Format And Type Fonts CCHHEEMMIICCAALL EENNGGIINNEEEERRIINNGG TTRRAANNSSAACCTTIIOONNSS VOL. 39, 2014 A publication of The Italian Association of Chemical Engineering www.aidic.it/cet Guest Editors: Petar Sabev Varbanov, Jiří Jaromír Klemeš, Peng Yen Liew, Jun Yow Yong Copyright © 2014, AIDIC Servizi S.r.l., ISBN 978-88-95608-30-3; ISSN 2283-9216 DOI:10.3303/CET1439169 Please cite this article as: Gartman T.N., Sovetin F.S., Proskuro E.A., Shvets V.F., Kozlovskiy R.A., Suchkov Y.P., Sapunov V.N., Loktev A.S., Levchenko D.A., Dedov A.G., 2014, Computation of the solid catalyzed gas phase reactions with a simultaneous choice of the scheme of the reactions for different composition of the initial reaction mixture, Chemical Engineering Transactions, 39, 1009-1014 DOI:10.3303/CET1439169 1009 Computation of the Solid Catalyzed Gas Phase Reactions with a Simultaneous Choice of the Scheme of the Reactions for Different Composition of the Initial Reaction Mixture Tamas N. Gartman a *, Filipp S. Sovetin a , Ekaterina A .Proskuro a , Valeriy F. Shvets a , Roman A. Kozlovskiy a , Yuriy P. Suchkov a , Valentine N. Sapunov a , Alexey S. Loktev b , Darya A. Levchenko b , Alexey G. Dedov b a Mendeleyev University of Chemical Technology of Russia, Miusskaya sq. 9, Moscow, 125047, Russian Federation b Gubkin Russian State University of Oil and Gas, Leninskiy Prospect, 65/1, 119991, Moscow, Russian Federation tngartman@gmail.com One of the features of the industrial heterogeneous catalytic reactions is an influence of qualitative and quantitative composition of the initial reaction mixture on the reactions proceeded. At the stage of the laboratory experiments it is possible to find the stoichiometry, kinetic equations and reaction constants for different components of the initial flow of the raw materials. It is important also to take into account multivariant composition of the initial flows. For these purposes we developed and realized an algorithm for using the model with a simultaneous choice of model equations depending on the composition of the initial reaction mixture. The algorithm was checked on the basis of an example of the aromatization of light alkanes with the different composition of the initial mixture. 1. Introduction Solving of the problems of investigation, optimization and design of the catalytic reactors is based on developing of the models of the chemical transformations and determination of the rate constants of the corresponding reactions. One of the characteristics of the process of developing of the models of the industrial reactors is the need for taking into account a variation of the composition, pressure and temperature of the raw materials in the reactor input (Chistyakov et al., 2013). Variation of these parameters of the initial flow gives different quality and quantity composition of the reaction products (House, 2007). These features are necessary to take into account both in the laboratory investigations and in the process of design of the mathematical model (Gartman and Klushin, 2008). For this reason, it is desirable to carry out experiments in the wide range of parameters of the raw materials and to take into account a variation of the composition of the initial mixture in the mathematical models (Dobrynkin et al., 2012). There is important in this case to develop an algorithm for solving identification task for a wide range of experimental data which includes various input parameters for reactors and allow to determine simultaneously one set of model parameters for using by simulation pilot and industrial reactor processes. Finally the mathematical model should have a complex structure with different equation systems depending on the parameters the raw’s streams of reactors (temperature, pressure and composition). This