Article pubs.acs.org/EF
Kinetic Modeling of Thermal Hydrocracking of a Paraffinic Feedstock Hossein Hajian and Farhad Khorasheh* Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran ABSTRACT: A kinetic model based on a mechanistic approach was developed for thermal hydrocracking of a paraffinic feedstock. The hydrocarbon feed was described as a mixture of representative molecules based on structural group analysis (SGA) where information from elemental analysis, H1, and C13-NMR of the feed were used to obtain the average concentration of various structural groups from which representative molecules were constructed. The behavior of the feedstock under reaction conditions was described in terms of the reaction of the individual molecules. The reaction of each of the representative molecules and the corresponding product distribution was based on free radical mechanisms. The product distributions from thermal hydrocracking of the feed were predicted as the sum of product distributions from each of the representative molecules and were in good agreement with experimental values.
1. INTRODUCTION The growing demands for middle distillate fuels and the limited amount of light and medium crude oil reservoirs place emphasis on development of process schemes, including hydrocracking for conversion of heavy petroleum fraction into valuable liquid products. Hydrocracking is a hydrogen addition process to convert heavier, less expensive crudes, into more valuable transportation fuels including gasoline, kerosene, and diesel. Appropriate kinetic models for hydrocracking reactions are crucial in process design considerations. Nevertheless, modeling of hydrocracking is a formidable task due to complexity and diversity of feedstock. Ideally, a kinetic model should account for the reaction of individual components present in a complex hydrocarbon feed. In practice, however, this would be cumbersome due to the presence of a great variety of structures that ultimately contribute to a very complex reaction network. To simplify this inherent complexity, different lumping schemes have been proposed. In the discrete lumping approach, components in the reaction mixture are lumped in to an appropriate number of pseudo components. A reaction network consisting of series and parallel reactions involving various lumps is constructed, and the corresponding kinetic parameters are evaluated from experimental data. Success of this approach is dependent on the number of lumps. More lumps generally lead to more accurate model predictions at the expense of more adjustable parameters. Investigations involving discrete lumping models are extensive, and the subject was recently reviewed.1 A continuous lumping model was also suggested for predicting hydrocracker yields that assumed the reaction mixture contained a continuum of pseudo components in terms of their boiling points.2 This model was used in reactor modeling, design, and control of hydrocracking reactions.3−5 An axial dispersion model utilizing the analogy between hydrocracking reactions and physical axial dispersion has also been proposed.6 Laxminarasimhan et al. (1996) developed a continuous kinetic model7 which has been applied by several investigators for modeling of hydrocracking of complex feedstocks.8−11 The main drawback of the lumped schemes is that their associated kinetic parameters are highly dependent on the type of the feedstock. Mechanistic models that are more fundamental have © XXXX American Chemical Society
been developed to overcome the shortcomings of the lumping models, albeit with extensive computations. Quann and Jaffe developed a structural oriented lumping procedure to describe molecules with vector notations and used them to generate the reaction network.12,13 Froment and co-workers as well as Schweitzer14−17 used the concept of single-events theory to describe the reaction of complex hydrocarbon mixtures by incorporating numerous elementary reaction steps and an algorithm to generate an extensive and detailed reaction network. Klein and co-workers also developed mechanistic models for complex hydrocarbon feeds with Monte Carlo simulations for different reactions.18−20 Mechanistic models at molecular level has this merit that their kinetic parameters are independent of the feed composition but have a major shortcoming due to extensive computations involving a large number of reactions for a heavy feedstock. In cracking processes, depending on the operating conditions, catalytic reactions may compete or couple with noncatalytic thermal reactions that produce reactive free radicals. At higher temperatures, thermal reactions become more important.21,22 Several investigators have studied thermal reactions during hydroprocessing of heavy oils. Ramirez et al. used a fivelumped model to study noncatalytic hydrocracking reactions of heavy oil and observed that thermal hydrocracking reactions occurred to a great extent even at moderate reaction temperatures.23 Trejo et al. studied the thermal decomposition of asphaltenes to investigate coke formation during cracking reactions.24 Martinez and Ancheyta developed a kinetic model for parallel thermal and catalytic reactions for hydroprocessing of heavy oils.25 Ramirez et al. studied the effect of reaction parameters on thermal hydrodesulfurization and demetallization of heavy crude oils.26 In the present work, a methodology is developed for modeling the thermal hydrocracking of a hydrocarbon feed in terms of a mechanistic approach for the individual reactions of a set of representative molecules that were constructed based on structural group analysis (SGA). The methodology is applied for thermal hydrocracking of a paraffinic feed in the C16 to C24 range. Received: November 14, 2015 Revised: February 20, 2016
A
DOI: 10.1021/acs.energyfuels.5b02686 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels
The gaseous products were separated from liquid products in a two stage (high and low-pressure) separator. Liquid products were characterized by simulated distillation, and gaseous products were analyzed by gas chromatography. Details of the reactor system and analyses are given elsewhere.27 Classification of products in terms of their boiling point and approximate carbon number is given in Table 1.
