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Modeling of catalytic coke formation in thermal cracking reactors
J. Anal. Appl. Pyrolysis 82 (2008) 134–139
Contents lists available at ScienceDirect
Journal of Analytical and Applied Pyrolysis journal homepage: www.elsevier.com/locate/jaap
Modeling of catalytic coke formation in thermal cracking reactors A. Mohamadalizadeh *, J. Towfighi, R. Karimzadeh Chemical Engineering Department, Tarbiat Modarres University, P.O. Box 14115-143, Tehran, Iran
A R T I C L E I N F O
A B S T R A C T
Article history: Received 24 September 2006 Accepted 17 February 2008 Available online 29 February 2008
At the start-up period, the most important mechanism in the coke production with a clean reactor surface is the catalytic mechanism. The study of this mechanism can be very useful for the better comprehension of the coke production process. In this paper, a model was designed for such a production through the utilization of a catalytic mechanism and a kinetic model, capable of interpreting the catalytic coke production on the reactor surface. For the determination of the model reliability, the experimental data related to the naphtha feed, existing in literature, were used. In addition, the constant parameters of the model, the velocity and the activation energy constants, associated to the kinetic model, were calculated. The results of the developed model were in satisfactory agreement with the experimental data. Eventually, the catalytic coke amount in comparison with the total coke production on the reactor surface and its significance were under investigation. ß 2008 Elsevier B.V. All rights reserved.
Keywords: Catalytic coke Modeling Kinetic Thermal cracking
1. Introduction The hydrocarbons thermal cracking is one of the most considerable processes in the petrochemical industries, resulting in olefin products. Among them, ethylene is the most interesting product. The undesirable product of the thermal cracking process is coke, which causes several problems in the thermal cracking reactors, and exits furnace from the process cycle. The coke deposits on the walls of the coil affect the operation of the pyrolysis coils with pressure drop increase, heat transfer reduction, hot spot and corrosion by carbonization. Several mechanisms participate in the coke production such as catalytic, homogeneous non-catalytic and heterogeneous non-catalytic mechanisms. The most significant mechanism in this production is the catalytic mechanism at the start-up period, provided that the reactor surface is clean. Studies proved that metals, present on the reactor surface, can catalyze the coke formation [1,2]. Furthermore, researchers employed a scanning-electron microscope equipped with EDAX to analyze the metal coke content [3]. Industrial cracking coils frequently contain different weight percentages of chromium, nickel and iron. In a review reported by Baker on the catalytic mechanism for the growth of carbon filaments, it was concluded that the available theories on this phenomenon failed to account for all the aspects of the experimental results [4]. Also, numerous experimental assessments, directed to the coke formation kinetics, have been published [5–7].
During the start-up of a furnace, the reacting gas mixture is in contact with the bare reactor walls. The filaments’ production mechanism includes the attraction of the hydrocarbon molecules on the surface and the production of carbon atoms. Initially, a hydrocarbon molecule is chemisorbed on the metal crystallite on the surface and by a surface reaction it is converted to coke. Carbon atoms, thus, are dissolved and diffused through the metal particles. By accumulation of these atoms in the metal crystals and by tension, the metal particles are plucked from the surface. In the next steps of the process, these particles may act as active sites in the catalytic coke production. As more carbon is deposited, a carbon filament is formed, carrying metal particles on top of it [8]. The carbon precipitation can give rise to structural deficiency in the carbon lattice, creating reactive carbon centers along the filament skin [9]. The hydrocarbon radicals and molecules from the gas phase are incorporated in these reactive sites, where lateral growth of the filaments occurs. As a consequence, a porous layer of interwoven filaments is formed. The resulting filamentous coke often contains 1–2 wt% metal. The filamentous coke is produced at temperature values from about 400 8C up to 1050 8C [10]. The objective of this study was the introduction of a kinetic model, which can interpret the production of the catalytic coke on the reactor surface and investigate the catalytic coke amount. Then, this amount was compared with the total coke produce on the reactor surface and its importance was evaluated. 2. Model development
* Corresponding author. Tel.: +98 21 88011001; fax: +98 21 88005040. E-mail address: [email protected] (A. Mohamadalizadeh). 0165-2370/$ – see front matter ß 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jaap.2008.02.006
The coke production rate through a catalytic and non-catalytic mechanism, in accordance with the process duration and with the
A. Mohamadalizadeh et al. / J. Anal. Appl. Pyrolysis 82 (2008) 134–139
135
Nomenclature A BC c C CS E e, f, g K rc S t X Y
rate of non-catalytic coke production (mg/m2 h) initial rate of catalytic coke production (mg/ m2 h) reduction constant of catalytic coke (h1) carbon which diffuses into the metal crystal catalytic coke on the surface activation energy constants rate constant rate of coke formation (mg/m2 h) active sites time (h) hydrocarbon molecules value of coke which remain on the surface in t duration (mg/m2)
Greek symbols a dC rC
dy ¼ A þ BC ect dt
(1)
The integration of the stated equation in the condition of y = 0 and t = 0 results in Y ¼ At þ Bð1 ect Þ
