Understanding the chain mechanism of radical reactions in n-hexane pyrolysis

Article abstract of DOI:10.1007/s11164-013-1468-6

Pyrolysis of n-hexane is interpreted in terms of a chain mechanism. The first-order kinetic equation fits experimental data adequately. The rate constant for feed conversion increases from 1.75 × 10^-2 to 3.79 × 10^-1 s^-1 with increasing temperature from 923 to 1,023 K, giving an apparent activation energy of 208.5 ± 1.0 kJ mol^-1. Initial primary products consist of hydrogen, C₁-C₄ paraffins, C₂-C₅ olefins, iso-hexanes, and coke. Quantitative interpretation of the chain mechanism shows that different products are formed from different elementary reactions with different selectivity. Increasing temperature promotes homolysis of the feed molecule and β-cracking of radicals and reduces the proportion of H abstraction by radicals, resulting in an increase in production of hydrogen and formation of a more dehydrogenated coke. The average reaction chain length decreases from 7.33 to 5.73 as the temperature is increased from 923 to 1,023 K.

Full text of DOI:10.1007/s11164-013-1468-6

Res Chem Intermed
DOI 10.1007/s11164-013-1468-6
Understanding the chain mechanism of radical
reactions in n-hexane pyrolysis
Da Li Yingxian Zhao
•
Received: 5 September 2013 / Accepted: 20 October 2013
Springer Science+Business Media Dordrecht 2013
ꢀ
Abstract Pyrolysis of n-hexane is interpreted in terms of a chain mechanism. The
first-order kinetic equation fits experimental data adequately. The rate constant for
-
feed conversion increases from 1.75 9 10 to 3.79 9 10
2
-1 -1
s
temperature from 923 to 1,023 K, giving an apparent activation energy of
with increasing
-
1
2
fins, C –C olefins, iso-hexanes, and coke. Quantitative interpretation of the chain
08.5 ± 1.0 kJ mol . Initial primary products consist of hydrogen, C –C paraf-
1 4
2
5
mechanism shows that different products are formed from different elementary
reactions with different selectivity. Increasing temperature promotes homolysis of
the feed molecule and b-cracking of radicals and reduces the proportion of H
abstraction by radicals, resulting in an increase in production of hydrogen and
formation of a more dehydrogenated coke. The average reaction chain length
decreases from 7.33 to 5.73 as the temperature is increased from 923 to 1,023 K.
Keywords n-Hexane ꢀ Pyrolysis ꢀ Radical reactions ꢀ Mechanism ꢀ
Selectivity
Introduction
As an important process in the production of light olefins, for example ethylene and
propylene, hydrocarbon pyrolysis has been the subject of a large number of studies
for many years [1–6]. The continuing expansion of the petrochemical industry, the
diversification of feedstock, and the increased price of oil have stimulated renewed
interest and research into the mechanism and kinetics of pyrolysis reactions [7–13].
It is commonly accepted that pyrolysis of hydrocarbons proceeds via a free-radical
chain mechanism [14–20], mainly including:
D. Li ꢀ Y. Zhao (&)
Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China
e-mail: zyx@nit.zju.edu.cn
123

D.Li, Y. Zhao
–
–
homolysis of hydrocarbons to form free radicals (initiation);
b-decomposition of free radicals or H-abstraction of radicals from hydrocarbons
propagation);
(
–
–
radical isomerization; and
recombination or disproportionation of radicals (termination).
By use of thermochemical data, for example enthalpy and bond-dissociation
energy [21, 22], researchers were able to generate a mechanistic model of
hydrocarbon pyrolysis including all possible elementary reactions. For a complex
system of hydrocarbon pyrolysis involving a variety of radicals (reactive
intermediates), such a mechanistic model could encompass a huge number of
elementary reactions. In n-hexane pyrolysis, for example, a kinetic model including
2
05 species and 1,403 elementary reactions has been suggested [23]. Obviously, all
the reactions may be thermochemically possible but only some are kinetically
feasible. Kinetic modeling based on thermochemical data could give information
about the thermodynamic possibility of a reaction occurring but could not confirm
the reaction has occurred. For practical application, the mechanism from
thermochemical analysis must be optimized on the basis of reaction feasibility,
and the kinetic model must be validated by experimental investigation.
In this work, pyrolysis of n-hexane was investigated in a gas-phase, plug-flow
quartz tube reactor at 923, 973, and 1,023 K. On the basis of the distribution of
primary products, the chain mechanism of radical reactions was developed to
interpret details of reaction kinetics and selectivity. We have also discussed the
effect of temperature on kinetics and selectivity in terms of reaction path
probabilities by using the chain mechanism postulate.
Materials and methods
Materials
n-Hexane of [99 % purity was obtained from Hangzhou Refinery China
Petrochemical Corporation and used without further purification.
Operating procedure
Reaction runs were conducted in a gas-phase, plug-flow quartz tube reactor with an
independently controlled two-zone heater. Pure n-hexane with no diluents was first
pumped into the preheating zone (20 cm 9 1.5 cm i.d.), vaporized, then transferred
to the reaction zone (15 cm 9 1.5 cm i.d.). Reaction runs were conducted by
changing the feed rate while keeping the total amount of feed constant. Before each
3
-1
run the reactor was pre-purged for 20 min with nitrogen (*200 cm min ), in situ.
During the reaction, liquid products were collected in a glass receiver cooled in ice
water and in a cold finger cooled in dry ice. Gaseous products were trapped in a gas
burette by downward displacement of water. At the end of each run the reactor was
3
-1
purged with dry nitrogen at 150 cm min for 20 min then washed with toluene.
1
23