2. MATERIALS AND METHODS The paraffinic feedstock was obtained from a refinery stream that had been hydrotreated and the amounts of heteroatom compounds containing sulfur, nitrogen, and oxygen, as well as aromatics compounds, were negligible. The feed primarily contained linear and branched alkanes as well as substituted cycloalkanes. The physical properties and the results from simulated distillation analysis of the feed are given in Table 1. Elemental analysis of the feed indicated that
3. THEORY 3.1. Representative Molecules. The first step in the development of the kinetic model was to characterize the mixture in terms of a representatitive set of molecules. In characterization of a complex hydrocarbon mixture by structural group analysis (SGA) data from a variety of analytical techniques including elemental analysis and H1- and C13-NMR are used to describe the mixture in terms of the concentration of a selected number of structural groups.28 SGA results for the paraffinic feed used in this study are given in Table 2. Representative molecules can then be constructed by using the structural groups as building blocks in such a way that the overall characteristics of the computer-generated molecules in terms of the concentration of various structural group as well as the overall molecular weight closely resemble those of the complex mixture.29 A set of 25 representative molecules for the feed are presented in Figure 1. 3.2. Product Distributions for Representative Molecules. Thermal cracking of paraffinic hydrocarbons proceeds via a free radical chain mechanism primarily consisting of chain initiation by C−C bond cleavage, chain propagation, and chain termination involving radical combination. Product distributions are determined by the propagation reactions, and contribution of initiation and termination reactions can be neglected due to the long-chain approximation.30 Reactions that occur in the propagation step involve hydrogen abstraction, radical decomposition, and radical addition. At high pressures, bimolecular addition and abstraction reactions are favored over the unimolecular radical decomposition. Decomposition reactions, on the other hand, have higher activation energies than hydrogen abstraction and radical addition reactions and are favored at high temperatures.31 Therefore, the product distributions are affected by reaction temperature and pressure. The conditions used in this study are characterized by high pressure and low-to-moderate temperatures. For experiments at the low temperature of 440◦C,
Table 1. Physical Properties of the Feed and Classification of Productsa product classification simulated distillation results of feed IBP 10 wt % 50 wt % 90 wt % FBP
260.2 302.5 351.7 406.7 466.5
°C °C °C °C °C
name of cut gases naphtha kerosene unreacted feed
carbon number
TBP range (°C)
C1−C4 C5−C9 C10−C14 C15−C24
260
Kinematic viscosity at 40 °C: 9.86 centistokes. Density at 15.6 °C: 0.8225 g/cm3.