(2)
In these equations rc is the coke production rate (mg/m2 h), A the rate of non-catalytic coke production (mg/m2 h), Y the coke production in the time period of t (mg/m2), BC the initial rate of catalytic coke production (mg/m2 h) and c is the reduction constant of catalytic coke (h1). For the attainment of a mechanism with a catalytic coke production, several different kinetic models have been proposed and their equation have been written and solved. The results of each model were compared with the experimental data [5] and their rate constants together with their error percentages were calculated. The experimental results, used for determining the reliability of the proposed kinetics, were extracted from Kumar and Kunzru articles and the produced coke at the beginning of the coke production process was considered as the produced catalytic coke on the surface [5,6]. In the suggested kinetics, the X factor was the coke precursor in the coke production. For each case, the X factor calculation of the rate constants was performed. Moreover, the calculation of the activation energy and the other parameters was carried out. Regarding the Arrhenius equation, the k0 and E0 constants of each reaction were also calculated: k ¼ k0 eE0 =RT
(3)
The corresponding results are the following: In the first step, it was assumed that this phenomenon could be explained by the mentioned kinetic model: K1
X þ S!XS K2 XS!C þ S þ nH2
Here X is the hydrocarbon molecules, S the active sites and C is the carbon that diffuses into the metal crystal. The respective equations are listed below: r S ¼ K 1 C X C S þ K 2 C XS r XS ¼ K 1 C X C S K 2 C XS r C ¼ K 2 C XS r H2 ¼ nK 2 C XS r X ¼ K 1 C X C S
coke deposition factor, constant coke thickness (m) coke density (kg/m3)
combination of the two mechanisms, is stated by Albright and Marek [11] as follows: rc ¼
Fig. 1. Comparison of the results of the first kinetic with the experimental data.
(4)
(5)
In these equations, C was the amount of the produced catalytic coke on the surface. In Fig. 1, the resulting values for the coke production rate, deriving from the stated mechanisms, were compared with the experimental data. Fig. 1 revealed that this kinetic model could not interpret the coke production process. This conclusion was based on the consideration of the calculated error and the curve, describing the comparison of the experimental data and the values of the coke production rate. On the grounds that this model did not provide any satisfactory resulting data, a second kinetic model was developed for the catalytic coke production: k1
X þ S @ XS K2 XS!C þ S þ nH2
(6)
The respective equations for the second kinetic model are the following: 0
r S ¼ k1 C X C S þ k1 C XS þ K 2 C XS 0 r XS ¼ k1 C X C S k1 C XS K 2 C XS r C ¼ K 2 C XS r H2 ¼ nK 2 C XS 0 r X ¼ k1 C X C S þ k1 C XS
(7)
The rate constants of each equation were calculated. Here C is the amount of the produced catalytic coke on the surface. Fig. 2 summarizes the attained values for the coke production rate by the stated mechanisms. After the comparison of the experimental data, it was concluded that this kinetic model could not interpret the catalytic coke production process either. This conclusion was derived considering the same criteria as in the first proposed kinetic model. Consequently, the design of a third kinetic model for the description of this process became necessary. This third kinetic model is K1
X þ S!XS K2 XS!CS þ nH2 K3
CS!eS þ fC þ gCS
(8)
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Table 1 The calculated errors and parameters for the third kinetic Parameter
Value
K K01 K02 K03
1.42 103 5.12 102 6.41 101
E01 E02 E03
1.19 103 4.4 102 7.38 102 8.3 103 2.00 101 2.8 101 13.00
E
e f g Error%
Here CS is the produced catalytic coke amount on the surface and C is the carbon amount, which diffuses into the metal. The equations of the above kinetic model are r S ¼ K 1 C X C S þ K 3 eC CS r XS ¼ K 1 C X C S K 2 C XS r CS ¼ K 2 C X K 3 C CS þ K 3 gC CS r C ¼ K 3 fC XS r H2 ¼ K 2 nC XS r X ¼ K 1 C X C S
(9)
For this model, the rate of the catalytic coke production was considered as the rate of the CS generation. Owing to the differences between the diffused carbon amount onto the surface and the amount of the released sites, the e, f, g coefficients were used. The rate constant of these equations and also the existing error percentage were calculated. The corresponding results are listed in Table 1. In addition, the comparison between the experimental data and the calculated values for the rate of the catalytic coke production is presented in Fig. 3. Interestingly, the calculated error in this case was much lower than those of the two previous cases. It was identified that the obtained curve of the kinetic model was to conform to the experimental data. The e and f calculated values were also reasonable. In detail, the e coefficient value was smaller than that of the f coefficient. This phenomenon could be attributed to two facts. First, on the fact that the diffused carbon amount was greater compared with that of the released sites and, secondly, on the fact that the carbon initially occupied the crystal pores and, then, plucked by tension the metal particles from the surface. The calculated values for the activation energy were also within the expected range. E01 is related to the absorption equation (the first equation). Its value was negative, indicating that the equation rate reduced with the temperature increase. This point is valid for all surface absorption equations. With respect to E02, its value was positive. With the temperature increase, the rate of the second equation increased, displaying the conversion of the attracted
Fig. 2. Comparison of the results of the second kinetic with the experimental data.