Radical reactions in n-hexane pyrolysis
Residues insoluble in toluene were regarded as coke. To quantify the amount of
coke formed during a run, carbon dioxide-free air was passed through the reactor
3
-1
(
*150 cm min ) at 1,073 K for 6 h. The water produced was collected two
Drierite tubes in series and the carbon dioxide in two Ascarite tubes. Complete
combustion to carbon dioxide was ensured by passing the dried combustion stream
through a reactor containing a combustion catalyst. The amount and composition
(H/C ratio) of the coke were determined from the weights of water and carbon
dioxide collected.
Analysis
All products were identified by use of an Agilent 5973 GC–MS. Gaseous products
were analyzed by use of an Agilent 6820 gas chromatograph. Liquid products were
analyzed by use of an Agilent 2010 gas chromatograph with a 60-m SE54 capillary
column and flame ionization detector. Products were eluted at 283 K followed by a
-
1
temperature program of 5 K min to 573 K.
Results and discussion
Chain reaction mechanism
A chain mechanism of free-radical reactions of n-hexane was formulated, and is
presented in Table 1. It consists of three main steps:
–
–
–
chain initiation by homolytic dissociation of C–H and C–C bonds in feed
molecules;
chain propagation by b-decomposition of free radicals or H-abstraction of
radicals from the feed molecules; and
chain termination by combination of two radicals.
Because of the activation energy required, disproportionation reactions of
radicals are kinetically insignificant in comparison with combination reactions of
radicals, which require zero activation energy, and thus are not taken into account,
to make the mechanism more feasible. Large radicals have a variety of isomers with
•
different skeletons or positions of the free electron. For example, the radical C H
6
13
could have more than 20 isomers. At the moment, we are unable to identify those
isomeric radicals with our current analytical method or to interpret the reactions of
each isomeric radical by use of the data available. Therefore, we have labeled a
radical without distinguishing its isomers, and also leave internal isomerization of
radicals as a matter to be further studied.
‘‘Coke’’ is a common generic name given to nonvolatile carbonaceous materials.
In the petroleum industry, coke is commonly defined as the materials insoluble in
benzene or toluene. In fact, the definition of ‘‘coke’’ is arbitrary and vague, but the
formation of coke in hydrocarbon pyrolysis may be a complex process involving a
variety of reactions, for example polymerization of free radicals, cyclization of alkyl
chains, dehydrogenation and aromatization of naphthenic rings, elimination of side
123

D.Li, Y. Zhao
Table 1 Chain mechanism of n-hexane pyrolysis
Elementary reaction path
Rate
constant
RPP
symbol
•
•
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
6
6
6
6
3
4
4
5
5
5
6
6
6
6
6
6
6
6
6
6
6
6
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
14 ? H ? C
6
H
13
Initiation
k
k
k
k
k
k
k
k
k
k
k
k
k
k
k
k
k
k
k
k
00
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
00
14 ? CH •
? C
H
•
3
5
11
01
01
2
H
5•
? C H
4
9•
02
02
14 ? C
•
14 ? 2C
3
H
7
03
03
•
•
7
9
9
? C
? C
? C
2
H
2
H
3
H
4
4
6
? CH
3
Propagation b-
decomposition
b32
b42
b43
b52
b53
b54
b62
b63
b64
b65
H60
H61
H62
H63
H64
H65
b32
b42
b43
b52
b53
b54
b62
b63
b64
b65
H60
H61
H62
H63
H64
H65
•
•
•
? C
2
H
5
•
? CH
3
•
•
11 ? C
2
3
4
2
3
4
5
H
H
H
H
H
H
H
4
6
8
4
6
8
? C
3
2
H
7
•
•
11 ? C
? C
H
5
11•
3•
? CH
? C
•
•
•
•
•
13 ? C
? C
? C
? C
4
3
2
H
H
H
9
7
5
3
•
13 ? C
•
13 ? C
•
13 ? C
10 ? CH
•
•
14 ? H ? H
2
? C
6
H
13
H-abstraction
3•
4
6
H
13•
14 ? CH ? CH
? C
•
•
•
14 ? C
14 ? C
14 ? C
2
3
4
5
H
H
H
H
5
7
9
? C
? C
? C
2
H
H
H
6
? C
? C
6
H
13
13
•
•
3
4
8
6
H
•
6 13
H
10 ? C
•
6 13
12 ? C H
•
14 ? C
•
11 ? C
5
H
•
13 , iso-C
14 ? iso-C
14 ? C H
6
6
H
13
Isomerization
Termination
K66 = k6,?/k6,-
•
6
H
13 ? iso-
k
H66
X
H66
•
C
6
H
13
•
•
•
•
•
CH
CH
CH
CH
3
3
3
3
? CH
3
? C
2
H
6
k
k
k
k
k
k
k
C11
C12
C13
C14
C22
C23
Coke
X
C11
X
C12
X
C13
X
C14
X
C22
X
C23
X
Coke
•
? C
? C
? C
2
3
4
H
H
H
5
7
9
? C
? C
? C
3
4
5
H
H
H
8
•
•
10
12
•
•
C
2
C
2
C
6
H
H
H
5
? C
2
3
H
5
7
? C
? C
4
H
10
12
•
•
5
? C
H
5
H
14 ? n
C
CxHy ? n
H
H
2
Coke formation
k
k
k
0i is the rate constant of feed consumption via the ith mode of the homolysis reaction
•
j i 2i?1
bij is the rate constant of olefin C H2j production from b-cracking of radical C H
•
H6i is the rate constant of feed consumption via an H-abstraction reaction by radical C
i
H
2i?1 to produce
i 2i?2
paraffin C H
•
k
Cij is the rate constant of paraffin Ci?j
•
H2(i?j)?2 production from a combination of radicals C
i
H
2i?1 and
C
j
H
2j?1 in a termination reaction
K66 is the equilibrium constant of isomerization between normal and isomeric hexyl radicals
chains on aromatic rings, and condensation and peri-condensation of aromatic rings
24, 25]. For the time being, we will use a simplified coke-forming reaction as
shown in the last line of Table 1; this will enable us to maintain mass and
[
1
23