a
the feed had 85.7 and 14.3 wt % carbon and hydrogen, respectively. H1-NMR spectra gave only two peaks in the aliphatic region. The first peak with chemical shift of 0.9 ppm represented hydrogen in aliphatic and naphthenic methyl groups (approximately one-third of total hydrogens), while the second peak at about 1.3 ppm represented hydrogens in aliphatic and naphthenic CH and CH2 groups. No aromatic hydrogens were detected. The relative abundance of various carbon groups from C13-NMR are given in Table 2. Thermal hydrocracking experiments were conducted in a continuous flow stainless steel tubular reactor of a 1 m length and a 2 cm internal diameter operating at a total pressure of 120 bar, reaction temperatures of 440 and 470 °C, and liquid residence times in the range from 0.67 to 2.0 h. Commercial purity (96.5%) hydrogen was used in the hydrocracking experiments. The volume ratio of hydrogen to liquid hydrocarbon feed was approximately 1000:1 to ensure an excess amount of hydrogen under reaction conditions. The feed consisted primarily of saturated linear, branched, and cyclic aliphatic compounds in the C16 to C24 range with an average molecular weight of about 275. The molar ratio of hydrogen to hydrocarbon feed at the reactor inlet was approximately 1500 mol/mol. Four electrical jackets were used to heat the reactor.
Table 2. C13-NMR Analysis and SGA Results for Feed
O: bound to aliphatic carbon. B
DOI: 10.1021/acs.energyfuels.5b02686 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels
Figure 1. Representative molecules for the paraffinic feedstock.
Figure 2. Chain propagation reactions for n-C16 based on a single-step mechanism.
hydrogenated and radical addition reactions to α-olefins could also be neglected. The product distributions for the single-step mechanism of Figure 2 were by solving the following differential equations of the plug flow reactor for each molecule and radical species:
a single-step cracking mechanism was used for each of the representative molecules. In the case of n-C16 for example, the reaction network for a single-step mechanism is shown in Figure 2 where radicals generated by hydrogen abstraction from the parent molecule undergo decomposition by β-scission with the resulting smaller radicals only participating in H-abstraction reactions. Furthermore, due to the presence of excess hydrogen under high pressure conditions, olefins are rapidly
dFi = net rate of formation of species i dV C
(1)
DOI: 10.1021/acs.energyfuels.5b02686 Energy Fuels XXXX, XXX, XXX−XXX
8.13
2.28
4.04
16
25
4.23
15
24
4.02
14
7.42
5.58
13
5.04
5.15
12
23
1.15
11
22
3.10
10
3.88
6.25
9
21
3.95
8
2.63
6.70
7
20
0.32
6
2.77
3.30
5
8.14
3.53
4
19
3.39
3
18
8.48
2
6.31
2.80
1
17
C1
molecule
D
7.05
3.33
16.13
3.02
6.68
8.12
8.56
2.04
10.45
2.96
11.42
12.78
10.10
9.53
0
9.59
18.12
12.60
7.50
2.61