Fig. 3. The comparison between the results of the third kinetic and experimental data.
advanced factor into coke on the surface. Finally, E03 presented a positive value, disclosing that with the temperature increase, the carbon sedimentation into the crystal increased. The K1, K2, K3 values were calculated in a specified temperature. For example, the temperature of the experimental data (1083 K) were K1 = 2466, K2 = 418, K3 = 45. It is evident that the K3 value is smaller than the K2 value, whereas K2 is smaller than K1. The small K3 value verified that the diffusion into the crystal was the controller of the catalytic coke production rate. Therefore, another mechanism should be defined to describe the catalytic coke production more accurately. For this reason, the last kinetic model, developed for the interpretation of this production, was K1
X þ S @ XS K2 XS!CS þ nH2
(10)
K3
CS!eS þ fC þ gCS The equations of the fourth kinetic model are as follows: 0
r S ¼ k1 C X C S þ k1 C XS þ K 3 eC CS 0 r XS ¼ k1 C X C S k1 C XS K 2 C XS r CS ¼ K 2 C XS K 3 C CS r C ¼ K 3 fC CS r H2 ¼ nK 2 C XS 0 r X ¼ k1 C X C S þ k1 C XS
(11)
The difference between this kinetic model and the third kinetic model was that the first reaction had been assumed to be reversible. Similarly to the previous model, in these equations, CS is the produced carbon amount on the surface and C is the carbon amount, which diffuses into the metal crystal. The rate of the catalytic coke production was regarded to be the rate of the CS production. Furthermore, the e, f, g coefficients were employed, due to the difference between the diffused carbon and the released sites. The constant values and the calculated error for the fourth model are depicted in Table 2. Apparently, in this model, the calculated error value is smaller compared with the former model. Also, the conformity of the experimental results and the results of this kinetic model are displayed in Fig. 4. In agreement with the third model, the calculated values for the e and f coefficients were found to be reasonable with the e coefficient being smaller than the f coefficient, indicating that the diffused carbon amount was higher than that of the released sites. In the final model, the calculated values for the activation energy were also found to be in a reasonable range. At first, E01, which is associated to the absorption reaction, illustrated a negative value. Subsequently, the reaction rate would diminish, if the temperature increased. This observation is true for all surface absorption
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137
Table 2 Parameters and calculated error for the fourth kinetic Parameter
Value
K K01 0 k01 K02 K03
2.14 103 2.60 1011 6.26 101 4.91 101
E E01 E001 E02 E03 e f g Error%
1.16 103 1.32 104 7.48 103 7.34 103 1.07 101 0.2 1.82 101 3.8
Fig. 5. The attraction rate of coke precursor by time.
Fig. 4. The comparison of the results of the fourth kinetic with experimental data.
reactions. Secondly, the E01 value was positive, disclosing that in repulsive reactions if the temperature increased, the rate would increase, as well. Thirdly, the E02 value was also positive, revealing that during a temperature increase, the conversion of the attracted advanced factor into coke on the surface would raise. Eventually, the E03 positive value demonstrated that the carbon sedimentation in the crystal would increase by increasing the temperature. 0 As in the previous model, the k1, k1 , K2 and K3 values were 0 14 calculated k1 = 3657, k1 ¼ 5:7 10 , K2 = 62 and K3 = 49. 0 The k1 resulting value in contrast with the k1 value is considerably smaller, exhibiting that the rate of the forward reaction is much higher than the rate of the reverse reaction. In fact, this result was expected from the first reaction, meaning that in the case of the advanced factor attraction of the coke production, the probability of its repulse from the surface was very low. Here, also the K3 value was smaller than the K2 and k1 values, confirming that the crystal diffusion consisted of the controller factor for the rate of the catalytic coke production.
decrease of the active sites, being the place of the coke attraction, the attraction rate of the precursor reduced. Moreover, this process was investigated in a longer period in order to observe the way that the developed model would change in a longer time frame and the way that it would predict each parameter. It was desirable to predict the attraction of the coke precursor on the surface. In Fig. 6, where these changes are summarized, the production rate constantly diminished until it reached the minimum level. At this point, the catalytic coke coverage was at the maximum surface. After the carbon diffusion into the surface, the tension application, the release of some metal atoms and their diffusion into the coke surface, the coke production gradually increased until it reached a constant level. Thereby, some of the metallic atoms (even though in a small quantity) regularly approached the surface, creating active sites for the attraction of the advanced factors for the coke production. Some investigations on the diffused carbon amount onto the surface were conducted. Fig. 7 presents that at the beginning of the coke production process, because of the crystal pores, the produced coke amount on the surface was partly diffused onto it. When the time elapsed, a higher carbon production took place on the surface and its sedimentation increased. However, when the pores were
3. Results and discussion After the examination of these four kinetic models, the fourth model was concluded to be the optimum one for the comprehension of the under study production. The next step was to discover how this kinetic model could explain the changes of the other factors, involved in this reaction, and their respective effects in this production. The curve of the coke precursor, attracted into the surface, is illustrated in Fig. 5. As it can be observed, the attraction and production rate of the attracted factor displays a descending curve, due to the occupation of the tubes surface by coke and the active sites reduction on the surface during the passage of time. With the
Fig. 6. The attraction rate of coke precursor for a longer period.