Radical reactions in n-hexane pyrolysis
stoichiometric balances without examining the details of the coke-forming
processes. We wish to present an additional report on the detailed mechanism
and kinetics of coke formation, radical isomerization, and production of minor and
secondary products in the future.
Kinetics of n-hexane conversion
By using the steady-state assumption of radical concentration for the mechanism in
Table 1, the first-order kinetic equation for overall conversion of n-hexane by
pyrolysis in a plug flow reactor was obtained:
e
ð1 þ eÞ
s ¼ ꢁ A X ꢁ
lnð1 ꢁ XÞ;
ð1Þ
A
where X is the conversion of feed, s is the space time, e is the volume expansion
coefficient, and the kinetic variable A is defined by the equation:
3
5
X
where k is the rate constant (given in a footnote for a specific elementary reaction in
X
A ¼
k0i þ
kH6nIn þ kH66K66I6;
ð2Þ
i¼0
n¼1
Table 1), K66 is the equilibrium constant between normal and isomeric hexyl rad-
icals, and I is the steady-state concentration of radical CnH2nþ1 ꢀ :
n
As illustrated in Fig. 1b, the experimental data are well fitted by the linear
Eq. (1), and the optimum value of the rate constant for feed conversion, A,
-
2
-2
determined from this fitting increases from 1.75 9 10
to 8.68 9 10
with increasing temperature from 923 to 973 to 1,023 K.
As shown in Fig. 2, the Arrhenius plot gives a straight line and leads to an
to
-
1 -1
3
.79 9 10
s
-
1
activation energy of 208.5 ± 1.0 kJ mol for n-hexane pyrolysis in the
temperature range 923 to 1,023 K. This value of the activation energy is slightly
-
1
higher than the value (187.5 ± 0.8 kJ mol ) reported by Pramanik and Kunzru
for n-hexane pyrolysis in a jet-stirred reactor in the temperature range
9
93–1,083 K [3].
Selectivity of elementary reactions
Optimum performance envelopes of the products
A method for determining the initial selectivity for products from experimental
product yields and feed conversion was defined. For each reaction product, the time-
averaged yield sampled from t = 0 to t is plotted against the time-averaged
f
conversion of the feed. Each of the plots is enveloped by a single curve, the
optimum performance envelope (OPE). According to the initial slope and
subsequent curvature of the OPEs, all the products can be selectively classified as
six patterns [26].
The OPEs of products from n-hexane pyrolysis at 923 K are presented in Fig. 3.
One can see that primary products consist of C –C paraffins, C –C olefins, iso-
1
4
2
5
123

D.Li, Y. Zhao
Fig. 1 a Theoretical curves and
experimental points for n-
hexane conversion versus space
time at 923, 973, and 1,023 K.
b Linear plots of Eq. (1) for n-
hexane pyrolysis at 923, 973,
and 1,023 K
(
a) 1
00
90
80
1023 K
973 K
7
6
5
4
3
2
1
0
0
0
0
0
0
0
0
923 K
0
.0
5.0
10.0
15.0
20.0
25.0
30.0
Space time (s)
(
b) 5.000
4
3
2
1
0
.000
.000
.000
.000
.000
0
.0
5.0
10.0
15.0
20.0
25.0
30.0
Space time, s
1
023 K
973 K
923 K
Fig. 2 Arrhenius plot for n-
hexane pyrolysis
0.000
experimental data
fitting line
-
1.000
2.000
3.000
4.000
5.000
-
-
-
-
0
.0009
0.0010
0.0011
0.0012
1/T (1/K)
hexanes, hydrogen, and coke. In addition to the primary products, pentanes and
hexenes are identified as secondary products, because the slopes at the origin of
their OPEs are zero.
1
23

Radical reactions in n-hexane pyrolysis
0
0
0
0
0
0
.500
.400
.300
.200
.100
.000
8.000
6
4
2
.000
.000
.000
0.000
0.0
0
.0
10.0 20.0 30.0 40.0 50.0
10.0 20.0 30.0 40.0 50.0
X (wt%)
X (wt%)
8
6
4
2
0
.000
.000
.000
.000
.000
12.000
0.000
.000
6.000
1
8
4
2
0
.000
.000
.000
0
.0
10.0 20.0 30.0 40.0 50.0
0
.0
10.0 20.0 30.0 40.0 50.0
X (wt%)
X (wt%)
2
2
1
1
0
0
0
.400
.000
.600
.200
.800
.400
.000
1
1
2.000
0.000
8
.000
6.000
4.000
2.000
0.000
0
.0
10.0 20.0 30.0 40.0 50.0
0.0
10.0 20.0 30.0 40.0 50.0
X (wt%)
X (wt%)
3
2
2
1
1
0
0
.000
.500
.000
.500
.000
.500
.000
10.000
8
6
4
2
.000
.000
.000
.000
0.000
0.0
0
.0
10.0 20.0 30.0 40.0 50.0
10.0 20.0 30.0 40.0 50.0
X (wt%)
X (wt%)
Fig. 3 Optimum performance envelopes for products from n-hexane pyrolysis at 923 K
123

D.Li, Y. Zhao
0
0
0
0
0
0
.050
.040
.030
.020
.010
.000
6
.000
5.000
4
3
2
1
.000
.000
.000
.000
0.000
0.0 10.0 20.0 30.0 40.0 50.0
0.0 10.0 20.0 30.0 40.0 50.0
X (wt%)
X (wt%)
1
0
0
0
0
0
.000
.800
.600
.400
.200
0.040
0
0
0
.030
.020
.010
.000
0
0.000
.0 10.0 20.0 30.0 40.0 50.0
0.0 10.0 20.0 30.0 40.0 50.0
X (wt%)
X (wt%)
6
5
4
3
2
1
0
.000
.000
.000
.000
.000
.000
.000
0
.0 10.0 20.0 30.0 40.0 50.0
X (wt%)
Fig. 3 continued
Initial selectivity for primary products
Table 2 gives initial selectivity for primary products from n-hexane pyrolysis at 923,
9
73, and 1,023 K.
Kinetically, selectivity for a product can be defined as the ratio of the rate of
product formation (r )/feed conversion rate (r ), that is:
j tot
1
23

