174
Ind. Eng. Chem. Fundam., Vol. 17, No. 3, 1978
Literature Cited
Rasquin, E. A., Lynn, S., Hanson, D. N., Ind. Eng. Chem. Fundam., 16, 103
Beychok. M. R., "Coal Gasification and the Phenosolvan Process", presented at the 168th National Meeting of the American Chemical Society, Atlantic City, N.J., 1974. Earhart, J. P., Ph.D. Thesis, University of California, Berkeley, Calif., 1975. Leva. M., Chem. Eng. Prog. Symp. Ser., 50 (lo),51 (1954). Mulligan, T. J., Fox, R. D.,Chem. fng., 83 (22),49 (1976). Newman, J., Ind. Eng. Chem. Fundam., 7 , 314 (1968). Rasquin, E. A., M. S. Thesis, University of California, Berkeley, Calif., 1977.
Sherwood, T, K,, ~
(1977). ~ , A,
L,, T l
~
i ~lnst, Chem, ~~ ~
,~36,39-7~ ~
(1940). Wurm, H.J., Gluckauf, 104 (12),517 (1968).
Received f o r review April 11,1977 Accepted April 20,1978
Modeling of Thermal Cracking Kinetics. 3. Radical Mechanisms for the Pyrolysis of Simple Paraffins, Olefins, and Their Mixtures K. Meenakshi Sundaram and Gllbert F. Froment' Laboratorium voor Petrochemische Techniek, Rijksuniversiteit, Gent, Belgium
Radical reaction schemes for the cracking of ethane, propane, normal and isobutane, ethylene, and propylene were set up. The kinetic parameters of these schemes were determined by fitting experimental data obtained under nonisothermaland nonisobaric conditions in a pilot plant. The set of continuity equations for both molecular and radical species was integratedusing Gear's algorithm for stiff differential equations. The reliability of the parameters was tested by simulating the cracking of binary and ternary paraffinic mixtures. A satisfactory fit of the results of mixtures cracking was obtained with a reaction scheme derived from the superposition of the schemes for single-component cracking.
Introduction Thermal cracking reactions mainly proceed via free radical mechanisms (Laidler, 1965). Many specific mechanisms have been proposed to explain the cracking of simple molecules. The majority of the mechanisms have been deduced from data obtained at subatmospheric pressures, low temperatures, and low conversions. Moreover, they were derived through the pseudo-steady-stateconcept which assumes the radical concentrations to be constant. This condition is not fulfilled in reality, neither in an industrial reactor nor even in an isothermal bench scale reactor (Edelson and Allara, 1973). For these reasons, at elevated temperatures the uncertainties in the parameters are high and sometimes attain orders of magnitude. In the present paper radical schemes for the cracking of normal and isoparaffins, olefins, and their mixtures are developed. The determination of their kinetic parameters is based upon experiments conducted in a pilot reactor under conditions as close as possible to those used in industry (Van Damme et al., 1975; Froment et al., 1976a,b, 1977). Continuity Equations Free radical reactions involve initiation, propagation or H-abstraction, and termination steps. The continuity equation for t h e j t h species in an isothermal reactor with plug flow may be written d F, dz
= -0Rj = -0
N
,E (sijri) 1-1
For nonisothermal and nonisobaric conditions the reaction rate ri has to be computed for the experimentally measured 0019-7874/78/1017-0174$01.00/0
gas temperature and total pressure profiles. It is assumed that the reactions are elementary and therefore the order corresponds to the molecularity. Also, the rate coefficients obey the Arrhenius relationship within the temperature range covered. The first-order differential equations represented by eq 1 are usually nonlinear and coupled, and hence analytical solutions are not possible. The concentrations of the radicals are much lower than those of the molecular species (e.g., vs. 10-2 M) so that the eigenvalues of the differential equations differ by orders of magnitude. With classical integration methods, an extremely small step size has to be used to ensure the stability of the numerical integration. To overcome the mathematical difficulties, pseudo-steady state for radical concentration has been assumed. This assumption allows the differential equations for the radicals to be replaced by algebraic equations (Snow, 1966; Pacey and Purnell, 1972b; Blakemore and Corcoran, 1969). In a recent communication the present authors (to be published) have quantified the errors induced by this assumption and shown that for reliable parameter estimates, the complete integration for the continuity equations for both molecular and radical species for the entire conversion range is essential, because the radicals vary significantly and continuously with conversion. Of the many currently available methods for integration of stiff differential equations (see Aiken and Lapidus, 1974, 1975a,b; Seinfeld et al., 1970; Sena and Kershenbaum, 1975a1, the one proposed by Gear (1971) seems to emerge. It is also adopted in this work. Gear's method can be applied to any degree of stiffness and allows for any degree of accuracy of integration with moderate computer time. It essentially uses the Adams-Moulten predictor-corrector method, which is an implicit technique. 0 1978 American Chemical Society
~
Ind. Eng. Chem. Fundam., Vol. 17, No. 3, 1978
Experimental D a t a The pilot reactor details and the experimental results used in this work have been reported already by Van Damme et al. (1975) and Froment et al. (1976a,b, 1977). Briefly, the results cover an outlet pressure of 1.2 to 2.2 atm abs with dilution factors ranging from 0.35 to 1.2 kg of steamkg of hydrocarbon. The outlet temperatures varied from 650 to 860 "C, depending upon the species cracked and the conversion level. The pressure drop varied from 0.3 to 0.5 atm and the Reynolds number from 5000 to 10 000. General R e m a r k s Concerning the Reaction Scheme In this work only the major reactions and a fraction of the minor reactions reported in the literature will be considered. The experimental product distribution is used as a guideline to limit the number of reactions. Recently, Sena and Kershenbaum (197513) proposed a method to discriminate between several possible radical mechanisms using the constraints imposed by stoichiometry and kinetics. Such a technique is useful for a small number of reactions only and is not applicable here. In each reaction scheme all the important radicals are considered, although all the products heavier than C5H10 have been lumped as a single component, C5+. Radicals heavier than