10.21
10.91
18.13
7.51
0
C2
13.28
12.70
9.91
8.37
0
15.31
16.14
21.08
12.93
0
22.08
29.89
14.65
0
4.31
18.08
7.77
28.80
26.43
5.75
19.24
20.56
29.46
11.65
4.69
C3
11.00
5.20
12.99
10.51
5.07
12.68
13.37
10.02
27.55
4.73
19.42
10.57
28.06
0
10.67
14.98
6.43
17.51
15.36
5.09
15.94
17.03
9.20
20.23
13.45
C4
8.85
15.12
25.09
0
5.83
10.21
10.76
13.28
21.80
7.09
19.68
0
4.73
6.33
4.50
12.05
18.02
3.89
13.72
0
12.83
13.71
0
14.51
4.88
C5
8.85
12.11
11.55
5.16
2.27
10.21
10.76
11.27
0
2.76
15.11
9.32
4.92
7.29
0
12.05
19.24
3.82
11.60
0
12.83
13.71
39.83
11.24
4.01
C6
8.85
7.04
0
2.36
1.74
10.21
10.76
0
0
2.73
8.06
11.05
5.66
3.04
0
12.05
7.80
7.19
0
0
12.83
13.71
0
13.34
0
C7
8.85
7.09
0
3.05
3.31
10.21
10.76
17.87
5.48
0
0
11.30
0
3.40
0
12.05
16.37
22.25
14.26
0
12.83
13.71
0
26.08
0
C8
8.85
8.37
0
8.68
0
10.21
10.76
16.31
12.08
0
0
11.06
26.30
0
0
12.05
0
0
8.84
0
12.83
13.71
0
13.34
0
C9
8.85
8.37
8.52
7.37
0
10.21
10.76
0
6.79
0
0
0
26.30
0
0
12.05
16.37
22.25
14.26
0
12.83
13.71
39.83
11.24
4.01
C10
8.85
8.37
8.38
5.42
0
10.21
10.76
16.31
12.08
0
0
11.06
0
3.40
0
12.05
7.80
7.19
0
0
12.83
13.71
0
14.51
4.88
C11
8.85
8.37
8.38
7.69
0
10.21
10.76
17.87
5.48
0
8.06
11.30
5.66
3.40
0
12.05
19.24
3.82
11.60
0
12.83
17.03
9.20
20.23
13.45
C12
8.85
8.37
8.52
5.42
0
10.21
10.76
0
0
0
15.11
11.05
4.92
7.29
0
12.05
18.02
3.89
13.72
0
15.94
20.56
29.46
11.65
4.69
C13
8.85
8.37
0
7.37
0
10.21
10.76
11.27
0
0
19.68
9.32
4.73
6.33
4.50
14.98
6.43
17.51
15.36
5.09
19.24
10.91
18.13
7.51
0
C14
8.85
8.37
0
8.68
0
10.21
10.76
13.28
21.80
2.73
19.42
0
28.06
0
10.67
18.08
7.77
28.80
26.43
5.75
10.21
3.53
3.39
8.48
2.80
C15
8.85
7.09
0
3.05
3.31
10.21
13.37
10.02
27.55
2.76
22.08
10.57
14.65
0
4.31
9.59
18.12
12.60
7.50
2.61
3.30
0
0
0
70.17
C16
Table 3. Stoichiometric Coefficients for Representative Molecules at 440°C (mol/100 mol of Paraffin Decomposed)
8.85
7.04
11.55
2.36
1.74
12.68
16.14
21.08
12.93
7.09
11.42
29.89
10.10
9.53
0
3.10
6.25
3.95
6.70
0.32
0
0
0
0
0
C17
8.85
12.11
25.09
5.16
2.27
15.31
8.56
2.04
10.45
4.73
4.23
12.78
5.58
5.15
1.15
0
0
0
0
86.23
0
0
0
0
0
C18
8.85
15.12
12.99
0
5.83
8.12
2.77
8.14
6.31
0
0
4.02
0
65.27
79.36
0
0
0
0
0
0
0
0
0
0
C19
11.00
5.20
9.91
10.51
5.07
2.63
0
0
0
2.96
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
C20
13.28
12.70
16.13
8.37
0
0
0
0
0
4.04
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
C21
7.05
3.33
7.42
3.02
6.68
0
0
0
0
75.69
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
C22
2.28
8.13
0
5.04
3.88
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
C23
0
0
0
37.18
71.22
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
C24
Energy & Fuels Article
DOI: 10.1021/acs.energyfuels.5b02686 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels
Figure 3. Chain propagation reactions for a radical of molecule 21 based on a three-step mechanism.