Radical reactions in n-hexane pyrolysis
Table 2 Initial weight and molar selectivity for products from n-hexane pyrolysis at different
temperatures
a
Product
Initial weight selectivity
Initial molar selectivity
923 K
973 K
1,023 K
923 K
973 K
1,023 K
Hydrogen
Methane
Ethane
0.0053
0.0843
0.0728
0.1907
0.0388
0.2121
0.0491
0.1566
0
0.0064
0.0831
0.0707
0.1962
0.0360
0.2140
0.0457
0.1564
0
0.0072
0.0820
0.0697
0.2008
0.0339
0.2153
0.0434
0.1562
0
0.2285
0.4530
0.2086
0.5856
0.0758
0.4344
0.0728
0.2405
0
0.2752
0.4467
0.2028
0.6026
0.0707
0.4382
0.0677
0.2402
0
0.3096
0.4410
0.1997
0.6168
0.0662
0.4410
0.0643
0.2399
0
Ethylene
Propane
Propylene
Butanes
Butenes
Pentanes
Pentenes
iso-Hexanes
Hexenes
Coke
0.0993
0.0155
0
0.0991
0.0081
0
0.0990
0.0051
0
0.1220
0.0155
0
0.1218
0.0081
0
0.1216
0.0051
0
0.0755
1.0000
0.0835
0.9992
0.0867
0.9993
0.0786
2.5153
0.0871
2.5606
0.0908
2.5959
Total
a
molecular wt: of reactant
molecular wt: of product
Molar selectivity ¼ weight selectiviy ꢂ
rj
Sj ¼
;
ð3Þ
rtot
where S represents he molar selectivity of the jth product.
j
To measure the relative rates of different elementary reactions, the reaction path
probability (RPP) is defined as:
rij
Xij ¼
;
ð4Þ
rtot
where X is the symbol for RPP, rtot is the overall rate of feed conversion, and r is
ij
the rate of the elementary reaction labeled with the subscript ‘‘ij’’.
Because production of a product may involve several elementary reaction paths,
there must be relationship between selectivity for products and RPPs of elementary
reactions. Mathematically, the selectivity for a product may be expressed as a linear
function of the corresponding RPPs. For production of ethylene, for example, we
have:
rC H ¼ rb32 þ rb42 þ rb52 þ rb62:
Dividing both left and right sides of this equation by the overall rate of feed
ð5Þ
2
4
conversion gives:
SC H ¼ Xb32 þ Xb42 þ Xb52 þ Xb62:
All such relationships together constitute a group of linear equations which can
ð6Þ
2
4
be normally expressed by a matrix equation as shown in the Appendix. By using
123

D.Li, Y. Zhao
experimental selectivity data for products to solve this matrix equation, data for all
RPPs can be obtained.
Reaction path probabilities of elementary reactions
Mathematical calculation of RPP for different elementary reactions in n-hexane
pyrolysis at 923 K is described in detail in the Appendix. Calculated RPP values of
all elementary reactions at different temperatures are presented in Table 3. By using
the RPP data we can quantitatively examine the reaction mechanism of n-hexane
pyrolysis in great detail.
Quantitative interpretation of the chain mechanism
Feed conversion reactions
The feed is consumed by three kinds of process:
–
–
–
direct homolysis of different C–C and C–H bonds in reaction chain initiation
Path I);
(
H-abstraction of different radicals from the feed molecules in reaction chain
propagation (Path II); and
the process associated with coke formation (Path III).
The total rate of n-hexane conversion is sum of the three kinds of reaction, as
follows:
3
6
X
X
roverall ¼ rPathI þ rPathII þ rPathIII ¼ rCoke þ
roi þ
rH6i
ð7Þ
0
0
According to definition in Eq. (4), we have:
3
6
X
X
1
¼
Xoi þ
XH6i þ Xcoke
ð8Þ
0
0
Scheme 1 shows the calculated RPP values for different paths in the processes of
reactant conversion at 923 K. Each individual RPP represents the fraction of feed
molecules which are consumed via that specific reaction. One can see that three
kinds of process contribute to overall conversion of the feed, and the ratio I:II:III is
0
.1364:0.7850:0.0786. It is obvious that feed is principally converted by
H-abstraction reactions in chain propagation, producing some of the paraffinic
products. By using this kind of quantitative information we can examine the
probabilities of the different elementary reactions in more detail. In Path I, for
example, four reaction paths contribute to conversion of the feed in a probability
ratio X03 : X02 : X01 : X00 of 0.0112:0.0225:0.0070:0.0957. In comparison with each
other, the homolysis of C–H bonds has the largest RPP value, probably because of
the large number of C–H bonds in the feed molecule. Homolysis of the different
C–C bonds in the feed molecules follows the order C –C & C –C [ C –C ,
c
c
b
c
a
b
simply because of higher dissociation energy of the C –C bond than that of C –C or
a
b
b
c
1
23

Radical reactions in n-hexane pyrolysis
Table 3 RPPs for n-hexane
pyrolysis at different
temperatures
Symbol
RPP at temperature (K):
9
23
973
1,023
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
00
0.0957
0.0070
0.0225
0.0112
0.3620
0.0797
0.0686
0.0020
0.0033
0.0017
0.1419
0.3625
0.2388
0.1220
0.0957
0.4530
0.1871
0.0177
0.0161
0.0000
0.0155
0.0215
0.0581
0.0073
0.0000
0.0494
0.0000
0.0786
0.1172
0.0073
0.0223
0.0112
0.3741
0.0846
0.0727
0.0021
0.0035
0.0018
0.1417
0.3620
0.2384
0.1218
0.1172
0.4467
0.1691
0.0070
0.0067
0.0000
0.0081
0.0337
0.0634
0.0052
0.0000
0.0558
0.0000
0.0872
0.1329
0.0076
0.0227
0.0113
0.3850
0.0882
0.0760
0.0021
0.0036
0.0018
0.1415
0.3614
0.2381
0.1216
0.1329
0.4410
0.1554
0.0002
0.0002
0.0000
0.0051
0.0443
0.0660
0.0010
0.0000
0.0631
0.0000
0.0908
01
02
03
b32
b42
b43
b52
b53
b54
b62
b63
b64
b65
H60
H61
H62
H63
H64
H65
H66
C11
C12
C13
C14
C22
C23
coke
•
•
•
C –C [21, 22]. In Path II, one can see that the smaller radicals H , CH , and C H
2
c
c
3
5
•
•
easily abstract H from the feed molecule, that radicals C H7 and C H are able to
3
4 9
•
abstract H from the feed, but that the RPP value of radical C H for abstraction of
11
5
H is zero, indicating that the ability of a radical to abstract H from the feed
•
decreases with increasing size. However, the RPP value for iso- C H is not zero,
6
13
possibly because of its relatively high concentration and the stable structure of this
radical.
Paraffin-production reactions
Paraffinic products are formed via two kinds of process—H-abstraction reactions of
radicals from feed molecules in reaction chain propagation and combination
123