C5H11- are not considered. Aromatic and naphthenic radicals and species are left out, for lack of relevant kinetic data. The pyrolysis of aromatic substances mainly yields coke and small molecules such as hydrogen and methane (Kinney and Delbel, 1954). For each radical at least one termination is considered. The pyrolysis is taken to be homogeneous; heterogeneous reactions on the wall are not considered. The complete reaction scheme is shown in Table I. The reactions to be selected in the simulation of the individual cracking of the paraffins and olefins considered here are shown in Table 11. Inclusion of molecular reactions was found to be necessary, a t least for olefin cracking. Each case is discussed separately in subsequent sections. Selection of P a r a m e t e r s Rate constants for several hundred reactions carried out a t low temperatures were recently compiled by Allara (personal communication). Rate constants for metathetical reactions of atoms and radicals have been reviewed recently by Kerr (1976) and earlier by Trotmann-Dickenson (1965). Rate constants for addition reactions are dealt with by Abbe1 (1976). Kunugi et al. (1969,1970) tabulated rate constants for many reactions of olefin cracking. The majority ofthe studies available in the literature are limited to low temperatures and low pressures, however. For satisfactory prediction at the high temperatures encountered in this work, adaptation of the frequency factor and/or activation energy was found to be necessary. Initially in this work the experiments were reduced to isothermality using the equivalent reactor volume concept (Hougen and Watson, 1947), discussed in detail by Froment et al. (1976a) and Van Damme et al. (1975). A set of parameters which can satisfactorily explain the observed product distribution at various conversions and temperatures was found by trial and error. However, when such parameters were applied to simulate unreduced nonisothermal and nonisobaric data, significant discrepancies between the experimental and calculated product distributions sometimes of the order of 100% were observed. This is not so surprising, since the equivalent reactor volume concept is strictly valid only for a single reaction or for a set of parallel reactions with identical activation energy. In radical reactions the activation energy varies from 0 kcal/mol for terminations to 80-100 kcal/mol for initiations, and hence it is not possible to get a unique equivalent reactor volume valid for all the re-
175
actions, It was therefore decided to deal with the data as obtained, that is to account for the temperature and pressure profile in the simulations required to determine the best values of the parameters. In the previous papers dealing with molecular models the parameters were estimated by nonlinear regression (Sundaram and Froment, 1977).Due to the large number of reactions this technique could not be applied here, so that the parameters were obtained by ordinary trial and error. I t should be added that unique values were selected for the parameters of reactions occurring in more than one cracking. The most reliable values of the parameters of such a reaction are of course obtained from that cracking in which the reaction is most abundant. Therefore, the final set of parameter values was only obtained through an iteration loop involving the data on the cracking of all the substances, superimposed upon the iteration loop dealing with the cracking of one hydrocarbon only. Finally all the reactions were added up to one large model which was found to be valid for mixture cracking too, without any further adaptation. E t h a n e Cracking Ethane cracking has been studied by many workers. Simple reaction schemes involving 6 to 1 2 reactions have been proposed (Pacey and Purnell, 1972b; Snow, 1966; Lin and Back, 1966a,b;Bradley and Frend, 1971). In the present work a total of 49 reactions, given in Table 11, were considered to be necessary to cover the range of conversions of practical importance. The reaction scheme accounts for 20 species (11molecular and 9 radical) which are also mentioned in Table 11. The radical concentrations along the reactor are shown in Figure 1, for a typical experimental temperature profile. The calculated conversion profile is also shown in Figure 1.The radical concentrations for some radicals like 1-C4Hg0do not change very much beyond 30% of the reactor length, although the temperature varies from 750 to 850 "C. Major radicals such as H- and CH3. vary significantly, however. Even under isothermal conditions they never attain steady state (Sundaram and Froment, to be published). Concentration profiles of hydrogen and methane are also shown in the same figure for comparison. It can be seen that the concentrations of molecular and radical species differ by more than seven orders of magnitude. The calculated and experimental product distributions for some of the major products are shown in Figure 2 as a function of ethane conversion. The agreement is excellent a t all conversion levels. It is found that an increase in the rate of the initiation leading to methyl radicals has a more pronounced effect on the C5+ yield than on the ethane conversion. The latter is much more favored by an increase in the rate of propagation C2Hs + Ha
-
CzH5. + H2
The decomposition of the ethyl radical into ethylene and H.
not only affects the product distribution but also the overall kinetics. I t has been argued that under normal pyrolytic conditions the latter reaction operates in its pressure-dependent region (Pacey and Purnell, 1972b;Blakemore et al., 1973).The results are uncertain, however, and due to lack of sufficient information first order is adopted here with the kinetic parameters recommended by Allara (personal communication). High selectivities for methane are observed at high temperatures
Ind. Eng. Chem. Fundam., Vol. 17, No. 3, 1978
176
Table I. Reaction Scheme for the Pyrolysis of Paraffins and Olefins A, s-lorL E, mol-' s-' kcal/mol source
reaction
no.
A, s-1orL E, mol-' 5-l kcal/mol source
reaction
no.
+
-
CHy + 3.0 x 109
19.0
e
1.0 x 108
9.2
d
43.
1.2 x 109
12.6
a
3. 4.
4.0 X 2.0 x 1.5 X 9.0 x
5.
2.0 x 10'6
82.0
a
44.
8.0 X lo8
a
9.0 x 8.0 x 3.5 x 3.5 x
10.4
6. 7. 8. 9.
1013
65.0 95.0 86.0 51 0
a a a
45.
2.0 x 108
8.3
a
a
46.
6.0 x 107
8.3
a
10.
8.0 X 2.0 x 8.0 X 1.0 x 2.5 x
1OI6
b
47.
2.0 x 109
12.6
a
48.
4.5 x 108
10.4
a
49.
1.5 x 109
10.4
a
50.
1.0x 109
18.8
d
51.
