehydrogenation catalyst. In this case, dienes and aromatic hydrocarbons are the main sources of coke. The kinetic model of the dehydrogenation process, according to the law of active mass is written down in the following way (Table 2). The initial conditions are s = 0 and Ci = C0i, where i is respective hydrocarbon (alkane, alkene, diene, etc.). The developed mathematical model is used as the basis for the dehydrogenation process simulation system that allows not only to optimize calculations, but also to predict the lifetime of Pt-catalysts. The kinetic model developed is formalized and quasihomogeneous. Therefore, the rate constants shall be regarded as effective, i.e. they are combination of constants of all intermediate stages.

Dehydrogenation reactor (Fig. 1) is a capacitive device with a radial entering of the raw material. Its overall dimensions are: D – 1675 mm, H – 7555 mm. The volume of the catalyst load is 3.14 m3. The application of an ideal plug flow model is suitable to describe the higher alkanes dehydrogenation process in a fixedbed reactor. According to the calculation of Reynolds (Re = 965.88, laminar flow) and Peclet numbers (Pe = 2494, PeT/PeD = 1.05  1.5) we can assume that diffusion plays insignificant role in the process of mass transfer which occurs by means of convection. For the dehydrogenation process, the reaction limited regime is observed (Thiele modulus Uj < 1, internal effectiveness factor gj = 0.98–1). For the mathematical description of hydrodynamic and heat model of industrial reactor dehydrogenation, some assumptions are accepted:    

The industrial reactor is considered an ideal plug flow reactor. Mass and heat transport occur by means of convection. There is an adiabatic operation. The formalized mechanism of hydrocarbons transformation (Fig. 2).

We put the value of the porosity of the catalyst layer (0.19– 0.58) for industrial dehydrogenation catalysts to take the characteristics of the catalyst layer in the model into account. It shows the proportion of the free volume, the unemployed solid phase for each particular type of catalyst. We assume that the conversion occurs only in the volume of the solid catalyst. Results are shown for a linear velocity of 12.74 m/s. An example of the kinetic equations for n-decane is given below:

8 k1 > > C 10 H22 ¢ C 10 H20 þ H2 > > > k1 > < k5

C 10 H22 ¢ i  C 10 H22 > > k5 > > > > k8 : C 10 H22 þ H2 ! C 5 H12 þ C 5 H12 dC C10 H22 ¼ k1 C C 10 H22 þ k1 C C10 H20 C H2  k5 C C10 H22 þ k5 C iC10 H22 dt  k8 C C10 H22 C H2 t ¼ 0; C C 10 H22 ¼ C 0C 10 H22

Fig. 3. Reactor for catalytic transformations of the radial type.

All the reactions are shown in Fig. 2 and Table 3. Modeling the process of C9–C14 hydrocarbons dehydrogenation represents a difficult task. Fair quantities of passing reactions cause high dimensionality of mathematical model, and demand determination of a great number of kinetic parameters (preexponential factors k0 and activation energies Ea) for all types of chemical reactions. For technical reasons, it is impossible to realize the kinetic experiment at the industrial installation. Therefore, a more effective option of determining the k0 Ea values is solving the reverse kinetic task [16]. When a finite-difference method of calculation is to be used to solve the differential equations system that describes a real chemical process, we use the net method [16]. Having the reactants concentrations as the input data, the reactions rates as the responses and an initial guess of unknown parameters (taken from the literature), the least square parameters estimate was found. Using this approach, the rate constants for the reactions at the industrial unit were defined (apparent rate constants). To verify the parameters found, the data from the industrial isomerization unit (Russian-based) was computed, starting from 2005 and up to now. The conditions in the simulations were the same as they were at the industrial unit. The simulation data therefore can be directly compared to the experimental data. The calculated composition of dehydrogenation (simulation results)

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Table 2 Normal alkanes dehydrogenation process kinetic model on basis of formalized scheme of hydrocarbons transformation. Compound group

Time dependency of the compound’s concentration

Alkanes

dC C n H2nþ2 ¼ k1 C C n H2nþ2 ðnparaffinÞ þ k17 C C n H2n ðolefin1Þ C H2  k2 C C n H2nþ2 ðnparaffinÞ þ k18 C C n H2n ðolefin2ðnÞÞ C H2  k6 C Cn H2nþ2 ðP paraffinÞ dt  k7 C C n H2nþ2 ðP paraffinÞ  k11 C C n H2nþ2 ðP paraffinÞ