where Fi is the molar flow rates of species i, and V is the reactor volume. The pseudosteady-state approximation was used for radical species at each increment of reactor volume. With this assumption, the above system of stiff differential equations reduce to a system of nonstiff differential equations and algebraic equations. Accordingly, at each increment of reactor volume, one can write the following equation for radical species: net rate of formation of radical i = 0
Once the radical concentrations are obtained, product distributions can be determined, and with the assumption that olefins are hydrogenated to give the corresponding alkanes, the following equivalent reaction can be written for the reaction scheme presented in Figure 2: 100n‐C16 → 3.53C1 + 10.91C2 + 20.56C3 + 17.03C4 + 13.71C5 + 13.71C6 + 13.71C7 + 13.71C8
(2)
+ 13.71C9 + 13.71C10 + 13.71C11
The above equation for the first radical in step I (RI1) of the network of Figure 2 is
+ 17.03C12 + 20.56C13 + 10.91C14 + 3.53C15
Stoichiometric coefficients can be obtained in a similar way for all other molecules presented in Figure 1 with products having the same carbon number grouped together. The stoichiometric coefficients for other representative molecules for the singlestep mechanism are given in Table 3. The relatively higher temperature of 470 °C would result in higher gas yields, and to account for the resulting product distribution, a three-step cracking mechanism was suggested where radicals undergo three successive decompositions prior to being stabilized by hydrogen abstraction. Three steps decomposition for one of the radicals of molecule 21 is shown in Figure 3. Ring-opening reactions were considered in cyclic compounds as shown in Figure 3. The stoichiometric coefficients for the three-step decomposition can be obtained by a similar procedure as described for the one-step decomposition. The equivalent reaction for n-C16 is
8
− k(dec)(p → p)[RI1] + {RT° −
∑ [RIL]}[n‐C16]6k(abs)(p,p) = 0 L=1
(3)
where the first term in eq 3 refers to disappearance of RI1 by β-scission decomposition and the second term refers to generation of RI1 from participation of radicals in step II in hydrogen abstraction from the parent molecule. Similar equations for each radical species result in a system of linear algebraic equations that can be solved to obtain the radical concentrations. To proceed with the solution of this system, estimates are required for both the total radical concentration (RT° ) and the concentration of the parent molecule, n-C16. An iterative procedure was implemented where eq 4 was used for an initial estimate for total radical concentrations that was updated by eq 5 in subsequent iterations. The concentration of parent molecule was obtained by Peng−Robinson equation of state. The Arrhenius parameters for abstraction, decomposition, initiation, and termination reactions were obtained from the literature.30,31 ⎡ 15ki ⎤1/2 [n‐C16]⎥ RT° = ⎢ ⎣ kt ⎦
° RT,new
⎡ 2(15k )[n − C ] i 16 =⎢ − ⎢⎣ kt
100n‐C16 → 17.30C1 + 190.22C2 + 20.50C3 + 16.87C4 + 13.67C5 + 13.67C6 + 13.67C7 + 16.87C8 + 20.50C9 + 11.15C10 + 6.83C11 + 6.83C12
⎤1/2 2⎥ ∑ [R i] ⎥⎦ i
(4)
+ 6.83C13 + 6.83C14 + 3.63C15
(5)
The stoichiometric coefficients for other molecules are given in Table 4. The stoichiometric coefficients for other temperatures between 440 °C to 470 °C can be obtained by interpolation using values reported in Tables 3 and 4. E