8.0 X lo8
16.2
d
52.
2.0 x 108
13.5
a
53.
4.0 X lo8
18.8
d
54.
8.0 X lo8
16.8
d
55.
1.0x 109
19.0
a
56.
1.0 x 108
9.2
d
57.
1.0 x 108
10.2
d
58.
2.0 x 108
10.4
a
59.
2.0 x 108
12.6
a
60.
1.0 x 108
13.4
a
61. 62. 63. 64. 65.
2.0 x 3.2 x 3.0 X 4.0 x 2.0 x 2.0 x 1.2 x
31.5 40.0 36.2 32.6 38.4 38.1 49.3 37.0 32.6 28.0 28.0 36.6 31.9 39.8 36.0 33.0 36.6 36.6 31.5 28.7
1. 2.
10l6 10'6
10l6 10'6
1017
10'6 10"
87.5 84.5 82.1 85.4
a
a a a
14.0 71.3
a
4.0
a a
1.0 x 10"
9.7 1.1 9.7
16.
9.0 x 1010
8.3
a
17.
5.0 X 1O1O
3.9
d
18.
5.0 X 1O1O
3.8
a
19.
3.0 X 1O1O
3.8
a
20.
1.5 X 10"
9.7
a
21.
9.0 x 1010
8.4
a
22.
1.0 x 10'1
8.4
a
23.
1.0 x 10'0
13.0
a
24.
3.8 X 10"
16.5
a
25.
2.0 x 109
12.2
a
26.
3.4 x 1010
11.5
a
21.
4.0 x 109
10.1
a
C4H7. 1.0 x 108
7.3
d
C4H7. 1.0 x 108
8.2
a
11. 12.
13. 14. 15.
+ + + + + + + + + +
-
CH4 28. l-C4H8 CHy CH4 29. 2-C4H8 C H r CH4 30. i-C4H8 C H r allyl CH4 31. n-C4Hlo CHy C4H9' CH4 32. n-C4Hlo + CHy C4H9' CH4 33. i-CQH10 + CH3. C4H9' + CH4 34. C3H6 CzH3.
10'6
lo8
10" 109
C
41. CzH4 CzH5C~HG 42.
a
3.0 X lo8
7.3
a
1-
3.5 x 10'0
11.6
a
2-
3.5 x 109
9.5
a
i-
9.5 x 109
9.0
a
C3H5- + 3.0 x 109
14.5
a
35.
3.0 x 109
18.8
a
36.
1.0 x 109
16.2
a
67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80.
37.
1.0x 109
13.0
a
81.
+
Me
-
+
38.
1.0x 109
18.0
a
39.
8.0 X
lo8
16.8
a
40.
1.0x 109
16.8
a
82. 83. 84. 85. 86. 87. 88. 2-C;Hi
109 1013 1O'O
1013 1013 1013 1014
1.0 x 101' 1.0x 1013
+ H.
-
1.3 1.5 1.5 2.9 1.5 1.3 2-C;Hg-
6.3 X
lo9
1.2 1.2
a
d a
d d a
d a a
a d d d d a
d a
d
D d a
d a
d
f g d d
Ind. Eng. Chem. Fundam., Vol. 17, No. 3, 1978
177
Table I (continued)
no.
reaction
A, s-lorL E, mol-' s-l kcal/mol source
89. 90. 91. 92. 93. 94. 95. 96. 97. 98.
1.0 x 10'0 2.0 x 108 1.5 X lo8 3.2 X lo8 3.2 X lo8 1.0 x 108 5.0 x 107 1.5 x 107 1.3 x 107 2.0 x 107
1.2 7.9 7.4 7.4 9.1 7.2 7.0 7.6 7.5 7.4
99.
1.3 x 107
6.9
100. 101. 102. 103. 104. 105. 106. 107. 108. 109. 110.
5.2 x 1014
a a
a h d a a d d d d
no.
--
reaction
115. 1-C3H7-+ C H r nC4H10 116. 2-C3H7*+ CH3. n C4H10 117. C4H7- + C H r C5+0 118. Me allyl CHY c5+ 119. CzHr CzHy C4H6 120. C4H7- + CzHr ---zC5+ 121. CzHy C2H.y nC4HlO 122. CzHs + C2H.y CzH4 CZH6 123. C3Hy + C2H.y C5+ 124. 1-C3H7' C2H.y c5+ 125. 2-C3H7' C2Hs c5+ 126. C4H7- + C2H.y C5+ 127. C3H.y + C3H.y C5+ 128. C4H7. + C3H5' C5+ 129. Me allyl C3HS -+ c5+ 130. C4H7*+ C4H7. C5+ 131. CzHz 2C Hz 132. CzH4 + Hz CzH6 133. CZH4 + C4H6 C6H10
+
+
+
+
+
A, s-lorL mol-'
E, kcal/mol source
lo9
0
a
3.2 X lo9
0
a
3.2 X 109 3.2 x 109
0 0
a a
1.3 X 10" 1.3 X 10'0 4.0 X lo8
0 0 0
a a
+ 5.0 X IO7
0
1
3.2 X
k
41.0 i 3.2 X 109 0 d 1.0 x 1010 0 a 8.0 X lo8 0 d 4.0 X 1Olo 0 i 2.0 x 10'0 a 0 8.0 X lo8 0 d 1.0 x 10'0 0 d 1.0 x 10'0 0 d 3.2 X 109 0 d 2.0 x 10'0 a 0 3.2 X 109 0 d 2.0 x 10'0 0 a 1.3 X 101" 0 d' 1.0 x 10'0 d 0 1.3 X 1O1O 0 a 1.0 x 10'0 0 d 1.0 x 10'0 0 d 3.2 X 109 0 d 111. 1.0 x 10'0 d 0 5.0 X 10l2 62.0 a 112. 1.3 X 1O1O 0 a 9.2 X lo8 32.8 m 113. 3.2 x 109 0 a 3.0 x lo7 27.5 n 114. 3.2 x 109 0 a a Estimated by authors. Kunugi et al. (1969). Kunugi et al. (1970). Recommended values by Allara. e Lin and Back (1969a). f Kurylo et al. (1971). 8 Yang (1962). Cventanovic and Irwin (1967). Lin and Back (196913).j Kurylo et al. (1970). Hiatt and Benson (1972). Lalonde and Price (1971). Sundaram and Froment (1977). VI Bowley and Steiner (1951). Products heavier than C5H10 are denoted as C5+.