Isoalkanes

dC Cn H2nþ2 ¼ k4 C C n H2nþ2 ðisoparaffinÞ  k6 C C n H2nþ2 ðP paraffinÞ  k7 C C n H2nþ2 ðP paraffinÞ  k11 C C n H2nþ2 ðP paraffinÞ dt

Alkenes-1

dC Cn H2n ¼ k1 C Cn H2nþ2 ðnparaffinÞ  k17 C C n H2n ðolefin1Þ C H2  k3 C Cn H2n ðnolefinÞ þ k19 C C n H2n2 ðndienÞ C H2  k9 C C n H2n ðP olefinÞ  k12 C C n H2n ðP olefinÞ  k15 C C n H2n ðP olefinÞ dt

Alkenes-2(n)

dC Cn H2n ¼ k2 C Cn H2nþ2 ðnparaffinÞ  k18 C C n H2n ðolefin2ðnÞÞ C H2  k21 C C n H2n ðolefin2ðnÞÞ  k9 C C n H2n ðP olefinÞ  k15 C Cn H2n ðP olefinÞ  k12 C C n H2n ðP olefinÞ þ k22 C C n H2n2 ðndienÞ C H2 dt

Isoalkenes

dC Cn H2n ¼ k4 C Cn H2nþ2 ðisoparaffinÞ  k5 C Cn H2n ðisoolefinÞ þ k20 C C n H2n2 ðisodienÞ C H2  k9 C Cn H2n ðP olefinÞ  k12 C C n H2n ðP olefinÞ  k15 C C n H2n ðP olefinÞ dt

Dienes

dC Cn H2n2 ¼ k3 C C n H2n ðolefin1Þ  k19 C Cn H2n2 ðndienÞ C H2 þ k21 C C n H2n ðolefin2ðnÞÞ  k13 C C n H2n2 ðP dienÞ  k22 C C n H2n2 ðndienÞ C H2  k10 C Cn H2n2 ðP dienÞ  k16 C C n H2n2 ðP dienÞ dt

Isodienes

dC Cn H2n2 ¼ k5 C C n H2n ðisoolefinÞ  k20 C Cn H2n2 ðisodienÞ C H2  k13 C C n H2n2 ðP dienÞ  k10 C Cn H2n2 ðP dienÞ  k16 C C n H2n2 ðP dienÞ dt

Cyclohadrocarbons

dC Cn H2n ¼ k6 C Cn H2nþ2 ðP paraffinÞ  k8 C Cn H2n ðCycloparaffinÞ dt

Arenes

dC Cn H2n6 ¼ k8 C C n H2n ðcycloparaffinÞ þ k7 C C n H2nþ2 ðP paraffinÞ þ k9 C C n H2n ðP olefinÞ þ k10 C C n H2n2 ðP dienÞ  k14 C Cn H2n6 ðarenÞ dt

Cracking gases

dC Cracking products ¼ k11 C C n H2nþ2 ðP paraffinÞ þ k12 C Cn H2n ðP olefinÞ þ k13 C C n H2n2 ðP dienÞ dt

Coke

dC CokeFormation products ¼ k14 C C n H2n6 ðarenÞ þ k15 C C n H2n ðP olefinÞ þ k16 C C n H2n2 ðP dienÞ dt

Hydrogen

dC H2 ¼ k1 C C n H2nþ2 ðnparaffinÞ  k17 C C n H2n ðolefin1Þ C H2 þ k2 C C n H2nþ2 ðnparaffinÞ  k18 C C n H2n ðolefin2ðnÞÞ C H2 þ k3 C C n H2n ðolefin1Þ  k19 C C n H2n2 ðndienÞ C H2 dt þ k21 C C n H2n ðolefin2ðnÞÞ þ k4 C C n H2nþ2 ðisoparaffinÞ  k22 C C n H2n2 ðndienÞ C H2 þ k5 C C n H2n ðisoolefinÞ  k20 C C n H2n2 ðisodienÞ C H2 þ k6 C C n H2nþ2 ðP paraffinÞ þ 3k9 C C n H2n ðP olefinÞ þ 4k7 C C n H2nþ2 ðP paraffinÞ þ 3k8 C C n H2n ðcycloparaffinÞ þ 2k10 C C n H2n2 ðP dienÞ

were in a very good agreement with each set of experimental data taken at the industrial unit for the whole period considered (9 years). The results of the rate constants estimation are given in Table 3.