D.Li, Y. Zhao
.
.
I.
Initiation
Homolysis)
H + C H
6
13
(0.0957)
(0.0070)
(
CH . + C H
.
.
3
5
11
(
0.1364)
.
C H + C H (0.0225)
2
5
4
9
.
.
C H + C H (0.0112)
3
7
3
7
+
+
H.
CH .
H + C H
.
2
6
13
(0.0957)
.
3
CH + C H
4
6 13
(0.4530)
(0.1871)
(0.0177)
II.
Propagation
H-abstraction)
+ C H
2
5
7
C H +
C H
6 13
.
2
6
(
.
C H
+ C H
.
6
14
3
C H + C H
3 8 6 13
(
0.7850)
.
+
+
C H
.
4
9
C H + C H
13
(0.0161)
4
10
6
.
C H
5
11
.
C H + C H
13
(0.0000)
(0.0155)
5
12
6
.
+
i-C H
6 13
.
iC H + C H
13
6
14
6
III. Coke formation
0.0786)
C H
+ 1.69H2 (0.0786)
6
10.62
(
Scheme 1 Reaction path probability (RPP) for n-hexane conversion by pyrolysis at 923 K
reactions between two radicals in reaction chain termination. The total rate of
paraffin production reactions should be equal to the total rate of elementary
reactions in the two kinds of process, that is:
6
2
3
6
X
Therefore, the total selectivity for paraffinic products equals the total RPP for
X X
X
rC H
¼
rC þ
rH6i:
ð9Þ
n
2nþ2
ij
n¼0
i¼1 j ꢃ i
i¼0
these elementary reactions as follows:
6
2
3
6
X
X X
X
SC H
¼
XC þ
XH6i:
ð10Þ
n
2nþ2
ij
n¼0
i¼1 j ꢃ i
i¼0
The RPPs for different H-abstraction reactions (XH6i) have been discussed above.
Scheme 2 shows the calculated RPP values for the different paths in the processes
of chain termination. One can see that besides production in the processes of chain
propagation, ethane, propane, and butanes are produced in the processes of chain
termination, with RPP values of 0.0215 (XC11), 0.0518 (XC12), and 0.0567
(
XC13 þ XC22), respectively. Because combination of two radicals requires no
activation energy [10], it may be concluded that the concentrations of radicals
involved in the chain termination processes follows the order:
•
•
•
•
C H [ CH [ C H [ C H . Because no pentanes are found in the products,
2
5
3
3
7
4 9
the RPP values for XC14 or XC23 must be zero.
Olefin-production reactions
Because olefinic products are formed solely via b-decomposition of radicals, the
total rate of olefin production reactions should equal to the total rate of radical b-
cracking reactions, that is:
1
23

Radical reactions in n-hexane pyrolysis
Scheme 2 RPPs of radical
combination reactions for chain
termination in n-hexane
pyrolysis at 923 K
+
+
CH3.
C H
(0.0215)
0.0581)
2
6
.
C H
2
5
(
C H
3
8
CH .
3
+ C H7.
3
C H
(0.0073)
(0.0000)
4
10
12
.
+
C H
4
9
C H
5
.
(0.0494)
(0.0000)
+
C H
C H
2
5
4
10
.
C H
2
5
.
+
C H
3 7
C H
5
12
5
6
iꢁ1
X
X X
rC H
¼
rbij:
ð11Þ
n
2n
n¼2
i¼3 j¼2
Consequently, the total selectivity for paraffinic products is equal to the total RPP
for these elementary reactions, i.e.:
5
6
iꢁ1
X
X X
SC H
¼
X :
bij
ð12Þ
n
2n
n¼2
i¼3 j¼2
The rate of a radical b-cracking reaction depends on by the size and
•
•
•
concentration of the radical. Obviously, the radicals H , CH and C H cannot
participate in b-decomposition reactions. Scheme 3 shows the calculated RPP
values for the b-cracking reactions of C –C radicals to produce different olefins. It
3
2 5
3
6
is apparent that ethylene is produced by b-cracking of propyl, butyl, pentyl, and
hexyl radicals, with RPPs of 0.3620 (Xb32), 0.0797 (Xb42), 0.0020 (Xb52), and 0.1419
(Xb62), respectively; propylene is produced by b-cracking of butyl, pentyl, and hexyl
radicals, with RPPs of 0.0686 (Xb43), 0.0033 (Xb53), and 0.3625 (Xb63), respectively;
butenes are produced by b-cracking of pentyl and hexyl radicals, with RPPs of
0
.0017 (Xb54) and 0.2388 (Xb64), respectively; and pentenes are produced solely by
b-cracking of hexyl radicals, with an RPP of 0.1220 (Xb65). For production of
ethylene to propylene to butenes to pentenes, the numbers of b-cracking reactions
decrease progressively from 4 to 3 to 2 to 1, with RPP values from 0.5856 to 0.4344
to 0.2405 to 0.1220.
Radical competitive reactions
Active intermediates in n-hexane pyrolysis include a variety of free radicals
•
C H
n
(n = 0, 1, 2, 3, 4, 5, 6), as shown in Table 1. Each radical is formed
via specific reaction paths and then competitively participates in a variety of
elementary reactions. Here we quantitatively analyze selectivity for elementary
2n?1
123

D.Li, Y. Zhao
Scheme 3 RPPs of radical b-
cracking reactions for chain
propagation in n-hexane
pyrolysis at 923 K
X¦Â32 (0.3620)
.
.
C H
CH
3
3
7
X¦Â42 (0.0797)
X¦Â52 (0.0020)
X¦Â62 (0.1419)
.
.
C H
C H
4
9
2
5
C H
+
+
2
4
.
.
.
C H
C H
5
11
3
7
C H
C H
.
6
13
4
9
X¦Â43 (0.0686)
.
CH3.
C H
C H
4
9
X¦Â53 (0.0033)
X¦Â63 (0.3625)
.
.
C H
C H
5
11
3
6
2
5
.
.
C H
C H
3 7
6
13
X¦Â54
(0.0017)
.
.
CH3.
C H
C H
5
11
C H
8
+
X¦Â64 (0.2388)
4
C H
.
6
13
2
5
X¦Â65 (0.1220)
.
CH3.
+
C H
C
5
H
10
6
13
reactions in which individual radicals participate during n-hexane pyrolysis at
23 K.
The radical H is formed by homolysis of C–H bonds in the feed molecule, and
9
•
then participates in a reaction in which H is abstracted from feed to produce
hydrogen with an RPP of 0.0957 (XH60), as shown in Fig. 4a.
•
The methyl radical (CH ) is formed by homolysis of C –C bonds in feed and by
3
a
b
b-cracking of C –C radicals; it then competes in reactions in which H is abstracted
3
6
from the feed, producing methane, and three other reactions in which it combines
•
•
•
with CH , C H , and C H radicals to produce ethane, propane, and butane,
3 7
3
2
5
respectively. As shown in Fig. 4b, this radical is most likely to participate in
H-abstraction, with an RPP of 0.4530 (XH61).
•
The ethyl radical (C H ) is formed by homolysis C –C bonds in feed and by b-
2
5
b
c
cracking of C –C radicals; it then competes in reactions in which H is abstracted
from the feed, producing ethane, and two other reactions in which it combines with
4
6
•
•
CH3 and C H radicals to produce propane and butane, respectively. As shown in
5
2
Fig. 4c, this radical is most likely to participate in H-abstraction, with an RPP of
.1871 (XH62).
The propyl radical (C H ) is formed by homolysis of the C –C bond in feed and
0
•
3
7
c
c
by b-cracking of C and C radicals; it then competes in reactions in which H is
5
6
abstracted from the feed, producing propane, the b-cracking reaction, producing
ethylene, and the reaction in which it combines with the CH3 radical, producing
•
1
23