+ +
-+
-+
-
+
+
+
+
+
-+
+
-
Table 11. Summary of Reaction Schemes for the Pyrolysis of Single Components total no. of reaccomponent tions molecular species radicals reactions considered ethane
propane
49 Hz= CH4, CzHz, CZH4, CZH6, C3H6, C3H8, C4H6r 1C4H8, n-C4HlO9c5+ 80 Hz, CH4, CzHz, CZH4, CZH6, C3H6, C3H.9, C4H6,1C4H8, n-C4HlO, c5+
n-butane
86 same as propane
Ha, CHr, CzH3*, 1, 3,4,10, 12, 13,23,24,41,61-65,67, CZH5.p 68,71,72, 78-82,84,86,90,95-98, C3H5', I-C~HT,C~H~~~01-104,106,108,111-114,117,119-122, . . 126,128; 130; 131 I-C~HY, C5H11. Ha, CH3., CzH3*, 1,2,10,12-17,23-28,34-36,41-44,50, 51,61-68,71-74,78-82,84-87, go, 93, CZHS, C3H5', 1-C3Hyr295-106,108,109,111-117,119-128,130, 131 C3H7', C4H7-,1-C4Hg', 2C4H9*,C5Hii1,3,4,10,12-17,20, 21, 23-28,31,32,34, same as propane
38,39,41,42,45,47,48,53,54,58,59, 61-68,71-74,78-82,~4-87,go, 92, 95-106,108,109,111-117,119-123,126-128,130,131 5,10-14,17-19,22-25,28-30,33,34,37, 40,42,46,49,52,55-57,60-64,66-70, 73-80,~1-95,97-99,101-107,109-114,
117-120,125,127-131 1,3,4,6, 10,12-14,23-25,34,41,61-68, 71-74,78-82,84-87,90,92,95-97,101-106,108,109,111-114,117, 119-128,130-133 7-10,12-14, 23-25,34,41,42,56,57, 61-68,71-74,78-82,84-87, go, 92, 95-106,108,109,111-117,119,120,
123-126,128,130,131
178
Ind. Eng. Chem. Fundam., Vol. 17, No. 3, 1978
100 -7
0
-11
2
6
0
10
20
30
LO
50
60
70 */a
80
90
IW
OF REACTOR LENGTH
Figure 1. Calculated concentration of radicals, hydrogen, and methane and conversion along the reactor for ethane cracking:Po = 2.0 atm abs; 6 = 1.0 kg of steam/kg of ethane; ,. experimental conversion; lines, calculated. YIELD wt % 50
YIELD wt %
f
!7
a
(0
2b
io
! I -10
6
ia
rb do io rtc %OF REACTOR LENGTH
$0
500
Figure 3. Calculated concentration of radicals, ethylene, and propylene and conversion along the reactor for propane cracking: Po = 2.0 atm abs; 6 = 0.4 kg of steam/kg of propane; propylene content of the feed, 3 wt %; experimental conversion;lines, calculated.
.,
The formation of primary products has already been discussed by Buekens and Froment (1968). The main initiation is C3H8
-
+ CHy
C2Hy
The probability of 2-C3H7-splitting into C2H4 and CH3- is extremely low under normal pyrolytic conditions (Leathard and Purnell, 1970). This radical mainly yields C3H6 and H-, while C2H4 and CH3. mainly originate from 1-C3H7-. The formation of acetylene is accounted for by the decomposition of vinyl radicals which are mainly produced by metathetical reactions with ethylene (Kunugi et al., 1969; Benson and Hougen, 1967). The decomposition of the allyl radical, produced by metathetical reactions with propylene, is also included Figure 2. Product distribution vs. ethane conversion:Po = 2.0 atm abs; 6 = 1.0 kg of steam/kg of ethane; points, experimental; lines, simulated. (or high conversions) in this work, confirming the results of Pacey and Purnell(1972a). Methane is formed primarily by CzH6 + CH3.
-
CzH5-
+ CH4
Lin and Back (1966a) used an activation energy of 10.8 kcal/ mol at low temperatures while at high temperatures Pacey and Purnell found a value of 21.5 kcal/mol. Since the temperature along the reactor varied from low to high values, a value of 16.5 kcal/mol, combined with a suitably modified frequency factor satisfactorily predicted the methane yields at all conversions and temperatures.
Propane Cracking The low-temperature pyrolysis of propane has been modeled by Allara and Edelson (1975) and by Laidler et al. (1962). High-temperature cracking has been studied by Buekens and Froment (1968), Herriott et al. (1972),and Van Damme et al. (1975). The importance of the allyl radical in alkane cracking, especially in propane cracking, has been pointed out by Buekens and Froment and has been confirmed later by Allara and Edelson. For this reason the unsaturated radicals CzHy, C3H5', and C4H7. are also considered in the present model. In propane cracking, hydrogen, methane, ethane, ethylene, and propylene are observed as primary products. Small quantities of acetylene, 1-butene, butadiene, and C5+ are observed a t high conversions. In the present model a total of 80 reactions between 11molecular species and 11radical species are considered (Table 11).
C3H5*
+
C2H2
+ CH3.
The decomposition and polymerization of this radical has been discussed recently by Froment et al. (1976b). Two possibilities have been considered for the formation of butadiene. According to Benson and Hougen (1967) CzH3. -k CzH4
+
C4H6
+ H.
whereas Kunugi et al. (1969) proposed C2H3.