We compared the calculated values of the output stream with the analogous experimental values to test the validity of the model. The values correspond to beginning of the catalyst lifetime, when its deactivation by coke is minimal.

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Table 3 Values of the main kinetic parameters of C9–C14 alkanes dehydrogenation process. Reaction

Kinetic parameter of the reaction

N-alkane ? Alkene-1 + H2 N-alkane ? Alkene-2(n) + H2 Alkene-1 + H2 ? N-alkane Alkene-2(n)+H2 ? N-alkane Alkene-1 ? N-diene + H2 Alkene-2(n) ? N-diene + H2 N-diene + H2 ? Alkene-1 N-diene + H2 ? Alkene-2(n) Isoalkane ? Isoalkene + H2 Isoalkene ? Izo-diene + H2 Izo-diene + H2 ? Isoalkene Alkane ? Cycloalkane + H2 Alkane ? Arene + 4H2 Alkene ? Arene + 3H2 N-diene ? Arene + 2H2 Cycloalkane ? Arene + 3H2 Alkane ? Cracking product Alkene ? Cracking product N-diene ? Cracking product Arene ? Coke formation product Alkene ? Coke formation product N-diene ? Coke formation product

Ea (kJ/mol)

k0

k

110 118 60 85 190 190 160 160 170 150 115 200 140 135 135 160 200 200 200 220 220 220

7.45  107 s1 8.03  107 s1 3.92  103 l s1 mol1 5.45  103 l s1 mol1 2.65  1011 s1 2.65  1011 s1 5.55  109 l s1 mol1 4.1843  109 l s1 mol1 2.1  1011 s1 8.30  108 s1 3.28  106 l s1 mol1 5.2  1010 s1 1.1  108 s1 1.4  108 s1 2.0  108 s1 9.0  1010 s1 1.0  1010 s1 1.0  1010 s1 1.0  1010 s1 5.5  1010 s1 4.8  1010 s1 5.0  1010 s1

0.5698 s1 0.5235 s1 0.2682 l s1 mol1 0.007 l s1 mol1 2.1079 s1 2.1079 s1 0.0436 l s1 mol1 0.0329 l s1 mol1 0.2178 s1 1.7688 s1 0.0342 l s1 mol1 0.0004 s1 0.0149 s1 0.0426 s1 0.0608 s1 0.4733 s1 0.0001 s1 0.0001 s1 0.0001 s1 0.000017 s1 0.000006 s1 0.000015 s1

Table 4 Calculated and experimental values of product concentration comparison for dehydrogenation process. Component

Alkanes Alkenes Dienes Isoalkanes Isoalkenes Isodienes Arenes Coke formation products Cracking products Hydrogen

Input component concentration (mass%)

Output component concentration (mass%)

97.14 0.0 0.0 2.98 0.0 0.0 0.98 0.0 5.46 94.54

The errors of calculating the primary components concentrations do not exceed 4% (Table 4), confirming the high accuracy of process kinetic parameters determined using the model. 4. The optimal technological parameters The realization of the potential of the catalysts depends on the hydrodynamic modes in the reactors and the technological conditions. In addition, the real (current) and the steady-state (optimum) activities of various commercial catalysts vary widely. The steadystate activity is regarded as the value that is established upon equalization of the rates of deactivation and self-regeneration of contact [17–19]. The deviation between the current activity and the optimum must be a quantitative criterion of determining the efficiency of the catalysts in terms of practical realization of their potential. The current activity of the catalysts as the relative value of which is determined by the ratio between the coke-free surface and the total surface :

aðtÞ ¼

SðtÞ ; Sðt0 Þ

ð3Þ

where S(t) – catalysis surface free of coke; S(t0) – total catalysis surface. The optimum technological parameters for improving the conversion of n-alkanes in the reactors can be found using the

Calculation

Experiment

86.94 9.28 0.49 2.71 0.28 0.02 0.28 55.72  10–3 6.17 93.83

86.93 9.27 0.5 2.69 0.29 0.02 0.29 55.94  10–3 5.94 94.06

Deviation of calculation (%)