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Fig. 9. The density of the active sites in comparison to the first mode. Fig. 7. Carbon diffusion rate into the surface.
filled, the carbon diffusion into the crystal reduced and the curve declined towards zero. Also, the diffused carbon amount onto the surface was also examined and the associated curve is illustrated in Fig. 8. Clearly, when the coke production process begins the diffused carbon amount increases until the free space in the crystal is occupied. Eventually, this amount reaches a stable value. This model was related to the time that the coke production process had not yet begun. As it was expected, with the pass of the time the active sites reduced on the surface because of the coke coverage. The amount of the active sites was descending as well as the rate of the catalytic coke production, which was descending exponentially, and it showed the descending progress of the active sites in the coke production (Fig. 9). The results of the investigation of catalytic coke produced in the longer period can be predicted. In Fig. 10 the changes for a longer period are shown. As it is observed the rate of catalytic coke production constantly decreases till it reaches the minimum. Here the catalytic coke coverage on the surface is maximum but by time passing and carbon diffusion into the surface and tension, some of the released metal atoms are diffused into the coke surface and act as active sites. In this way the coke production process again
Fig. 8. Amount of diffused carbon into the surface.
gradually increases till it reaches a constant value. At this point some of the metal (even though small quantity) regularly reaches the surface and act as active sites for coke precursor attraction and catalytic coke production. Because of the hydrocarbons plurality, the coke was expected to be produced by other molecules under similar kinetic model. K 11
X þ S @ XS K 12
X þ S @ XS .. . K 1n
X þ S @ XS K 21
X 1 S!C 1 S þ nH2 K 22
X 2 S!C 2 S þ nH2 .. . K 2n
X n S!C n S þ nH2 K 31
C 1 S!e1 S þ f 1 C þ g 1 S K 32
C 2 S!e2 S þ f 2 C þ g 2 S .. . K 3n
C n S!en S þ f n C þ g n S
Fig. 10. The coke production rate for a longer period.
(12)
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139
start-up stage, when the reactor surface was clean, the catalytic mechanism was the main mechanism. However, when the surface was covered by coke, its importance diminished and its effect on the coke production process became weaker. 4. Conclusion Owing to the carbon coverage on the surface and the pores of the metallic crystals, the amount of metals reaching the surface would be lower than the diffused carbon. Eventually, with the pass of time the coke production was reduced.
Fig. 11. Catalytic coke produced on the tube surface of thermal cracking reactor (Arak petrochemical company).
Four heterogeneous models were studied with the fourth one providing the best results: k1
X þ S @ XS K2 XS!CS þ nH2 K3
CS!eS þ fC þ gCS
Fig. 12. Coke produced on the tube surface of thermal cracking reactor (Arak petrochemical company).
Here each X1, X2, . . . Xn may symbolize one of the coke precursors in the catalytic coke production. 3.1. The comparison of the catalytic coke amount with the total amount of the produced coke For this comparison, the thickness calculations of the produced coke on the tubes (Arak petrochemical company) were prepared with the SHAHAB software (produced by the TMU Olefin Research Group). The produced coke thickness was calculated on the reactor surface in a certain time period with the aid of the equation below [12]: DdC ¼
aMC r C Dt rC
(13) 3
In this equation a = 1.3, rC = 1500 kg/m , MC = 130 kg/kmol and dC is coke thickness. The catalytic coke, produced at the 45 m of the reactor length, is depicted in Fig. 11. Fig. 12 displays the curve representing the produced coke thickness with the total mechanisms of the coke production on the tube surface of the thermal cracking reactor. The thickness comparison of the produced coke in these two conditions revealed that the thickness of the produced catalytic coke on the surface was much smaller than the total amount of the produced coke on the reactor surface. This phenomenon could be attributed to the effect of the catalytic mechanism. During the
The rate of the forward reaction was much higher than the rate of the reverse reaction. In fact, this phenomenon was expected from the first reaction, to be more exact, in the case of the attraction of the advanced factor of the coke production, the probability of its repulse from the surface was very low. The K3 value was smaller than the K2 and k1 values, indicating that the crystal diffusion was the controller factor of the catalytic coke production rate. At the beginning of the coke production process, because of the crystal pores, some of the produced coke amount on the surface was diffused into it. Afterwards, a greater carbon production took place on the surface and its sedimentation increased. In the end, when the pores were filled, the carbon diffusion into the crystal diminished. The rate of the catalytic coke production constantly reduced until it reached its minimum value. After the carbon diffusion into the surface and the tension application, some of the released metal atoms were diffused into the coke surface, consisting of active sites. In this way, the coke production process again gradually increased up to a constant value. At this point, a small metal quantity could regularly approach the surface, creating active sites for the coke precursor attraction and the catalytic coke production. The catalytic coke modeling is of great importance for the startup process. All the same, in the total procedure of the coke production it has a limited role.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
L.F. Albright, C.F. McConnell, ACS Symp. Ser. 183 (1979) 205. R.T.K. Baker, D.J.C. Yates, J.A. Dumesic, ACS Symp. Ser. 202 (1982) 1. L.F. Albright, C.F. McConnell, K. Welther, ACS Symp. Ser. 183 (1979) 175. R.T.K. Baker, Carbon 27 (1989) 315. P. Kumar, D. Kunzru, Can. J. Chem. Eng. 63 (1985) 598. P. Kumar, D. Kunzru, Can. J. Chem. Eng. 65 (1987) 280. D. Sahu, D. Kunzru, Can. J. Chem. Eng. 66 (1988) 808. J. Towfighi, M. Sadrameli, A. Niaei, M.S. Masoumi, in: Proceedings of the International Conference on Computational Science, vol. 1, 2002, p. 723. A. Lacava, E. Fernandez, L. Isaacs, M. Caraballo, ACS Symp. Ser. 202 (1982) 89. L.F. Albright, J.C. Marek, Ind. Eng. Chem. Res. 27 (1988) 743. L.F. Albright, J.C. Marek, Ind. Eng. Chem. Res. 27 (1988) 751. R.S. Huntrods, J.A. Nighswander, A.K. Mehrotra, L. Behie, Chem. Eng. Res. Des. 67 (1989) 632.