+ CzH4
C4H7'
4
-+
C4H6
C4H7-
+ Ha
The second possibility was retained. It should be noted that the methyl allyl radical or 3-butenyl radical C4H7- exists in isomeric foms (Beckwith, 1973). No distinction between these is made here, except for those forms derived from isobutene. Termination by vinyl, allyl, and methyl allyl radicals is also considered. Whittle (1972) reports that disproportionation of allyl radicals is far less abundant than recombination. The ratio between the two at temperatures ranging from 164 to 190 "C is 0.008. Since termination is nearly independent of temperature, it is assumed that the same ratio holds well at the normal pyrolytic temperatures and hence only recombination is retained here. The other unsaturated radicals are treated in the same manner. H-transfer reactions involving allyl radicals are important at high temperatures since the concentration of allyl radicals is higher than that of any'other radical. This work confirms the part played by the allyl radical which has been neglected by most of the workers in alkane pyrolysis. Computed concentrations of radicals and of a few molecular species along the reactor are shown in Figure 3, along with the
Ind. Eng. Chern. Fundarn., Vol. 17, No. 3, 1978
179
Figure 4. Product distribution VS. propane conversion: Po = 2.0 atm abs; 6 = 0.4 kg of steam/kg of propane; points, experimental; lines, simulated.
Figure 5. ~~kcoefficient activation energy for propane cracking considered as a first-order reaction and derived from pseudo-isothermal radical simulations.
Table 111. Comparison of Product Distributions Obtained by Nonisothermal and by Isothermal Simulations of Propane Crackinga
which are nonsignificant at the 95% confidence level, probably result from too strong a correlation between ko and a. A much better fit is obtained by the relation
species CH4 C2H4 C3H6 C4H6
non-iso
yield in wt % is0 is0 (800 "C) (775 "C) 16.8 26.8 17.7 0.65
16.6 26.0 17.9 0.62 1.4 1.3 c5+ a 6 = 0.4 kg/kg; conversion = 66%.
16.8 26.4 17.8 0.6 1.4
exptl 16.3 25/6 18.1 0.9 1.0
experimental temperature profile. The experimental and calculated propane conversions are also shown in the same figure. An example of an isothermal simulation is given elsewhere (Sundaram and Froment, to be published). The calculated and experimental product distribution for the major species are compared in Figure 4. Van Damme et al. (1975) found that the product distribution is nearly independent of temperature when plotted vs. the conversion. This is illustrated by the comparison of the product distributions given in Table I11 obtained by nonisothermal simulation and by isothermal simulations a t two temperature levels. It is of interest to mention here that an isothermal simulation a t 800 O C based upon the pseudo-steady-state approximation yielded the following product distribution (in wt %) a t 66% conversion: CH4, 17.3; CzH4, 22.8; C3H6, 14.0; C4H6, 1.2; Csf, 2.4. This clearly shows that the pseudo-steady-state approximation leads to errors which are not acceptable. The overall order for the disappearance of propane is 0.9 a t 50% conversion and 775 "C and 1.08 a t 65% conversion and 800 "C which is close to the first-order experimentally found by Van Damme et al. (1975) and by Buekens and Froment (1968). The latter authors have reported that the pyrolysis is strongly inhibited. They introduced an inhibition function multiplying the initial first-order rate coefficient of the propane disappearance. The variation of the rate coefficient with conversion as obtained from an isothermal radical simulation at 800 "C is shown in Figure 5 . The global first-order rate coefficient varies over a factor of 5 between conversions ranging from 30 to 65%. Consequently, the reaction scheme presented here accounts for the inhibition, although a factor of 5 is somewhat high. For the "data" shown in Figure 5 the inhibition law, k = h o / l + ax,, proposed by Buekens and Froment for the global first-order kinetics, yields ko = 7.5841 X lo4 and a = 2.005 X lo4. These unrealistically high values,
k=
+ +
1 bX, c dX,
-
1 - 1.2318Xp 1.9862 X 7.7074 X 10-2X,
+
in which all the parameters are significant at the 95% probability level. The F-test also indicates that the latter expression is superior to the former. The model also accounts for the effect of the total pressure and of the partial pressure of propane on the global rate coefficient observed by Van Damme et al. (1975). The activation energy of the propane conversion taken as a first-order process and obtained from pseudo-isothermal simulations at 775 and 800 OC was found to be a function of conversion, represented in Figure 5 . The trend is in agreement with that observed experimentally by Buekens and Froment, but the values of the activation energy are somewhat high. n-Butane Cracking Low-temperature pyrolysis of n-butane has been modeled by Blakemore and Corcoran (1969), Blakemore et al. (1973), Powers and Corcoran (1974), and Allara and Edelson (1975). Pacey and Purnell (1972~)have proposed a model for hightemperature cracking. In n-butane pyrolysis, ethane, ethylene, methane, propylene, hydrogen, and small quantities of 1-butene, acetylene, and butadiene were found as products. The details of the reaction scheme are shown in Table 11. Under normal pyrolytic conditions two initiations, one leading to ethyl radicals and one to methyl and 1-propyl radicals, are predominant. Leathard and Purnell(l970) have shown that the l-C4H9* radical mainly yields ethylene and an ethyl radical, while the 2-C4Hyradical mainly yields propylene and a methyl radical. The isomerization of l-C4Hy proposed by Lin and Back (1966b) is also considered. This is one of the major reactions in n-butane pyrolysis. Figure 6 shows the conversion and radical concentration profiles along an isothermal reactor at 800 "C. It is clear that none of the radicals ever attains a constant value. Also, the concentration of radicals and molecules differs sometimes by nine orders of magnitude. In Figure 7 a calculated product distribution for the major species obtained from nonisothermal simulation is compared with experimental values. Isobutane Cracking Buekens and Froment (1971) have proposed a reaction mechanism for isobutane cracking. Recently Bradley (1974)
Ind. Eng. Chem. Fundam., VoI. 17, No. 3, 1978
180
I
10
60
'0
20
-
l
' S
-
b
-
2
-15
-i
L -0 -05
d
05
1
i 5
210g(V,/Fe)
Figure 6. Calculated concentration of radicals and molecules and conversion for isothermal cracking of n-butane: T = 800 O C ; Po = 2.0 atm abs; 6 = 0.44 kg of steadkg of butane. YIELD wt
-15 - -3
-25
1
.2
3
U
d
0
s
r
15
!~log~":Fol
Figure 8. Calculated concentration of radicals, molecules, and conversion along an isothermal reactor for isobutane cracking: T = 775 "C; Po = 1.4 atm abs; 6 = 0.4 kg of steam/kg of butane.