0.01 0.11 2.00 0.74 3.45 0.00 3.45 0.40 3.77 0.25

developed integrated criterion for estimating the service state of catalysts for the dehydrogenation of higher n-alkanes. This makes it possible to predict the real service life of catalysts, subject to process conditions and the composition of feedstock. The patent search reveals that the data in [18–20] on the practical use of the dehydration process, its laws, the properties of used catalysts, and the methods used to study the causes of their deactivation does not allow us to solve the problem mentioned. The properties of the dehydrogenation Pt-catalysts vary considerably during the service life: the effective specific surface area changes as a result of heat treatment and the accumulation of coke (accompanied by a change in its porous structure and a decrease in the number of active sites), and the catalyst is poisoned by harmful impurities [21]. Studies of the deactivation of catalysts by means of mathematical simulation confirm the existence of the optimum region for the occurrence of the self-regeneration reaction on Pt sites. Under conditions of the thermodynamic equilibrium of the reaction system, the rates of formation and hydrogenation of intermediate condensation products are equal. A decrease in the specific surface area due to coke formation is thus reversible, because the catalyst operates at high temperatures in a hydrogen bearing environment. This means it is possible to perform the process in an optimum region that corresponds to the thermodynamic equilibrium of the reactions of the formation and hydrogenation of coke forming structures.

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According to the theory of active sites, the surface of a catalyst at the stage of formation in preparation and operation (regeneration and feedstock cycle) is an open system (the reaction mixture affects the formation of an active surface); its formation is governed by the technological conditions, the composition of feedstock, and the concentration of the promoters. In this regard, the deactivation of a catalyst is an unsteady, nonequilibrium process of the formation of coke forming structures on its surface [22]. The functioning of the catalyst surface is due to quasistationary states that correspond to the optimum (steadystate) catalyst activity in the feedstock cycle. In this case, the thermodynamic equilibrium between the reactions of coke formation and the hydrogenation of intermediate condensation products is established in the nonequilibrium process of deactivation. The long-term maintenance of the stationary state in the reactions under nonequilibrium conditions of deactivation can be performed by controlling the temperature and the contact time [17]. For the nonequilibrium process of the formation of an active surface of catalysts, it is generally necessary and sufficient to meet the following conditions [23]: (i) the nonlinearity of the reaction system (i.e., the degree of impact on the reaction process) is not proportional to a change in the parameters under control (contact time, temperature, and flow rate of promoters); (ii) the nonequilibrium of the reaction system and quasistationary states; (iii) the reversibility of chemical reactions. In industrial catalysis, the natural criterion of stability is the catalyst lifetime. However, the estimation of this criterion is very time-consuming under laboratorial conditions. Moreover, the conditions of laboratorial experiments must be maximally close to the industrial ones, and this also causes additional expenses. Therefore, the following indirect parameters are applied: (1) the rate of temperature growth compensating the activity decrease, (2) the level of steady-state (optimal) activity, and (3) the number of regenerations endured by a catalyst. All these criteria allow us to estimate a catalyst under steadystate operational conditions. To solve any multi-criterion problem, it is necessary to define a generalized efficiency criterion reflecting the influences of technological conditions, volume and composition of processed raw materials. The definition of the steady-state catalyst activity is given in [24]: it settles when the rates of catalyst deactivation and self-regeneration become equal. Determining the equilibrium conditions for the coke formation and the dehydrogenation of intermediate condensation products, it is possible to calculate the catalyst operational mode corresponding to its maximally possible lifetime at a specified yield of the target product [25,26]. In the dehydrogenation process, the criterion of the technological mode optimality is either the maximal yield of the target product per unit of time regardless the stability of a catalyst or, on the contrary, the time of catalyst operation at a fixed yield of the target product. The maximal economic benefits can be reached by regulating the process operational mode (temperature, pressure, or flow rate of hydrogen-containing gas) for a certain catalyst type and raw material composition [27,28]. In the process of dehydrogenation, the pressure is nearly constant, the hydrogen/raw materials molar ratio, and the temperature are chosen so as to provide a specified yield and quality of the target product. In this case, the most important LAB quality characteristic is its biodegradability determined by the concentration of alkenes in the product and also by the branching index of hydrocarbons coming to the alkylation stage.