Radical reactions in n-hexane pyrolysis
X00 (0.0957)
+ C H
6
14
.
.
H
C H + H2
6 13
XH60 ( 0.0957)
(a)
+
C H
6 14
X01
C H + CH4
.
XH61 (0.4530)
2XC11(0.0430)
6
13
.
X¦Â32
+CH3
(0.5613)
C H
2
6
.
X¦Â43
CH3
.
+
+
C H
2
5
.
XC12
X¦Â54
C H
(0.0581)
3
8
.
C H
3
7
X¦Â65
C H
X
C13 (0.0073)
4
10
(b)
+
+
C H
6
14
.
C H + C H
XH62 (0.1871)
6
13
2
6
X02
.
CH3
X¦Â42
X¦Â53
X¦Â64
( 0.3441)
C H
C H
XC12 ( 0.0581)
2XC22 (0.0989)
3
8
.
5
2
+C H .
2
5
C H
4
10
(c)
+
+
C H
6 14
2
X03
.
C H + C H8 XH63 (0.0177)
6
13
3
(0.3869)
.
CH3
X¦Â52
X¦Â63
C H .
XC13
(0.0073)
X¦Â32 (0.3620)
3
7
C H
4
10
.
C H + CH
3
2
4
(d)
+
C H
6
14
.
C H + C H XH64
6
13
4
10
(0.0161)
X02
(0.1644 )
.
C H
C H
4
.
4
9
2
+ C H X¦Â42 (0.0797)
X¦Â62
2
5
.
C H + CH
X¦Â43
(0.0686)
3
6
3
(e)
+
C H
6
14
.
C H + C H
12
XH65 (0.0000)
X¦Â52 (0.0020)
X¦Â53 (0.0033)
6
13
5
X01 (0.0070)
C H
C H .
+
3 7
2
4
.
11
C H
5
5.
C H + C H
2
3
6
.
C H + CH3
X
¦Â54 (0.0017)
4
8
(
f)
•
•
3
radical.
Fig. 4 The reaction path probability (RPP) for different radicals. a The H radical. b The CH
radical. e The C
•
•
•
•
•
13
c The C
2
H
5
radical. d The C
radical. h Internal H-abstraction from the C
3
H
7
4
H
9
radical. f The C
5
H
11 radical. g The C
6
H
•
6
H13 radical
butane. As shown in Fig. 4d, this radical is most likely to participate in the b-
cracking reaction, with an RPP of 0.3620 (Xb32).
•
The butyl radical (C H ) is formed by homolysis of C –C bonds in feed and by
4
9
b
c
b-cracking of C radicals; it then competes in reactions in which H is abstracted
6
123

D.Li, Y. Zhao
X00
XH60
XH61
XH62
XH63
.
C H + C H
X¦Â62 (0.1419)
2
4
4
9
7
.
(
0.8808)
C H
C
3
H
6
+ C H
X¦Â63 (0.3625)
X¦Â64 (0.2388)
X¦Â65 ( 0.1220)
3
.
6
13
.
C H + C H
4
8
2
5
.
C H + CH3
5
10
XH64
XH65
.
+ C
H
.
iso-C H
6
14
+
XH66
(0.0155)
13
6
13
iso- C H
C H
6
14
6
(g)
.
C H + C H (X¦Â63)
3
6
3
7
.
1,5 shift
.
..
.
.H
(
2-hexyl)
.
C H + C H
(X¦Â62
)
.
2
4
4
9
1,4 shift
(
1-hexyl)
C H + C H (X¦Â64
.
)
.
4
8
2 5
C H + CH3. (X¦Â65
.
....
H
5
10
)
(
3-hexyl)
(h)
Fig. 4 continued
from the feed, producing butane, and two other b-cracking reactions to produce
ethylene and propylene; the RPPs are 0.0161 (XH64), 0.0797 (Xb42), and 0.0686
•
(
cracking reactions.
Xb43) respectively. As shown in Fig. 4e, C H is most likely to participate in b-
4
9
•
As shown in Fig. 4f, the pentyl radical (C H11 ) is formed solely by homolysis of
5
C –C bonds in feed; it then competes in three b-cracking reactions producing
a
b
ethylene, propylene, and butenes with RPP of 0.0020 (Xb52), 0.0033 (Xb53), and
0
low, the concentration of C H11 must be insignificant.
.0017 (Xb54), respectively. Because the RPP values for all three reactions are very
•
5
•
•
Figure 4g shows that hexyl radicals (C H13 and iso-C H ) are formed by
6 13
6
homolysis of C–H bonds in feed and H-abstraction from the feed by a variety of
radicals; they then competes in four b-cracking reactions, producing ethylene,
propylene, butene, and pentene with RPP of 0.1419 (Xb62), 0.3625 (Xb63), 0.2388
(
Xb64), and 0.1220 (Xb65), respectively. The normal hexyl radical may undergo
internal hydrogen abstraction before b-cracking. As shown in Fig. 4h, the 1-hexyl
radical can participate directly in b-cracking, producing ethylene (Xb62), or be
transformed into a 2-hexyl radical via a 6-membered ring (1–5 transfer of H atom)
followed by b-cracking to produce propylene (Xb63), or be transformed into a
3
-hexyl radical via a 5-membered ring (1–4 transfer of H atom) followed by two
alternative b-cracking reactions to produce butenes (Xb64) or pentenes (Xb65). Each
of the four hexyl radical b-cracking reactions has a significantly high RPP value,
indicating the hexyl radical is present at high concentration and is very prone to b-
•
•
cracking. The normal C H
radical can also be isomerized to the iso-C H
6 13
6
13
1
23