YIELD %
4"'
%4
I
15-1
'
I7
x
/
CIHS
I io
Figure 7. Product distribution vs. n-butaneconversion:Po = 2.0 atm abs; 6 = 0.4 kg of steadkg of butane; points, experimental; lines, simulated.
io
io
C3H5-
+
C3H4
+ He
Methylacetylene is not detected in propane cracking, however, nor in n-butane cracking, in spite of the high concentration of the allyl radical. It is only observed in isobutane cracking, not even in propylene cracking. Therefore, methylacetylene could be formed from isobutane and/or isobutene which are not present as products in the cracking of the other species considered. Schugerl and Happel (1972) have shown that in isobutene cracking, methylacetylene is indeed a primary product. Also, methylacetylene is only a secondary product in isobutane cracking (Froment et al., 1977). I t may be concluded that methylacetylene is formed from the methyl allyl radical C4H7-obtained from isobutene by metathetical reactions
60
71
Figure 9. Product distribution vs. isobutane conversion: PO= 1.4 atm abs; 6 = 0.4 kg of steamkg of butane; points, experimental; lines, simulated. C4H7-
also proposed a mechanism to explain the product distribution obtained in shock tube pyrolysis. In the present work, hydrogen, methane, propylene, and isobutene were observed as major products and small amounts of ethylene, allenes (propadiene and methylacetylene), 2-butene, butadiene, and higher aromatics were found (Froment et al., 1977). The proposed mechanism, consisting of 86 reactions and involving 14 molecular species and 12 radicals, is shown in Table 11. Reactions leading to the primary products have been discussed by Buekens and Froment (1971). Although small amounts of both propadiene and methyl acetylene are observed, the latter is the more stable compound. Hence, they are considered as a single component, C3H4.It is reported that methylacetylene is formed by the decomposition of the allyl radical (Swarc, 1949; Amano and Uchiyama, 1963,1964)
50
-+
C3H4
+ CHy
This methyl allyl radical is an isomer of the unsaturated radical C4Hy considered earlier. This mechanism also explains the high selectivities for methane and the low selectivities for isobutene at high isobutane conversions. Formation of trans-2-butene is accounted for by the reaction i-C4H9' Z-C4Hs H-
-
+
The formation of 2-C4H8from 2-C4Hg-is not considered, since the former is not found in n-butane or propane cracking. T o explain the high selectivity for ethylene at high temperatures, Bradley (1974) introduced the reactions which proceed via "forbidden" routes i-C4Hg- C2H4 C2Hb' -+
+
Instead, in the present study, metathetical reactions involving vinyl radicals and unimolecular decomposition of C4H7-radicals account for ethylene formation. Calculated concentrations of the radicals, molecules, and conversion, along an isothermal reactor operating at 775 "C are shown in Figure 8. The product distribution obtained from nonisothermal simulation is shown in Figure 9 as a function of isobutane conversion. It can be seen that the agreement between the experimental and calculated values is quite satisfactory.
Olefins Cracking In this section the cracking of ethylene and of propylene is modeled on the basis of the extensive experimental results recently reported by Froment et al. (1976b).
Ind. Eng. Chem. Fundam., Vol. 17, No. 3, 1978 XI%)
TI'CI
YIELD.wt %
6oLl
log C, iradicals)
178
181
YlELDIwt % I C ~ l
t
A; I8O0
,780
I
v C2H6
loo
C2*6
60
50
60
70
80
90
1500
0
100
IO
20
30
LO
60
50
% O F REACTOR LENGTH
Figure 10. Calculated concentration profiles and product distribution along the reactor for ethylene cracking: PO = 1.5 atm abs; 6 = 0.4 kg of steamkg of ethylene; points, experimental; lines, simulated. Benson and Hougen (1967),Boyd et al. (1968), and Kunugi et al. (1969) have proposed radical mechanisms for ethylene cracking. According to Leathard and Purnell (1970), only radical reactions would take place in paraffins pyrolysis, but Danby et al. (1955) concluded that in the decomposition of 1-butene molecular reactions also occur. Silcocks (1955) has reported that nitric oxide inhibits the ethylene cracking. Yet, he does not exclude molecular reactions: methane would be formed from 1-butene by such a mechanism while 1-butene itself is formed by bimolecular collisions between ethylene and ethane or between ethylene only. The kinetic data on the addition of ethylene and butadiene extrapolated from the low-temperature values of Bowley and Steiner (1951) indicate that this reaction is as important as any other propagation reaction. The high yields of the Cb+ fraction, even at low conversions, indicate that many polymerization and condensation reactions are taking place. The high molecular weight radicals are mainly pradicals and these mainly decompose into high molecular weight olefins which further react by condensation. For these reasons a few molecular reactions are included in the scheme proposed here. The major H-transfer reactions involve reactions of He and CHa. yielding a vinyl radical. The addition reaction CzH4
+ H-
-+
C2H5.
is also important. As a consequence, a t moderate conversions, the methane selectivity is increased by
+ CH3. CzH3. + CH*
CzH4 + C2Hy --* C3H6 CzH4
+ CH3.