DOI: 10.1021/acs.energyfuels.5b02686 Energy Fuels XXXX, XXX, XXX−XXX
15.18
42.14
18.10
10.77
24
25
15
23
19.68
14
22
32.12
13
11.14
36.99
12
12.90
11.65
11
21
4.95
10
20
15.22
9
13.59
31.77
8
36.81
27.98
7
19
26.94
6
18
4.25
5
9.25
16.20
4
36.66
17.30
3
17
40.71
2
16
6.34
49.87
1
C1
molecule
13.87
C3
F
41.83
17.73
27.31
39.72
59.56
16.74
10.91
18.04
38.41
42.81
96.30
7.22
19.19
20.50
51.45
197.62
157.15
67.36
53.30
31.36
192.71
192.32
11.70
23.10
41.96
73.06
36.70
15.28
16.10
21.59 108.29
73.70
42.85
149.95
65.17
91.42
65.36
36.78
191.39
93.44
126.76
49.45
46.26
190.84
190.22
96.29
43.27 104.48
72.67
C2
9.76
10.67
23.86
36.75
4.92
12.57
13.25
14.58
36.89
6.04
23.29
23.02
23.71
9.13
12.34
14.84
48.08
14.82
16.52
7.33
15.79
16.87
20.61
45.01
15.90
C4
8.84
13.84
22.15
2.12
7.10
10.19
10.73
27.39
32.89
8.28
22.18
50.50
6.83
8.69
7.44
12.03
15.52
19.31
27.44
1.67
12.79
13.67
4.63
15.04
9.51
C5
8.84
11.76
19.99
9.41
4.12
10.19
10.73
16.63
0
4.51
14.79
16.31
32.11
8.64
8.34
12.03
22.53
19.51
23.77
22.71
12.79
13.67
27.78
9.48
15.75
C6
8.84
7.13
25.06
4.83
3.84
10.19
10.73
4.27
10.01
9.20
23.30
14.04
11.97
12.21
12.76
12.03
7.76
14.78
0
0
12.79
13.67
8.47
16.21
0
C7
8.84
7.19
13.51
3.01
8.43
10.19
10.73
23.12
9.10
0
14.79
10.62
2.04
5.07
7.33
12.03
13.98
15.74
14.37
7.81
12.79
16.87
15.71
15.09
37.76
C8
8.84
8.44
1.79
13.06
0
10.19
10.73
16.98
14.64
16.60
16.17
17.25
14.64
11.44
2.57
12.03
1.89
0
9.76
6.36
15.79
20.50
5.07
9.79
2.00
C9
8.84
8.44
11.88
9.55
14.06
10.19
10.73
0
9.52
2.66
0
0
19.14
18.61
6.84
14.84
12.61
14.32
8.36
12.52
19.19
11.15
26.40
7.51
21.19
C10
8.84
8.44
4.63
2.75
2.33
10.19
10.73
11.46
5.65
3.63
0
13.07
0
15.68
7.33
18.04
14.20
9.83
0
0
10.44
6.83
2.16
4.87
15.49
C11
8.84
7.19
7.06
7.61
4.40
10.19
13.25
10.16
2.41
2.66
9.17
4.73
13.93
12.54
9.17
9.81
8.75
9.72
15.45
18.77
6.40
6.83
5.88
10.04
10.03
C12
8.84
7.13
11.87
6.31
2.33
12.57
16.10
0
12.38
13.40
11.22
2.74
6.05
1.90
13.06
6.01
10.13
2.22
9.40
4.10
6.40
6.83
11.24
5.60
2.56
C13
8.84
11.76
0
8.27
10.18
15.28
8.76
8.65
7.77
0.98
9.58
9.13
2.64
15.55
11.38
6.01
2.74
8.95
3.16
15.13
6.40
6.83
10.81
4.27
21.42
C14
8.84
13.48
9.39
15.33
0.55
8.31
5.37
5.97
7.66
17.99
7.04
0.93
13.44
0
15.32
6.01
3.04
11.69
13.90
8.68
6.40
3.63
3.58
8.94
3.01
C15
9.76
9.75
2.06
3.37
14.33
5.09
5.37
5.81
11.57
9.86
5.72
7.53
4.45
6.58
2.64
6.01
9.98
7.51
4.44
17.35
3.40
0
0
0
0
C16
Table 4. Stoichiometric Coefficients for Representative Molecules at 470°C (mol/100 mol of Paraffin Decomposed)
11.70
8.44
4.28
25.31
12.40
5.09
5.37
12.00
6.21
10.14
6.63
13.31
5.67
21.70
14.40
3.20
6.78
4.12
7.15
0.36
0
0
0
0
0
C17
10.33
5.55
12.11
2.89
10.40
5.09
5.37
0.78
6.43
1.76
4.39
7.32
5.81
6.72
1.30
0
0
0
0
19.91
0
0
0
0
0
C18
4.42
5.46
5.39
1.66
0.66
5.09
2.85
8.57
6.65
4.29
0
4.27
0
0
18.55
0
0
0
0
0
0
0
0
0
0
C19
4.42
2.11
3.45
3.08
2.65
2.71
0
0
0
12.54
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
C20
4.42
6.29
7.59
6.41
15.48
0
0
0
0
5.44
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
C21
4.42
2.11
7.62
3.96
4.12
0
0
0
0
17.32
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
C22
1.93
8.06
0
7.55
6.78
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
C23
0
0
0
0
15.72
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
C24
Energy & Fuels Article
DOI: 10.1021/acs.energyfuels.5b02686 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels
Figure 4. Sensitivity analysis of estimated parameters of the model.