Radical reactions in n-hexane pyrolysis
radical and then abstract H from the feed to produce isohexane, with an RPP of
0
.0155 (XH66).
Coke-formation reaction
Coke formation in hydrocarbon pyrolysis is a common phenomenon, but may occur
via a complex mechanism which is an interesting and complicated subject. For the
moment, however, to avoid this complexity, we do not examine the details of the
coke-forming process; instead, we have treated coke formation as a side-chain
reaction independent of various main-chain reactions, as shown in Table 1.
Because coke formation is generally accompanied by production of hydrogen,
and the H/C ratio of coke always lower than that of the feed, we assume coke is
formed by the pathway:
XcokeC6H14 ! mCCxHy þ mHH2;
where Xcoke is the RPP of the coke-formation reaction, C H represents the formal
ð13Þ
x
y
formula of the coke ‘‘molecule’’ and will serve to balance the stoichiometry for
x and y, and m and mH represent the numbers of moles of coke and hydrogen
C
formed when Xcoke mole of feed is converted via reaction (Eq. 13). These will
enable us to maintain mass and stoichiometric balances without examining coke-
forming processes in detail.
The assumption that the molar selectivity for coke (m ) equals the RPP for the
C
coke-forming reaction (Xcoke), i.e., m = Xcoke, gives values of 0.0786 and 0.1328,
C
respectively, for m and m for n-hexane pyrolysis at 923 K, and a formal formula
H
C
for coke of C H10.62, which represents the loss of approximately 3.4 atoms of
6
hydrogen per molecule of feed converted to coke.
Effect of temperature on selectivity and mechanism
Bu use of the RPP data in Table 3, the effect of temperature on the selectivity of
each individual elementary reaction in n-hexane pyrolysis can be analyzed. Here,
for conciseness, we discuss the effect of temperature on initiation, propagation, and
termination of the chain reaction mechanism.
Effect of temperature on reaction chain initiation
As described above, the reaction chain for n-hexane is initiated by homolysis of the
C–C and C–H bonds in the feed molecule. The total RPP value for the initiation
ꢀ
ꢁ
P
3
reactions
X0i increases from 0.1364 to 0.1581 to 0.1745 with increasing
i¼0
temperature from 923 to 973 to 1,023 K; in particular, the RPP for C–H bond
homolysis ðX Þ increases substantially, from 0.0957 to 0.1172 to 0.1329, with no
0
0
significant change in the RPPs of C–C bond homolysis ðX01; X02; X03Þ. These
123

D.Li, Y. Zhao
values indicate that increasing the temperature generally promotes the reactions of
chain initiation, because homolysis of C–H bonds requires higher activation energy
than homolysis of C–C bonds in feed.
Effect of temperature on reaction chain propagation
The reaction chain is propagated via b-cracking of radicals and H-abstraction from
feed molecules by radicals. As the temperature is increased from 923 to 973 to
ꢀ
ꢁ
P P
XHi decreases from 0.7851 to 0.7548 to 0.7348.
3
iꢁj
1
,023 K, the total RPP value for radical b-cracking reactions
Xbij
i
j¼2
increases from 1.3825 to 1.4027 to 1.4191, and the total RPP value for radical
ꢀ
ꢁ
P
6
i¼0
H-abstracting reactions
Among these, the RPP for the iso-hexane forming reaction ðXH66Þ decreases from
0
.0155 to 0.0081 to 0.0051, indicating that b-cracking reactions of radicals require
higher activation energy than H-abstraction reactions. Therefore, increasing the
temperature enhances the b-cracking of radicals, reduces the contribution of radical
H-abstraction reactions to overall conversion of n-hexane, and reduces the
selectivity of feed isomerization.
Effect of temperature on reaction chain termination
The reaction chain is terminated by the combination of radicals. The total RPP value
3
ꢀ
ꢁ
P
P
2
for the termination reactions
XCij increases from 0.1346 to 0.1581 to
i¼1
.1745 as the reaction temperature is increased from 923 to 973 to 1,023 K. In fact,
j ꢃ i
0
the total rate of initiation reactions must be equal to the total rate of termination
reactions when the chain reaction reaches a stable state. Therefore, increasing the
temperature also promotes chain-termination reactions.
Effect of temperature on kinetic chain length (KCL)
The average kinetic chain length may be defined as the ratio of the feed conversion
rate to the initiation reaction rate, which can be calculated by use of the equation:
3
6
P
P
r0i þ
rH6i þ rcoke
r0i
roverall
1
i¼0
i¼0
KCL ¼ r
¼
¼
:
ð14Þ
3
3
P
P
initiation
X0i
i¼0
i¼0
Kinetically, the KCL represents the average number of chain events which
follows an initiation event. By substituting RPP data from Table 3 in Eq. (14), the
KCL of n-hexane pyrolysis at 923 K is calculated to be 7.33, indicating that for each
feed molecule homolysis a further 6.33 molecules react by chain processes. This, in
turn, means that chain processes are responsible for 86.4 % of total n-hexane
conversion. The KCL reduces from 7.33 to 6.33 to 5.33 with increasing temperature
1
23