Contents lists available at ScienceDirect
Journal of Analytical and Applied Pyrolysis journal homepage: www.elsevier.com/locate/jaap
Modeling of catalytic coke formation in thermal cracking reactors A. Mohamadalizadeh *, J. Towfighi, R. Karimzadeh Chemical Engineering Department, Tarbiat Modarres University, P.O. Box 14115-143, Tehran, Iran
A R T I C L E I N F O
A B S T R A C T
Article history: Received 24 September 2006 Accepted 17 February 2008 Available online 29 February 2008
At the start-up period, the most important mechanism in the coke production with a clean reactor surface is the catalytic mechanism. The study of this mechanism can be very useful for the better comprehension of the coke production process. In this paper, a model was designed for such a production through the utilization of a catalytic mechanism and a kinetic model, capable of interpreting the catalytic coke production on the reactor surface. For the determination of the model reliability, the experimental data related to the naphtha feed, existing in literature, were used. In addition, the constant parameters of the model, the velocity and the activation energy constants, associated to the kinetic model, were calculated. The results of the developed model were in satisfactory agreement with the experimental data. Eventually, the catalytic coke amount in comparison with the total coke production on the reactor surface and its significance were under investigation. ß 2008 Elsevier B.V. All rights reserved.
Keywords: Catalytic coke Modeling Kinetic Thermal cracking
1. Introduction The hydrocarbons thermal cracking is one of the most considerable processes in the petrochemical industries, resulting in olefin products. Among them, ethylene is the most interesting product. The undesirable product of the thermal cracking process is coke, which causes several problems in the thermal cracking reactors, and exits furnace from the process cycle. The coke deposits on the walls of the coil affect the operation of the pyrolysis coils with pressure drop increase, heat transfer reduction, hot spot and corrosion by carbonization. Several mechanisms participate in the coke production such as catalytic, homogeneous non-catalytic and heterogeneous non-catalytic mechanisms. The most significant mechanism in this production is the catalytic mechanism at the start-up period, provided that the reactor surface is clean. Studies proved that metals, present on the reactor surface, can catalyze the coke formation [1,2]. Furthermore, researchers employed a scanning-electron microscope equipped with EDAX to analyze the metal coke content [3]. Industrial cracking coils frequently contain different weight percentages of chromium, nickel and iron. In a review reported by Baker on the catalytic mechanism for the growth of carbon filaments, it was concluded that the available theories on this phenomenon failed to account for all the aspects of the experimental results [4]. Also, numerous experimental assessments, directed to the coke formation kinetics, have been published [5–7].
During the start-up of a furnace, the reacting gas mixture is in contact with the bare reactor walls. The filaments’ production mechanism includes the attraction of the hydrocarbon molecules on the surface and the production of carbon atoms. Initially, a hydrocarbon molecule is chemisorbed on the metal crystallite on the surface and by a surface reaction it is converted to coke. Carbon atoms, thus, are dissolved and diffused through the metal particles. By accumulation of these atoms in the metal crystals and by tension, the metal particles are plucked from the surface. In the next steps of the process, these particles may act as active sites in the catalytic coke production. As more carbon is deposited, a carbon filament is formed, carrying metal particles on top of it [8]. The carbon precipitation can give rise to structural deficiency in the carbon lattice, creating reactive carbon centers along the filament skin [9]. The hydrocarbon radicals and molecules from the gas phase are incorporated in these reactive sites, where lateral growth of the filaments occurs. As a consequence, a porous layer of interwoven filaments is formed. The resulting filamentous coke often contains 1–2 wt% metal. The filamentous coke is produced at temperature values from about 400 8C up to 1050 8C [10]. The objective of this study was the introduction of a kinetic model, which can interpret the production of the catalytic coke on the reactor surface and investigate the catalytic coke amount. Then, this amount was compared with the total coke produce on the reactor surface and its importance was evaluated. 2. Model development
* Corresponding author. Tel.: +98 21 88011001; fax: +98 21 88005040. E-mail address: [email protected] (A. Mohamadalizadeh). 0165-2370/$ – see front matter ß 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jaap.2008.02.006
The coke production rate through a catalytic and non-catalytic mechanism, in accordance with the process duration and with the
A. Mohamadalizadeh et al. / J. Anal. Appl. Pyrolysis 82 (2008) 134–139
135
Nomenclature A BC c C CS E e, f, g K rc S t X Y
rate of non-catalytic coke production (mg/m2 h) initial rate of catalytic coke production (mg/ m2 h) reduction constant of catalytic coke (h1) carbon which diffuses into the metal crystal catalytic coke on the surface activation energy constants rate constant rate of coke formation (mg/m2 h) active sites time (h) hydrocarbon molecules value of coke which remain on the surface in t duration (mg/m2)
Greek symbols a dC rC
dy ¼ A þ BC ect dt
(1)
The integration of the stated equation in the condition of y = 0 and t = 0 results in Y ¼ At þ Bð1 ect Þ
(2)