model allowed to make automatically choice between different equation systems which describes processes for inlet streams with different parameters of raw to the reactor (Gartman et al., 2014). The procedure of the mathematical model design was investigated by treatment of experimental data of processing of light alkanes into aromatics (Gartman et al., 2009). The significance of the investigated process derives from necessity of an expansion of the source of raw materials, especially cheap ones, for aromatics production. Such a source is light alkanes (for example associated gas). https://e.mail.ru/compose/?mailto=mailto%3atngartman@gmail.com http://www.lingvo-online.ru/ru/Search/Translate/GlossaryItemExtraInfo?text=%d1%81%d1%8b%d1%80%d1%8c%d0%b5%d0%b2%d0%b0%d1%8f%20%d0%b1%d0%b0%d0%b7%d0%b0&translation=source%20of%20raw%20materials&srcLang=ru&destLang=en 1010 Figure 1: The kinetic data of consumption of initial reagents and formation of products (sorted by type of hydrocarbons): symbols – experimental, lines – calculated 2. Experimental section The experiments were carried out in a laboratory tube flow isothermal reactor with a fixed-bed of the catalyst. The length of the reactor was 450 mm and diameter 10 mm. Promoted ZSM-5 was used as a catalyst. Particle size of the catalyst was 0.5 - 1 mm. Catalyst loading was 1 – 2 g. The mixture of propane (81 %) and butane (19 %), and the mixture of propane (14.8 %), butane (10.2 %), i-butane (37.2 %) and butane (36.8 %) were used as a raw material. The range of conditions were: temperature 520 – 650 o C, pressure 0.1 MPa, WHSV 0.5 – 15 g/(g∙h). The composition of the inlet and outlet mixtures was determined by GC. The experimental data on changing of reaction mixture composition in dependence of WHSV showed that the main products where: alkanes C1-C2, light olefins C3-C4 and aromatics C6-C9. The preliminary kinetic treatment of the whole array of the experimental data (46 experiments) showed that consumption of initial reagents was well described by first-order kinetics, and the products were formed by parallel-consecutive reactions (Figure 1). 3. Mathematical model of the chemical transformations On the base of the obtained data the minimal system of reactions (27 reactions) describing these transformations was proposed: 1. C3H8+ H2→ CH4 + C2H6 2. 2C4H10 + 2H2 → 2 CH4 + C2H6 3. 4C3H8 → 3C2H4 + 2C3H6 +4H2 4. 4 C4H10 → 3C2H4 +2C3H6 + C4H8 +4H2 5. C2H4 + H2→ C2H6 6. 2C3H6 +3H2→ 3C2H6 7. 3 C2H4 → C6H6 + 3H2 8. 2C3H6 → C6H6 + 3H2 9. 3C4H8→ 2C6H6 + 6H2 10. 7C2H4 → 2C6H5CH3 + 6H2 11. 7C3H6 → 3C6H5CH3 + 9H2 12. 7 C4H8 →4C6H5CH3 + 12H2 13. 4C2H4 → p-C6H4(CH3)2 + 3H2 14. 8C3H6 → 3 p -C6H4(CH3)2 + 9H2 15. 2C4H8 → p -C6H4(CH3)2 + 3H2 16. 2C3H8 → C6H6 + 5H2 17. 7C3H8 → 3C6H5CH3 + 16H2 18. 8C3H6 → 3 p -C6H4(CH3)2 + 9H2 19. 3C3H10 → 2C6H6 + 9H2 20. 7 C4H10 →4C6H5CH3 + 19H2 21. 2C4H10 → p -C6H4(CH3)2 + 5H2 22. 5 C6H6→ 3C10H8 + 3H2 23. 10 C6H5CH3→ 7C10H8 + 12H2 24. 5 p-C6H4(CH3)2 → 4C10H8 + 9H2 25. C2H6 + H2 → 2CH4 26. C4H10+H2 → C3H8 + CH4 27. C2H6 + CH4 → C3H8+H2 1011 Mathematical model of the chemical transformations was developed using the following assumptions: isothermal conditions, quasi-homogeneous kinetics and ideal gas phase. On the basis of the above scheme of the reactions the following system of twelve differential equations were used for description of all the chemical transformations including experiments with and without butane in the starting mixture: _ _ g k dm nd (1) where _ n – is the vector of mole of twelve key components, mk – is current mass of catalyst, g – is the vector of rates of formation (consumption) of the components which are determined by means of matrix equation: __ g r    , where  - given by the matrix of stoichiometric coefficients; r - are rates of the reactions. Values