--*
In ethylene cracking a total of 66 reactions are considered including three molecular reactions, as shown in Table 11. Typical radical and molecular concentration profiles are shown in Figure 10. It should be added that all high molecular weight substances are lumped into a single species, C5+ and that, since Cb+ decomposition was not considered due to a lack of information, this introduces some error into the product distribution. Propylene cracking yields high amounts of acetylene in the present work when compared with the work of Laidler and Wojciechowski (1960) and Ingold and Stubbs (1951). The acetylene formation is accounted for by the decomposition of allyl radical, as discussed by Froment et al. (1976b) and considered previously in propane cracking C3H5-
-
CzH2
+ CHy
The condensation and decomposition zones of this radical in
70
80
90
100
% O F REACTOR LENGTH
Figure 11. Calculated concentration profiles and product distribution along the reactor for propylene cracking: Po = 1.5 atm abs; 6 = 1.0 kg of steamkg of propylene; points, experimental; lines, simulated.
0
10
20
30
LO
50
60
70
80
90
100
%OF REACTOR LENGTH
Figure 12. Calculated concentration profiles and product distribution along the reactor for the cracking of a mixture containing 42.2:18.4: 39.4 wt % ethane-propane-n-butane:PO = 1.56 ata; 6 = 0.4 kg/kg of mixture; points, experimental; lines, simulated. propylene cracking have been discussed by Froment et al. (1976b). A condensation such as C3H6
+ C4H6
-
polymer
is also reported in the literature (Bowley and Steiner, 1951). No reliable kinetic data are available, however. The reaction scheme for propylene cracking is shown in Table 11. Typical concentration profiles are shown in Figure 11.For an improvement of the fit, radicals heavier than C5Hlr and more molecular reactions would have to be considered.
Mixture Cracking Reaction schemes for the cracking of paraffinic mixtures have been proposed by Murata et al. (1974) and Kubota et al. (1969). The parameters obtained from single-component cracking had to be adapted to get a satisfactory fit of the mixture cracking, however. In the present work the cracking of binary and ternary mixtures containing ethane, propane, normal, and isobutane experimentally studied by Froment et al. (1976a, 1977) was simulated. The reaction scheme for mixture cracking was obtained by superposition of the schemes for single-component cracking. There was no need to adjust the parameters to come to a satisfactory fit of the results. The interaction which has been reported (Froment et al., 1977) in the cracking of mixtures is directly accounted for by the detailed reaction schemes set up for the cracking of single components. Calculated concentration profiles are shown in Figure 12 for an
182
Ind. Eng. Chem. Fundam., Vol. 17, No. 3, 1978
ethane-propane-n -butane mixture and are compared with the experimental values. In mixture cracking the ratios of concentrations of radicals are altered, so that reactions which are not significant in single-component cracking may become important in mixture cracking. This is the case for the H-transfer reaction C3H6
+ H*
-+
C3Hv
+ Hz
Allara has quoted two sets of values for the kinetic parameters of this reaction ( A = 1.0 X l o l l , 5.0 X lolo; E = 3.8, 5.0). Kunugi e t al. (1970) have used A = 2.5 X lo9 and E = 1.1. Since this reaction is not very important in propane and nbutane cracking because of the low concentration of H - radical, any value can be used without much error. In mixtures cracking, however, the Ha concentration is increased, due to ethane decomposition. Only Kunugi's values gave satisfactory results, whereas the other values predicted too much decomposition of propylene. Isomerization of 1-C4Hg-to 2-C4Hg. is also an important reaction in mixture cracking. Conclusions The proposed reaction mechanisms satisfactorily predict the experimental results of single-component cracking for a wide range of temperatures. The kinetic parameters were obtained from the nonisothermal data under relaxation of the pseudo-steady-state hypothesis used hitherto in kinetic analysis and which has been shown to distort the values of the kinetic parameters (Sundaram and Froment, to be published). A unique set of kinetic parameters was used for each reaction irrespective of the feed components. Since the parameters were obtained from a simultaneous consideration of the cracking of various single components, the reliability of the parameters is thought t o be greatly improved as compared with previous attempts. The superposition of the reaction schemes for single-component cracking does account for the interaction observed in mixture cracking. The complete reaction scheme presented here now allows an accurate simulation of industrial gas cracking. Acknowledgment The support of the Process Data Group of K.T.I., Zoetermeer, the Netherlands, is gratefully acknowledged. Nomenclature A = frequency factor, s-l or L mol-l s-l E = activation energy, kcal/mol Fj = molar flow rate of j t h component, mol/s Fo = inlet molar flow rate of hydrocarbon, mol/s h = reaction rate coefficient, s-l N = number of reactions n = reactionorder P = pressure, atm abs P o = outlet pressure, atm abs R = gas constant, kcal/mol K Rj = rate of formation of j t h component per unit volume of reactor, mol L-l s-l ri = reaction rate of i t h reaction, mol L-l s-l sij = stoichiometric coefficient of j t h component in i t h reaction T = temperature, "C or K T o = outlet temperature, "C or K V = reactor volume, L V , = equivalent reactor volume, L x = conversion of key component X B = n-butane conversion, % X ~ B = isobutane conversion, % X , = propane conversion, %