In these equations rc is the coke production rate (mg/m2 h), A the rate of non-catalytic coke production (mg/m2 h), Y the coke production in the time period of t (mg/m2), BC the initial rate of catalytic coke production (mg/m2 h) and c is the reduction constant of catalytic coke (h1). For the attainment of a mechanism with a catalytic coke production, several different kinetic models have been proposed and their equation have been written and solved. The results of each model were compared with the experimental data [5] and their rate constants together with their error percentages were calculated. The experimental results, used for determining the reliability of the proposed kinetics, were extracted from Kumar and Kunzru articles and the produced coke at the beginning of the coke production process was considered as the produced catalytic coke on the surface [5,6]. In the suggested kinetics, the X factor was the coke precursor in the coke production. For each case, the X factor calculation of the rate constants was performed. Moreover, the calculation of the activation energy and the other parameters was carried out. Regarding the Arrhenius equation, the k0 and E0 constants of each reaction were also calculated: k ¼ k0 eE0 =RT
(3)
The corresponding results are the following: In the first step, it was assumed that this phenomenon could be explained by the mentioned kinetic model: K1
X þ S!XS K2 XS!C þ S þ nH2
Here X is the hydrocarbon molecules, S the active sites and C is the carbon that diffuses into the metal crystal. The respective equations are listed below: r S ¼ K 1 C X C S þ K 2 C XS r XS ¼ K 1 C X C S K 2 C XS r C ¼ K 2 C XS r H2 ¼ nK 2 C XS r X ¼ K 1 C X C S
coke deposition factor, constant coke thickness (m) coke density (kg/m3)
combination of the two mechanisms, is stated by Albright and Marek [11] as follows: rc ¼
Fig. 1. Comparison of the results of the first kinetic with the experimental data.
(4)
(5)
In these equations, C was the amount of the produced catalytic coke on the surface. In Fig. 1, the resulting values for the coke production rate, deriving from the stated mechanisms, were compared with the experimental data. Fig. 1 revealed that this kinetic model could not interpret the coke production process. This conclusion was based on the consideration of the calculated error and the curve, describing the comparison of the experimental data and the values of the coke production rate. On the grounds that this model did not provide any satisfactory resulting data, a second kinetic model was developed for the catalytic coke production: k1
X þ S @ XS K2 XS!C þ S þ nH2
(6)
The respective equations for the second kinetic model are the following: 0
r S ¼ k1 C X C S þ k1 C XS þ K 2 C XS 0 r XS ¼ k1 C X C S k1 C XS K 2 C XS r C ¼ K 2 C XS r H2 ¼ nK 2 C XS 0 r X ¼ k1 C X C S þ k1 C XS
(7)
The rate constants of each equation were calculated. Here C is the amount of the produced catalytic coke on the surface. Fig. 2 summarizes the attained values for the coke production rate by the stated mechanisms. After the comparison of the experimental data, it was concluded that this kinetic model could not interpret the catalytic coke production process either. This conclusion was derived considering the same criteria as in the first proposed kinetic model. Consequently, the design of a third kinetic model for the description of this process became necessary. This third kinetic model is K1
X þ S!XS K2 XS!CS þ nH2 K3
CS!eS þ fC þ gCS
(8)
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Table 1 The calculated errors and parameters for the third kinetic Parameter
Value
K K01 K02 K03
1.42 103 5.12 102 6.41 101
E01 E02 E03
1.19 103 4.4 102 7.38 102 8.3 103 2.00 101 2.8 101 13.00
E
e f g Error%
Here CS is the produced catalytic coke amount on the surface and C is the carbon amount, which diffuses into the metal. The equations of the above kinetic model are r S ¼ K 1 C X C S þ K 3 eC CS r XS ¼ K 1 C X C S K 2 C XS r CS ¼ K 2 C X K 3 C CS þ K 3 gC CS r C ¼ K 3 fC XS r H2 ¼ K 2 nC XS r X ¼ K 1 C X C S
(9)
For this model, the rate of the catalytic coke production was considered as the rate of the CS generation. Owing to the differences between the diffused carbon amount onto the surface and the amount of the released sites, the e, f, g coefficients were used. The rate constant of these equations and also the existing error percentage were calculated. The corresponding results are listed in Table 1. In addition, the comparison between the experimental data and the calculated values for the rate of the catalytic coke production is presented in Fig. 3. Interestingly, the calculated error in this case was much lower than those of the two previous cases. It was identified that the obtained curve of the kinetic model was to conform to the experimental data. The e and f calculated values were also reasonable. In detail, the e coefficient value was smaller than that of the f coefficient. This phenomenon could be attributed to two facts. First, on the fact that the diffused carbon amount was greater compared with that of the released sites and, secondly, on the fact that the carbon initially occupied the crystal pores and, then, plucked by tension the metal particles from the surface. The calculated values for the activation energy were also within the expected range. E01 is related to the absorption equation (the first equation). Its value was negative, indicating that the equation rate reduced with the temperature increase. This point is valid for all surface absorption equations. With respect to E02, its value was positive. With the temperature increase, the rate of the second equation increased, displaying the conversion of the attracted
Fig. 2. Comparison of the results of the second kinetic with the experimental data.