135

The optimal catalyst operation mode corresponds to the maintenance of the catalyst activity at its optimal level by varying the independent process parameters: catalyst type, temperature, raw material flow rate, pressure, hydrogen-containing gas, circulation ratio, raw material quality. The rate of the temperature increase at the reactor inlet, as well as the hydrogen-containing gas flow rate must provide the equilibrium conditions for coking and hydrogenation of intermediate condensation products. In this case, the maximal yield of the target product will correspond to the maximally possible lifetime of a Pt-catalyst. In order to estimate the influence of the raw material composition on the yield of target n-alkenes used further in the alkylation, the contribution of each of C9–C14 components to the quantitative characteristics of the products (yield of target LABs) was determined. The range of hydrocarbon concentrations at the inlet of dehydrogenation reactor was chosen in accordance with the interval of their variation in the real raw materials. The calculation results are shown in Fig. 4. From the dependences given it is clear that the yield of alkenes grows with an increase in the C10–C13 hydrocarbons concentrations, whereas the increase in the concentration of C14 hydrocarbons hardly influences the yield of the target product. It should be noted that the changes in the concentrations of C12 and C13 hydrocarbons have the most profound effect corresponding to a sharper ascent of the curves. The greatest contribution of these hydrocarbons to the yield of the target products can be explained by the fact that the concentrations of C9 and C14 hydrocarbons in the raw material is two orders less than that of C10–C13 hydrocarbons. Thus, the latter make the major contribution to the formation of alkenes. The calculations were performed for the different catalysts loaded into the dehydrogenation reactor of an industrial unit during different periods of its operation. Obviously, the application of the mathematical model of this process provides the choice of the optimal catalyst type taking into account the composition of raw materials. Dehydrogenation catalysts differ in content of the base metal–platinum (KD1 – 1.06 wt.%, KD2 – 0.99 wt.%, and KD3 – 0.92 wt.%), Supported catalysts KD2 and KD3 apply the cordierite-Al2O3, the catalyst support KD1 – c-Al2O3. Moreover, the KD3 catalyst comprises structure-promoting additives (potassium), thereby increasing its stability. Different reaction abilities of C9–C14 alkanes in the reactions of dehydrogenation determine the optimal dehydrogenation catalyst activity corresponding to the equilibrium conditions between the reactions of coking and the hydrogenation of intermediate condensation products. In this paper, the main optimization criterion implies that the least coke is formed while the desired alkene production level is maintained by getting advantage of different raw alkanes reactivity. Fig. 5 illustrates the generalized scheme reflecting the interconnections between the target reaction and the side reactions producing the condensation monomer, i.e., the coke forming component. The scheme includes the possibility of the formation of target n-alkenes directly from initial n-alkanes by splitting hydrogen from them. According to this scheme, the condensation monomer can be formed from dienes and aromatic hydrocarbons. In this case, in the synthesis of n-alkenes, we deal with competitive reactions in which the target product (n-alkene) and the condensation monomer (aromatic hydrocarbon) are formed from the same initial components (n-alkanes) in the course of dehydrogenation and dehydrocyclization through the formation of intermediate products (dienes).

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Fig. 4. Alkene yield depending on the concentration of (a) C10, (b) C11, (c) C12, (d) C13, and (e) C14 hydrocarbons in the raw materials.

Fig. 5. Formation of the condensation monomer in the synthesis of n-alkenes.

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The constants of target and side reactions of the process of dehydrogenation relate as in the following equation: 0 km

0

¼ k  Fm;

0 kk

0

¼ k  Fk;

F k ¼ Ak  ebk C k ;

ð5Þ

where bm and bk are the poisoning coefficients for the metal and acidic sites of the catalyst respectively, Am  Ak  1,

bm ¼

1 T1

 T12

C k2  C k1

;

DT ¼ T 2  T 1 ;

ð6Þ

T2 is the compensation temperature, and Ck2 and Ck1 are the fractions of coke on a catalyst. Therefore the rate of chemical reactions on metal sites of a catalyst can be determined as follows: 0

Eij

W ij ¼ C i  kij  ebm Ck  eRT ;

E1

0

E2

0

E3

0

E4

C apoM  k3  eb3 ck  eRT ¼ C k  C H2  k4  eb4 Ck  eRT :

ð4Þ

where Fm and Fk are the deactivation functions for the metal and acidic sites respectively. Here,

F m ¼ Am  ebm C k ;

0

C apoM  k1  eb1 ck  eRT ¼ C k  C H2  k2  eb2 Ck  eRT ;