of r are based on the analysis of experimental data and calculated as follows: ;c;c;c;c 10410483831041048383 44332211 HCHCHCHCHCHCHCHC KkrKkrKkrKkr  ;c;c;c;c 6363424263634242 88776655 HCHCHCHCHCHCHCHC KkrKkrKkrKkr  ;c;c;c;c 8484636342428484 12121111101099 HCHCHCHCHCHCHCHC KkrKkrKkrKkr  ;c;c;c;c 8383848463634242 2 1616151514141313 HCHCHCHCHCHCHCHC KkrKkrKkrKkr  ;c;c;c;c 10410410410483838383 2 2020 2 1919 2 1818 2 1717 HCHCHCHCHCHCHCHC KkrKkrKkrKkr  10810887876666104104 c;c;c;c 242423232222 2 2121 HCHCHCHCHCHCHCHC KkrKkrKkrKkr  ;c 62622525 HCHC Kkr  ;c 1041042626 HCHC Kkr  ;c 62622727 HCHC Kkr  Where: i c – is the concentration of i-component [mass % relative to the mass of propane]; i K – is the conversion factor for the rate of the reaction to [mol/(g(cat) h)] i HC i M m K 100 )0( 83 (i = 1, 2…..m) (2) Mi – is the molar mass of i-component [g/mol]. The following equation was used for conversion of any of 27 rate constants to any other temperature:  )0(_ _ k k  , where  – is factor taking account the dependence of the rate constants on the temperature:           TT B e 11 _ 0 , where T0 = 813 K (540 o C), B – is a determined coefficient [K]. As a result, 28 coefficients )0(_ k and coefficient B of the system of differential Eq(1) were the fit parameters. Calculations were made by means of the fourth-order algorithm of Runge-Kutta and the procedure used makes it possible automatically to choose the system of the differential equation for each composition of the starting material. 1012 4. Determination of kinetic parameters of the chemical transformations The task of parametric identification of the model (system of Eq(1)) was solved simultaneously for all the three sets of experimental data with and without butene and i-butane in the starting material with the general criteria for minimization of the target function:       f u m i i calc ii S 1 1 2exp  (3) where: ωi – is mass. % of the components (starting materials and products), “calc” – calculated by model, “exp” – experimental data; m – is the number of the components (starting materials and products); f – is the number of the experimental points; α1, α2, ….. αm – are weight coefficients. After the procedure of minimization of mismatch criterion was reduced from 261,125 to 17,900 with using Generalized Least Squares methods, adequate description of experimental data was received and 28 parameters of the kinetic equations were determined: ; 1 02.0 )0( 1 h k  ; 1 05.0 )0( 2 h k  ; 1 04.0 )0( 3 h k  ; 1 01.0 )0( 4 h k  ; 1 04.0 )0( 5 h k  ; 1 09.0 )0( 6 h k  ; 1 05.0 )0( 7 h k  ; 1 05.0 )0( 8 h k  ; 1 11.0 )0( 9 h k  ; 1 03.0 )0( 10 h k  ; 1 02.0 )0( 11 h k  ; 1 05.0 )0( 12 h k  ; 1 005.0 )0( 13 h k  ; 1 004.0 )0( 14 h k  ; 1 09.0 )0( 15 h k  ; hmass. % 1 1075.4; hmass. % 1 101.25 ; hmass % 1 105.75 7-)0( 18 5-)0( 17 7-)0( 16       kk k ; h 1 0.8; h 1 1.28; h 1 0.32; h 1 0.004; h 1 0.003; h 1 0.003 ; hmass. % 1 1095.1; hmass. % 1 109; hmass. % 1 102.95 )0( 27 )0( 26 )0( 25 )0( 24 )0( 23 )0( 22 5-)0( 21 5-)0( 20 6-)0( 19        kkkkkk kkk 1)0( 28 6000   KBk Partly the results of the kinetic model reconciliation for one of the experimental point (Number 11 from the all number of 46 experimental points) listed in Table 1. Table 1: Results of the kinetic model reconciliation. Comparison of the calculated and experimental data for one of the experiments Parameter of the flows P; KPa WHSW; g/(g∙h) G; g/h t; o C 100 5.52 11.04 575 Components Input composition in % mass Output composition in % mass Calculated Data with above defined parameter set Experimental Data CH4 0.63 4.87 5.46 C2H6 1.99 8.01 3.7 C3H8 76.55 43.82 42.03 C4H10 18.03 13.63 6.78 C2H4 0 7.63 7.4 1013 Table 1 (Continued): Results of the kinetic model reconciliation. Comparison of the calculated and experimental data for one of the experiments C3H6 2.26 7.83 6.52 H2 0 1.57 1.23 C6H6 0 3.92 4.97 C7H8 0 7 9.38 C6H4(CH3)2 0 1.12 2.65 C10H8 0 0.44 0.46 In Figure 1 below the composition of the reaction mixture is presented for one of the experiment where synthesis of the aromatic compounds is proved (lines 9–12). Figure 1: The composition of the reaction mixture along the tube of the reactor in experiment from set No 1. 