Fig. 3. The comparison between the results of the third kinetic and experimental data.
advanced factor into coke on the surface. Finally, E03 presented a positive value, disclosing that with the temperature increase, the carbon sedimentation into the crystal increased. The K1, K2, K3 values were calculated in a specified temperature. For example, the temperature of the experimental data (1083 K) were K1 = 2466, K2 = 418, K3 = 45. It is evident that the K3 value is smaller than the K2 value, whereas K2 is smaller than K1. The small K3 value verified that the diffusion into the crystal was the controller of the catalytic coke production rate. Therefore, another mechanism should be defined to describe the catalytic coke production more accurately. For this reason, the last kinetic model, developed for the interpretation of this production, was K1
X þ S @ XS K2 XS!CS þ nH2
(10)
K3
CS!eS þ fC þ gCS The equations of the fourth kinetic model are as follows: 0
r S ¼ k1 C X C S þ k1 C XS þ K 3 eC CS 0 r XS ¼ k1 C X C S k1 C XS K 2 C XS r CS ¼ K 2 C XS K 3 C CS r C ¼ K 3 fC CS r H2 ¼ nK 2 C XS 0 r X ¼ k1 C X C S þ k1 C XS
(11)
The difference between this kinetic model and the third kinetic model was that the first reaction had been assumed to be reversible. Similarly to the previous model, in these equations, CS is the produced carbon amount on the surface and C is the carbon amount, which diffuses into the metal crystal. The rate of the catalytic coke production was regarded to be the rate of the CS production. Furthermore, the e, f, g coefficients were employed, due to the difference between the diffused carbon and the released sites. The constant values and the calculated error for the fourth model are depicted in Table 2. Apparently, in this model, the calculated error value is smaller compared with the former model. Also, the conformity of the experimental results and the results of this kinetic model are displayed in Fig. 4. In agreement with the third model, the calculated values for the e and f coefficients were found to be reasonable with the e coefficient being smaller than the f coefficient, indicating that the diffused carbon amount was higher than that of the released sites. In the final model, the calculated values for the activation energy were also found to be in a reasonable range. At first, E01, which is associated to the absorption reaction, illustrated a negative value. Subsequently, the reaction rate would diminish, if the temperature increased. This observation is true for all surface absorption
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Table 2 Parameters and calculated error for the fourth kinetic Parameter
Value
K K01 0 k01 K02 K03
2.14 103 2.60 1011 6.26 101 4.91 101
E E01 E001 E02 E03 e f g Error%
1.16 103 1.32 104 7.48 103 7.34 103 1.07 101 0.2 1.82 101 3.8
Fig. 5. The attraction rate of coke precursor by time.
Fig. 4. The comparison of the results of the fourth kinetic with experimental data.
reactions. Secondly, the E01 value was positive, disclosing that in repulsive reactions if the temperature increased, the rate would increase, as well. Thirdly, the E02 value was also positive, revealing that during a temperature increase, the conversion of the attracted advanced factor into coke on the surface would raise. Eventually, the E03 positive value demonstrated that the carbon sedimentation in the crystal would increase by increasing the temperature. 0 As in the previous model, the k1, k1 , K2 and K3 values were 0 14 calculated k1 = 3657, k1 ¼ 5:7 10 , K2 = 62 and K3 = 49. 0 The k1 resulting value in contrast with the k1 value is considerably smaller, exhibiting that the rate of the forward reaction is much higher than the rate of the reverse reaction. In fact, this result was expected from the first reaction, meaning that in the case of the advanced factor attraction of the coke production, the probability of its repulse from the surface was very low. Here, also the K3 value was smaller than the K2 and k1 values, confirming that the crystal diffusion consisted of the controller factor for the rate of the catalytic coke production.
decrease of the active sites, being the place of the coke attraction, the attraction rate of the precursor reduced. Moreover, this process was investigated in a longer period in order to observe the way that the developed model would change in a longer time frame and the way that it would predict each parameter. It was desirable to predict the attraction of the coke precursor on the surface. In Fig. 6, where these changes are summarized, the production rate constantly diminished until it reached the minimum level. At this point, the catalytic coke coverage was at the maximum surface. After the carbon diffusion into the surface, the tension application, the release of some metal atoms and their diffusion into the coke surface, the coke production gradually increased until it reached a constant level. Thereby, some of the metallic atoms (even though in a small quantity) regularly approached the surface, creating active sites for the attraction of the advanced factors for the coke production. Some investigations on the diffused carbon amount onto the surface were conducted. Fig. 7 presents that at the beginning of the coke production process, because of the crystal pores, the produced coke amount on the surface was partly diffused onto it. When the time elapsed, a higher carbon production took place on the surface and its sedimentation increased. However, when the pores were
3. Results and discussion After the examination of these four kinetic models, the fourth model was concluded to be the optimum one for the comprehension of the under study production. The next step was to discover how this kinetic model could explain the changes of the other factors, involved in this reaction, and their respective effects in this production. The curve of the coke precursor, attracted into the surface, is illustrated in Fig. 5. As it can be observed, the attraction and production rate of the attracted factor displays a descending curve, due to the occupation of the tubes surface by coke and the active sites reduction on the surface during the passage of time. With the
Fig. 6. The attraction rate of coke precursor for a longer period.