2 = reactor length coordinate, m 6 = dilution factor, kg of steam/kg of hydrocarbon D = area of cross section of the reactor including conversion factor from m3 to L L i t e r a t u r e Cited Abbel, P. I., "Comprehensive Chemical Kinetics", C. H. Bamford and C. F. H. Tipper, Ed., Vol 18, p 111, Elsevier, Amsterdam, 1976. Aiken, R. C., Lapidus, L., AIChEJ., 20, 368 (1974); 21, 817 (1975a); 21, 1227 (1975b). Allara, D. L., "A compilation of kinetic parameters for the thermal degradation of n-alkane molecules", personal communication. Aliara. D. L., Edeison, D., Int. J. Chem. Kinet., 7, 479 (1975). Amano, A., Uchiyama M., J. Phys. Chem., 67, 1242 (1963); 68, 1133 (1964). Beckwith, A. L. J.. "Organic Chemistry Series One", Vol. IO,p 1, Butterworths. London, 1973. Benson, S. W.. Hougen, G. R., J. Phys. Chem., 71, 1735 (1967). Blakemore, J. E., Corcoran, W. H., Ind. Eng. Chem. Process Des. Dev., 8, 206 (1969). Biakemore, J. E., Barker, J. R.. Corcoran. W. H., Ind. Eng. Chem. Fundam., 12, 147 (1973). Bowely. D., Steiner, H.,Discuss. Faraday SOC., 10, 198 (1951). Boyd, M. L., Wu, T. M., Back, M. H., Can. J. Chem., 46, 2416 (1968). Bradley, J. N., Frend. M. A,, J. Phys. Chem., 75, 1492 (1971). Bradley, J. N.. Proc. Roy. Soc., London, Ser. A, 337, 199 (1974). Buekens, A. G., Froment, G. F., Ind. Eng. Chem. Process Des. Dev., 7, 435 (1968). Buekens, A. G., Froment, G. F., Ind. Eng. Chem. Porcess Des. Dev., 10, 309 (1971). Cventanovic, R. J., Irwin, R. S., J. Chem. Phys., 46, 1694 (1971). Danby, C. J., Spall, 8.C., Stubbs, F. J., Hinselwood, C., Proc. Roy. SOC.London, Ser. A, 228, 448 (1955). Edelson, D., Allara, D. L., AIChEJ., 19, 638 (1973). Froment, G. F., Van de Steene. B.O., Van Damme, P., Narayanan, S., Goossens, A. G., ind. Eng. Chem. Process Des. Dev., 15, 495 (1976a). Froment, G. F., Van de Steene, B. O., Goossens, A. G., paper presented at the 172nd National Meeting of the American Chemical Society, San Francisco, Calif., Aug 1976b. Froment, G. F., Van de Steene, B. O., Van Den Berghe, P. J., Goossens, A. G., AIChE J., 23, 93 (1977). Gear, C. W.. "Numerical Initial Value Problems in Ordinary Differential Equations", Prentice-Hall, Englewood Cliffs, N.J., 1971. Herriott, G. E., Eckert, K. E., Albright, L. F., AIChE J., 18, 84 (1972). Hiatt, R., Benson, S. W., J. Am. Chem. SOC., 94, 6886 (1972). Hougen, 0. A., Watson, K. M., "Chemical Process Princlples", Vol. 111, Wiiey, New York, N.Y., 1947. Ingold, K. U., Stubbs, F. J., J. Chem. Soc., 1749 (1951). Kerr, J. A., "Comprehensive Chemical Kinetics", C. H. Bamford and C. F. H. Tipper, Ed., Vol. 18, p 39, Elsevier, Amsterdam, 1976. Kinney, C. R., Delbell, E., Ind. Eng. Chem., 46, 548 (1954). Kubota, K., Morita. N., J. Chem. SOC.Jpn., 72, 616 (1969). Kunugi, T., Sakai, T., Soma, K., Sasaki, Y.. Ind. Eng. Chem. Fundam., 8, 374 (1969). Kunugi, T., Sakai, T., Soma, K., Sasaki, Y., Ind. €ng. Chem. Fundam., 9, 319 (1970). Kurylo, M. J., Peterson, N. C., Braun, W., J. Chem. Phys., 53, 2776 (1970). Kurylo, M. J., Peterson, N. C., Braun, W., J. Chem. Phys., 54, 4662 (1971). Lalonde, A. C., Price, S. J., Can. J. Chem., 49, 3367 (1971). Laidler, K. J., "Chemical Kinetics", McGraw-Hill, New York, N.Y., 1965. Laidler. K. J., Wojciechowski, B. W., Proc. Roy. Soc. London, Ser. A, 259, 257 (1960). Laidler, K. J., Sagert, N. H., Wojciechowski, B. W., Proc. Roy. SOC.London, Ser. A, 270, 242 (1962). Leathard, D. A., Purnell, J. H., Ann. Rev. Phys. Chem., 21, 197 (1970). Lin, M. C., Back. M. H., Can. J. Chem., 44, 2357 (1966a). Lin, M. C., Back, M. H., Can. J. Chem., 44, 2369 (1966b). Murata, M., Takeda, N., Saito, S., J. Chem. Eng. Jpn., 7, 286 (1975). Pacey, P. D., Purnell, J. H., J. Chem. Soc., Faraday Trans. 1, 68, 1462 (1972a). Pacey, P. D., Purnell, J. H., Ind. Eng. Chem. Fundam., 11, 233 (1972b). Pacey, P. D., Purnell, J. H., Int. J. Chem. Kinet., 4, 657 (1972~). Powers, D. R., Corcoran, W. H., Ind. Eng. Chem. Fundam., 13, 351 (1974). Schugerl, H., Happel, J.. Ind. Eng. Chem. Process Des. Dev., 8,419 (1969). Seinfeld, J. H., Lapidus. L., Hwang, M., Ind. Eng. Chem. Fundam., 9, 266 (1970). Sena. M. P., Kershenbaum, L. S., AIChE Symp. Ser. No. 147, 71, 111 (1975a). Sena, M. P., Kershenbaum, L. S., AIChE J., 21, 1220 (1975b). Snow, R. H., J. Phys. Chem., 70, 2780 (1966). Silcocks. C. G., Proc. Roy. SOC.London, Ser. A, 233, 465 (1955). Sundaram. K. M., Froment. G. F., Chem. Eng. Sci., 32, 601, 609 (1977). Swarc, M., J. Chem. Phys., 17, 284 (1949). Trotman-Dickenson. A. F., Adv. Free-Radical Chem., 1, 1 (1965). Van Damme, P. S., Narayanan, S., Froment, G. F., AIChE J. 21, 1065 (1975). Whittle, E., "Physical Chemistry Series One", Vol. 9, p 75, Butterworths, London, 1973. Yang, K., J. Am. Chem. SOC., 84.3795 (1962).
Received for reuiew February 22,1977 Accepted April 20,1978