ð7Þ

where Wij is the ith hydrocarbon conversion rate in the jth reaction; Ci is the ith hydrocarbon concentration in the mixture; k is the constant of the jth chemical reaction for the ith hydrocarbon; and Eij is the ith hydrocarbon activation energy in the jth reaction. Under the equilibrium conditions of the coking and the hydrogenation of intermediate condensation products, if their main sources are aromatic hydrocarbons and dienes, the following equations are true:

Hence, the steady-state catalyst activity is determined by the total amount of coke on the catalyst surface, the raw material composition, and the hydrogen concentration. 5. Solving the technological problems with the mathematical model The model calculations allow us to conclude that the real operational mode of the KD3 catalyst did not correspond to optimal mode for the catalysts of this type (Fig. 6a–c). As for the calculated mode, the catalyst lifetime is being chosen as an optimization parameter; i.e., the coke formation on the catalyst is minimized, while the yield of the target product remains fixed at the desired level. Again, this is possible due to different reactivities of alkanes in raw stock, which contents are continuously changed. At the same yield of the target product, it is possible to decrease the process temperature profile by 10–15 °C and, accordingly, reduce the concentration of byproducts (dienes) to 0.2–0.3% instead of 0.4– 1.0 wt%, and the concentration of coke on the catalyst to 1.5–2.0 wt%. The optimization was also carried out for the KD1 catalyst (Fig. 6a_1–c_1), also showing a considerable potential for increasing the cost-effectiveness of the catalysts along with their operational lifetime. The KD1 and KD2 catalysts are out of date but the model calculations show that their optimal operational modes can also be found.

Fig. 6. Changes in the (a), (a_1) inlet temperature of dehydrogenation reactor, (b), (b_1) coke concentration and (c), (c_1) diene concentration on the catalysts (a)–(c) KD3 and (a_1)–(c_1) KD1 in their (1) optimal and (2) current operational modes, having the least coke formation as the criterion of optimization.

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exception. Therefore, it is expected that the catalyst would provide maximum output of the high-quality product. The developed computer modeling system allows testing different catalysts to choose the optimum for given technological parameters and raw stock composition [29]. In this paper three catalysts were compared – KD1, KD2, and KD3. The desired product yield determines the LAB output in the end; side product yield determines the quality LAB (the less the amount of side product the better). It is shown in Fig. 8 that KD3 is most appropriate under the given conditions as it secures highest yield of quality desired product. At the same time, the price of this catalyst is about the same as its predecessor, which makes it the best choice. 6.2. Water supply into the dehydrogenation reactor

Fig. 7. Changes in the (a) inlet temperature of reactor and (b) diene concentration in the (1) optimal and (2) current operational modes of the KD3 catalyst, having the least diene formation as the criterion of optimization.

The model calculations performed for the currently used KD3 catalyst show that its operational temperature mode maintained in the reactor is close to the optimal one, and this is testified by a sufficiently long cycle of its operation (up to 8 months instead of the average of 5–6 months). But at this duration of catalyst operation the dienes concentration becomes too high, so the catalyst mode in this process should be optimized in the direction of decreasing the byproduct concentrations (Fig. 7). One of the optimization options implies that the desired alkene yield is specified based on the chromatographic data taken at specific times. The optimal temperature, coke concentration on the catalyst, and the outlet byproduct concentrations are fitted so as to provide the required yield of the target alkenes. The model calculations show that at the same specified values for the yield of the target product, maintaining the optimal temperature reduces (up to 40 rel.% by the end of the working cycle) the dienes output, which generally determines the quality of further synthesized alkyl benzene. A twofold decrease in the concentration of the coke-forming components on the catalyst surface is also achieved, prolonging the catalyst lifetime. The capabilities of the developed software package are the following: -

-

Monitoring the plant operation, computing different parameters of LAB production including products output, temperatures, and catalyst operation characteristics. The system takes raw stock composition into account. The ability to test the performance of different catalysts. The forecasting feature. Automatic computing of different reconstruction options. Control and technical support for the plant.