Figure 5. Experimental (symbols) and predicted (lines) product yields at 440 °C vs residence time (1/VVH). Feed: □, solid line; kerosene: Δ, long dashed line; and naphtha: o, short dashed line.
3.3. Reaction Rate Constant for Decomposition of Representative Molecules. First-order rate constants for decomposition of representative molecule are given by the Arrhenius eq 6 and depended on both the structure of the molecule and its molecular weight.
⎛ E ⎞ ⎟ k = A exp⎜ − ⎝ RT ⎠
The following expressions were used for noncyclic and cyclic paraffins, respectively: Ai = A n ‐ bθi1/ α , Ai = Ac θi1/ α ,
(6) G
θi =
θi =
TBPi TBPref − n
TBPi TBPref − c
(7)
(8) DOI: 10.1021/acs.energyfuels.5b02686 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels
Figure 6. Experimental (symbols) and predicted (lines) product yields at 470 °C vs residence time (1/VVH). Feed: □, solid line; kerosene: Δ, long dashed line; and naphtha: o, short dashed line.
Figure 7. Experimental (symbols) and predicted (lines) gas yields at 440 and 470 °C vs residence time (1/VVH). Gas at 470 °C: Δ, solid line; gas at 440 °C: × , long dashed line.
where An‑b and Ac are the pre-exponential factor at the reference temperature, taken as the minimum boiling point temperature, for noncyclic and cyclic paraffins, respectively, and θi is dimensionless temperature. α, An‑b, and Ac along with activation energy, E/R, are positive constants as adjustable model parameters. 3.4. Reactor Model and Kinetic Parameter Estimation. The reactor was considered as an ideal plug flow reactor under isothermal conditions. The overall product distribution was obtained as the sum average of products from the reaction of each of the representative molecules reacting according to the stoichiometric coefficients reported in Tables 3 and 4 for reaction at 440 and 470◦C, respectively. A Runge−Kutta algorithm was used to solve the reactor design equation for each molecule. For comparison of
predicted product distributions with experimental data, boiling point cuts were defined with carbon number ranges according to Table 1. The adjustable model parameters were obtained by minimizing the following objective function, OF, using the Levenberg−Marquardt algorithm in MATLAB: 4
OF =
1 6
2
3
− yieldical )2 /yieldiexp ∑ ∑ ∑ (yieldiexp ,j ,j ,j k=1
i=1 j=1
(9)
where the first summation refers to each of the four defined boiling cuts, the second summation refers to the two temperature levels, the third summation refers to the three space velocity levels, and yield is defined as the ratio of the weight of each cut to weight of total products. H
DOI: 10.1021/acs.energyfuels.5b02686 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels
Figure 8. Experimental (symbols) and predicted (lines) product yields at 470 °C vs residence time (1/VVH) based on a two-step mechanism. Feed: □, solid line; kerosene: Δ, long dashed line; and naphtha: o, short dashed line.
Figure 9. Predicted and experimental values of product yields at different reaction temperatures and space velocities.