1 – methane, 2 – ethane, 3 – propane, 4 – butane, 5 – ethylene, 6 – propene, 7 – butene, 8 – hydrogen, 9 – benzene, 10 – toluene, 11- p-xylene, 12 – naphthaleneComputer modelling of polytrophic reactor of catalytic process of aromatization of light alkanes The pilot reactor for modeling was a tube with a fixed-bed of catalyst (mass of the catalyst was 1,000 g) with a jacket heated by furnace gas. Computer model of polytrophic reactor was developed on the basis of Eq(1) by adding the equation of the heat balance: k TR k dm dN q N q Ndm dT N T CM F C 1 pk T p  (4) Where:    27 1j j R j R rHq ; )( TTkq T TT  ; R q – is the rate of heat [J/g]; T q – is the rate of heat allocation [J/m 2 ]; R H - is the enthalpy or reaction [J/mol]; F T – is the area of heat exchange [m 2 ]; k T – is the heat- exchanger coefficient [W/(K*m 2 )]; TT – is the temperature in the shell of tube reactor; Cp – is the heat capacity [J/(mol*K)]; N – is the total number of moles in the mixture. The developed model makes it possible to take into account variation of mathematical model which depends on the composition of the initial mixture and to vary in the wide range parameters of the starting flow: feed rate in the range of 0.6 – 12 g/(g∙h), temperature in the input of the reactor in the range of 550 – 645 o C, temperature of the furnace gas in the jacket in the range of 675 – 725 o C. As it follows from the above, an increase in the temperature in the input of the reactor and in the jacked caused an increase in the aromatics content but an increase in the feed rate worked in the reverse direction. The highest overall 1014 yield of aromatics was about 40 %. It was received with the parameters of the process listed in Tables 2 & 3. Table 2: Compositions (% mass) of feed and output at WHSV = 0.6 g/(g∙h), G = 600 g/h, P = 0.1 MPa, t(input) = 600 o С Components Input Output CH4 C2H6 C3H8 C4H10 C2H4 C3H6 C4H8 H2 C6H6 C7H8 p-C6H4(CH3)2 C10H8 0 1.74 80.64 14.96 0 2.36 0.31 0 0 0 0 0 18.78 5.70 16.95 6.81 5.09 4.43 0.07 2.58 13.59 16.94 5.36 3.62 Final parameters of the process modelling in the pilot reactors are given in Table 3. Table 3: Final parameters of the process modelling Conversion of the starting material; % 71.21 Selectivity of aromatics formation; % 56.49 Yield of aromatics; % 40.22 Average heat load; MJ/h 2.08 Average temperature; o С 598 5. Conclusion The mathematical model of important industrial process of transformation of light alkanes into aromatics was designed. The model is applicable for calculating of the composition of products mixture in processing paraffines to aromatics considering 27 reactions, which were choose on the base of analysis of experimental data. Algorithm of calculation included a choose of mathematical model equation depending on the composition of the initial reaction mixture. References Chistyakov A.V., Murzin V.Yu., Gubanov M.A., Tsodikov M.V., 2013. Pd-Zn containing catalysts for ethanol conversion towards hydrocarbons, Chemical Engineering Transactions., 32, 619-624. Dobrynkin N.M., Batygina M.V., Noskov A.S., Besson M., Gallezot P., 2012. Wet air oxidation of organic acids and phenol for odour control proceses. Chemical Engineering Transactions, 30, 277-282. Gartman T.N., Sovetin F.S., Proskuro E.A., Shvets V.F., Kozlovskiy R.A., Suchkov Yu.P., Sapunov V.N., Loktev A.S., Dedov A.G., 2014. 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