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Fig. 9. The density of the active sites in comparison to the first mode. Fig. 7. Carbon diffusion rate into the surface.
filled, the carbon diffusion into the crystal reduced and the curve declined towards zero. Also, the diffused carbon amount onto the surface was also examined and the associated curve is illustrated in Fig. 8. Clearly, when the coke production process begins the diffused carbon amount increases until the free space in the crystal is occupied. Eventually, this amount reaches a stable value. This model was related to the time that the coke production process had not yet begun. As it was expected, with the pass of the time the active sites reduced on the surface because of the coke coverage. The amount of the active sites was descending as well as the rate of the catalytic coke production, which was descending exponentially, and it showed the descending progress of the active sites in the coke production (Fig. 9). The results of the investigation of catalytic coke produced in the longer period can be predicted. In Fig. 10 the changes for a longer period are shown. As it is observed the rate of catalytic coke production constantly decreases till it reaches the minimum. Here the catalytic coke coverage on the surface is maximum but by time passing and carbon diffusion into the surface and tension, some of the released metal atoms are diffused into the coke surface and act as active sites. In this way the coke production process again
Fig. 8. Amount of diffused carbon into the surface.
gradually increases till it reaches a constant value. At this point some of the metal (even though small quantity) regularly reaches the surface and act as active sites for coke precursor attraction and catalytic coke production. Because of the hydrocarbons plurality, the coke was expected to be produced by other molecules under similar kinetic model. K 11
X þ S @ XS K 12
X þ S @ XS .. . K 1n
X þ S @ XS K 21
X 1 S!C 1 S þ nH2 K 22
X 2 S!C 2 S þ nH2 .. . K 2n
X n S!C n S þ nH2 K 31
C 1 S!e1 S þ f 1 C þ g 1 S K 32
C 2 S!e2 S þ f 2 C þ g 2 S .. . K 3n
C n S!en S þ f n C þ g n S
Fig. 10. The coke production rate for a longer period.
(12)
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start-up stage, when the reactor surface was clean, the catalytic mechanism was the main mechanism. However, when the surface was covered by coke, its importance diminished and its effect on the coke production process became weaker. 4. Conclusion Owing to the carbon coverage on the surface and the pores of the metallic crystals, the amount of metals reaching the surface would be lower than the diffused carbon. Eventually, with the pass of time the coke production was reduced.
Fig. 11. Catalytic coke produced on the tube surface of thermal cracking reactor (Arak petrochemical company).
Four heterogeneous models were studied with the fourth one providing the best results: k1
X þ S @ XS K2 XS!CS þ nH2 K3
CS!eS þ fC þ gCS
Fig. 12. Coke produced on the tube surface of thermal cracking reactor (Arak petrochemical company).
Here each X1, X2, . . . Xn may symbolize one of the coke precursors in the catalytic coke production. 3.1. The comparison of the catalytic coke amount with the total amount of the produced coke For this comparison, the thickness calculations of the produced coke on the tubes (Arak petrochemical company) were prepared with the SHAHAB software (produced by the TMU Olefin Research Group). The produced coke thickness was calculated on the reactor surface in a certain time period with the aid of the equation below [12]: DdC ¼
aMC r C Dt rC
(13) 3
In this equation a = 1.3, rC = 1500 kg/m , MC = 130 kg/kmol and dC is coke thickness. The catalytic coke, produced at the 45 m of the reactor length, is depicted in Fig. 11. Fig. 12 displays the curve representing the produced coke thickness with the total mechanisms of the coke production on the tube surface of the thermal cracking reactor. The thickness comparison of the produced coke in these two conditions revealed that the thickness of the produced catalytic coke on the surface was much smaller than the total amount of the produced coke on the reactor surface. This phenomenon could be attributed to the effect of the catalytic mechanism. During the
The rate of the forward reaction was much higher than the rate of the reverse reaction. In fact, this phenomenon was expected from the first reaction, to be more exact, in the case of the attraction of the advanced factor of the coke production, the probability of its repulse from the surface was very low. The K3 value was smaller than the K2 and k1 values, indicating that the crystal diffusion was the controller factor of the catalytic coke production rate. At the beginning of the coke production process, because of the crystal pores, some of the produced coke amount on the surface was diffused into it. Afterwards, a greater carbon production took place on the surface and its sedimentation increased. In the end, when the pores were filled, the carbon diffusion into the crystal diminished. The rate of the catalytic coke production constantly reduced until it reached its minimum value. After the carbon diffusion into the surface and the tension application, some of the released metal atoms were diffused into the coke surface, consisting of active sites. In this way, the coke production process again gradually increased up to a constant value. At this point, a small metal quantity could regularly approach the surface, creating active sites for the coke precursor attraction and the catalytic coke production. The catalytic coke modeling is of great importance for the startup process. All the same, in the total procedure of the coke production it has a limited role.
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