4. RESULTS AND DISCUSSION The optimum model parameters were An‑b = 1.25 × 1011 h−1, Ac = 7.45 × 1010 h−1, α = 0.0679, and E/R = 20748 K. Sensitivity analysis was applied for each of the optimized parameters by means of perturbations in the range of −20 to +20 to ensure that the set of parameters correspond to the global minimum and not local minimum.32 As can be seen in Figure 4, the estimated parameters represented a global
optimum as all parameters gave the same minimum of the objective function at 0% perturbation. The predicted and experimental weight % of kerosene, naphtha, gas, and unreacted feed as a function of residence time are presented in Figures 5, 6, and 7 for reaction temperature of 440 and 470 °C, indicating that the agreement between predicted and experimental values was satisfactory. Proper error bars could not be placed for the experimental product distributions since only one repeat I
DOI: 10.1021/acs.energyfuels.5b02686 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels
employed in this study. Higher reaction temperatures would require additional decomposition steps.
experiment was performed. On the basis of the results from the repeat experiment, however, the error in the product yields for different cuts can be estimated at ±5%. For temperatures between 440 and 470 °C, the stoichiometric coefficients can be obtained by interpolation using values reported in Tables 3 and 4. For comparison, a two-step decomposition mechanism was also considered for reaction temperature of 470 °C, and the predicted and experimental weight % of product and unreacted feed are presented in Figure 8, indicating that although the overall feed conversion was accurately predicted over the entire range of conversions, the error in predicted yields of product cuts was more pronounced at higher conversions. At higher temperatures, decomposition reactions become more significant, leading to an increase in the yield of lighter products. A three-step decomposition mechanism is therefore required to accurately predict the product distribution at higher temperatures, especially at higher residence times. At the more moderate temperatures below 470 °C, a two-step decomposition model can accurately predict the experimental data over the entire range of conversions. It was found that ringopening reactions did not significantly affect the model results for the one-step mechanism at low reaction temperatures. With increasing temperature, however, their contribution toward product distribution became significant. Cyclic compounds have higher boiling point relative to branched hydrocarbon with the same molecular weight. At the same temperature, therefore, branched compounds crack more easily than cyclic compounds of the same carbon number. While ring opening reactions for naphthenic compounds can be neglected at low temperatures, they would become more significant at higher temperatures and should be considered in the model. Parity plots illustrating a comparison between predicted and experimental product yields and unreacted feed are presented in Figure 9 for different reaction temperatures and space times along with the values of slope, intercept, and correlation coefficient (R2) of the straight line fit. The model predictions were found to be satisfactory as slope and R2 were very close to one, and the intercept was close to zero for each cut. The residual plots indicating the difference between the experimental and predicted values presented in Figure 10 show that
5. CONCLUSIONS A simple mechanistic kinetic model was proposed for thermal hydrocracking of a paraffinic feed. The feed was characterized in terms of a number of representative molecules generated from structural analysis of the feed. The product distribution was obtained as the sum average of products from the reaction of individual molecules. The stoichiometric coefficients for thermal hydrocracking were obtained by a single-step mechanism at the low temperature and a three-step mechanism at the high temperature. Ring opening of the naphthenic compounds were included, and olefins were assumed to be hydrogenated rapidly. Predicted values of overall conversion and product yields were in good agreement with experimental values. To extend the analysis to other refinery feeds that contain a variety of aromatic and heteroatom structures, it would be necessary to perform SGA for such feeds and represent them with additional molecules that contain aromatic and heteroatom structures and include the reaction of these structures.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Tel: 98 21 66165411. Fax: 98 21 66022853. Notes
The authors declare no competing financial interest.
■
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Figure 10. Standardized residual plots of product yields.
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DOI: 10.1021/acs.energyfuels.5b02686 Energy Fuels XXXX, XXX, XXX−XXX
Article
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DOI: 10.1021/acs.energyfuels.5b02686 Energy Fuels XXXX, XXX, XXX−XXX