6. Impact on the technology 6.1. Testing different catalysts Nowadays, the great part of every petrochemical plant’s inputs is purchasing costly catalysts. The LAB production is not an

A survey of the scientific literature and patent databases showed that many works deal with the problem of increasing the on-stream time of dehydrogenation catalysts and enhancing the selectivity of the process by metering the amount of water supplied to the reactor. Certain modes of water feed to the dehydrogenation reactor were described so as to maintain the optimum moisture content in the system, which in turn must be determined by the degree of catalyst deactivation by coke-generating compounds, the feedstock composition, and process conditions. For example, the effect of water admixture on the dehydrogenation of alkanes having a carbon number of 7–20 (mainly n-dodecane) on a platinum catalyst is studied in [18–20]. A favorable effect of the introduction of water into the reaction medium was revealed. It was recommended to supply water in an amount of 400–3000 ppm. Bloch et al. [19] reported the results of study of the effect of water on the dehydrogenation of alkanes with a higher carbon number of 10–18 (dehydrogenation of n-dodecane inclusive). Investigation of the effect of different concentrations of water in the reactor (0, 400, 1400, and 3000 ppm) showed that water reduces the initial catalyst activity, but the selectivity successively increases from 86.5% to 93.1%. It was argued that the stability of the catalyst increases in this case. The necessity of increasing the concentration of feed water with the increasing process temperature and the lowering activity of the catalyst for dehydrogenation of higher alkanes having a carbon number of 5–18 was substantiated in [20]. The optimal flow rate depends on the catalyst composition, feedstock nature, and hydrogen-rich gas flow rate. Important feature of catalysts (besides the high cost) is its lifetime which is a characteristic of each certain catalyst and can be up to 10 or 11 months in case of modern catalyst types. In the end of its lifetime the catalyst loses its characteristics due to deactivation, so it is necessary to change it. The way to extend the life time of the dehydrogenation catalyst is supplying increasing amounts of water into the reactor. We have developed the method of quantitative computing the amount of water supply and realized it in the software [30,31]. Initially water supply into dehydrogenation was at low constant level (Fig. 9). It was later determined that increasing the water supply is effective in terms of prolonging the life time of the catalyst and lowering the operating temperature while keeping the desired conversion level. The special software module allows calculating the amount of water to supply. The input parameters for the module include the operational conditions and the production targets. Coke is a product of the polymerization reactions of hydrocarbons (Fig. 2). The amount of water depends on its concentration on the surface of a catalyst, which is determined by solving the system of equations of the model. Changing the oxidation reaction conversion of amorphous coke by means of water allowing to calculate the optimal supply of water in the reactor depending on the temperature and degree of

E.V. Frantsina et al. / Chemical Engineering Journal 238 (2014) 129–139

139

Fig. 8. Yields of the desired and side products with different catalysts loaded.

optimize the process of C9–C14 n-alkane dehydrogenation on a Ptcatalyst. Software package developed by our group is integrated into the industrial control system of the target plant, allowing the engineering staff to monitor the plant operation real-time. The recommendations concerning the water supply are implemented at the industrial plant; the corresponding methods are protected by the appropriate legal documents. References

Fig. 9. Prediction calculation of the dynamics of coke buildup at fixed and increasing water flow rates.

catalyst deactivation as a basis for a method which is described in the article [32]. Calculations showed that the increased supply of water can make the lifetime of KD3 catalyst longer for up to 20%, meaning up to 390 days of operation instead of approximately 320. 7. Conclusions The offered level of mechanism formalization implies the association of hydrocarbons into reacting groups by DGr values. Reactivities of the compounds are estimated using the NDDO quantum-chemical method with the PM3 procedure. On the one hand, this level of mechanism formalization does not overload the mathematical description. On the other hand, it permits to take formation of the alkenes and dienes with double bonds in different positions into account, as well as formation of the isoalkanees. The software-implemented model of the process allows calculating the material and thermal balances of the reactor with enough accuracy, as well as investigating the influence of changes in different technological conditions on the process efficiency. The sensibility of the dehydrogenation process to changes in the raw stock contents and the technological conditions is illustrated with the use of the model developed. Therefore, the process must be conducted under the optimal conditions for present type of feedstock and the desired product yield. As shown by the calculations, the catalyst in the optimal mode is much more slowly deactivated by coke. This means a 2– 3 months increase in the operating cycle duration (initially 8 and 10 months for different types of catalysts). At the same time, the dienes concentration is decreased by 30–40% in the target product. The physicochemical analysis, kinetic modeling, and the combination of full-scale industrial and computational experiments, helped

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