Radical reactions in n-hexane pyrolysis
from 923 to 973 to 1,023 K, indicating that the contribution of homolysis (initiation)
to feed conversion increases from 13.6 to 15.8 to 18.8 %.
Effect of temperature on the formation of coke and hydrogen
As the temperature is increased from 923 to 973 to 1,023 K, the probability of
coke formation (Xcoke) is found to increase from 0.0786 to 0.0872 to 0.0908
(
Table 3). Experimental analysis shows the atomic ratio of H/C in coke decreases
from 1.77 to 1.73 to 1.69, and selectivity for hydrogen increases from 0.2285 to
.2752 to 0.3096, as the temperature is increased from 923 to 973 to 1,023 K. By
0
use of Eq. (13) we calculated that the selectivity for hydrogen produced in
association with coke formation increases from 0.1326 to 0.1578 to 0.1763. These
results indicate that production and dehydrogenation of coke are more prevalent at
higher temperature.
Conclusions
Investigation of n-hexane pyrolysis provides insight into radical reactions in
hydrocarbon pyrolysis. Interpretation of kinetics and selectivity for elementary
reactions is capable of yielding detailed information about the chain reaction
mechanism in n-hexane pyrolysis.
1
n-Hexane pyrolysis is initiated by homolysis of C–C and C–H bonds in feed
molecules, propagated by b-cracking reactions of radicals and H-abstraction
from the feed by radicals, and terminated by combination reactions between two
radicals. The first-order kinetic equation derived from the chain mechanism fits
-
1
experimental data well, giving 208.5 ± 1.0 kJ mol as the activation energy of
the n-hexane conversion reaction. The overall reaction rate constant increases
-
2
-1 -1
from 1.75 9 10 to 3.79 9 10
,023 K.
The initial primary products are hydrogen, C –C paraffins, C –C olefins, iso-
s
with increasing temperature from 923 to
1
2
1
4
2
5
hexanes, and coke, which are obtained via a variety of elementary reaction
paths of different selectivity. At 923 K, for example, pyrolysis of n-hexane
occurs via three paths: homolysis of bonds in the feed molecule, abstraction of
H from the feed by free radicals, and coke formation. The RPP values for the
three reaction paths are 0.1364, 0.7850, and 0.0786, respectively. Methane and
•
iso-hexanes are formed by H-abstraction from the feed by the CH and iso-
3
•
C H
6
radicals, with RPP values of 0.4530 and 0.0155, respectively. Some
C –C paraffins are formed by H-abstraction by C –C radicals, with RPP of
13
2
4
2
4
0
.2209, others by recombination of two radicals, with RPP of 0.1364. C –C
2 5
olefins are formed by b-cracking of radicals, for which total molar selectivity•
is 1.3825. Hydrogen is formed either by H-abstraction from the feed by the H
radical or by coke formation; these two processes contribute 43 and 57 % to
hydrogen production.
123

D.Li, Y. Zhao
•
3
Examination of the competing reactions of the different radicals C H
n 2n?1
(n = 0-6) shows the radicals participate in different elementary reactions with
•
different selectivity. At 923 K, for example, the smallest radical, H , participates
solely in abstraction of H from the feed, forming H , with an RPP value of
2
•
0
cracking reactions, producing ethylene, propylene, butenes, and pentenes, with
.0957, whereas the largest radical, C H , readily participates in four b-
6
13
•
RPP values of 0.1419, 0.3625, 0.2388, and 0.1220, respectively. C H
6
may
13
•
also be isomerized into iso-C H
6
which can abstract H from the feed to
13
produce isomeric hexanes, with an RPP value of 0.0155. Increasing the
temperature promotes homolysis of the feed molecule and b-cracking of
radicals, reduces the proportion of H-abstraction by radicals, and increases coke
and hydrogen production. The average reaction chain length (KCL) decreases
from 7.33 to 5.73 when the temperature is increased from 923 to 1,023 K.
Appendix
Application of Eqs. (3) and (4) to the reactions producing olefins during n-hexane
pyrolysis (Table 1), furnishes the matrix equation:
2
3
Xb32
Xb42
Xb43
6
7
6
7
6
6
7
7
6
7
6
7
6
7
6
7
6
7
6
7
6
7
2
3
6
7
7
6
2
3
6
7
7
7
7
7
7
7
7
7
7
7
6
7
7
7
7
7
7
7
7
7
7
7
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
6 X
6 S
b52
b53
C2H4
C3H6
6
6
6
6
6
6
6
6
6
6
6
6
6
4
7
7
7
7
7
7
7
7
7
7
7
5
6
6
6
6
6
6
0
1
6 X
6 S
6
6
6
6
6
6
6
6
¼
ð15Þ
0
0
0
6 Xb54 7
6 SC H 7
4
8
6
7
7
6
7
7
6
6
6
7
6
7
6
7
6
7
0
6 Xb62 7
4 SC H 5
5
10
6
7
6
7
6
7
6
7
7
6
X
b63
6
7
6
7
6
7
6
7
6
Xb64
7
6
7
6
4
7
5
Xb65
Similarly, for reactions producing paraffins (including H ), we have:
2
1
23

Radical reactions in n-hexane pyrolysis
2
3
XH60
XH61
XH62
6
7
6
7
6
6
7
7
6
7
6
7
6
7
6
7
6
7
6
6
6
7
7
7
2
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
7
XH63 7
SH ꢁ mH
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
4
7
7
7
2
7
7
7
7
6
6
6
6
6
6
6
6
6
6
6
6
6
7
7
7
7
7
7
7
7
7
7
7
7
7
0 7
7
X
X
7
7
7
7
7
SCH4
H64
7
7
7
0
0
1
0
0 7
7
7
7
SC2H6
H65 7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
0
0
0
1
1
0
7
7
XH66 ¼ 6
SC H 7
7
3
8
6
6
6
6
6
6
6
6
6
6
6
4
7
7
7
7
7
7
7
7
7
7
7
5
7
7
0
0
0
0
1
0
0
0
0
1
0
1
0
7
XC11 7
S
C4H10
7
7
7
0
0
0
0
0
1
0
0
0
0
1
0
1
7
XC12 7
SC5H12
7
7
7
0
0
0
0
0
0
1
0
0
0
0
0
0 5
6
6
7
7
X
SiC H
14
C13
6
6
7
6
7
6
6
7
7
XC14
6
7
6
7
6
7
6
6
7
7
XC22
6
7
6
4
7
5
XC23
ð16Þ
In view of the chain mechanism in Table 1, the net reaction rates for each
individual radical may be written:
ꢀ
d½H ꢄ
ꢀ
¼
k ½C H ꢄ ꢁ k ½C H ꢄ½H ꢄ
ð17Þ
00
6
14
H60
6
14
ds
ꢀ
d½CH ꢄ
3
ꢀ
ꢀ
ꢀ
11
¼
k01½C6H14ꢄ þ kb32½C3H ꢄ þ kb43½C4H ꢄ þ kb54½C5H ꢄ
7
9
ds
ꢀ
ꢀ
ꢀ
ꢀ
þ kb65½C6H ꢄ ꢁ kH61½C6H14ꢄ½CH ꢄ ꢁ kC11½CH ꢄ½CH ꢄ
13
3
3
3
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
9
ꢁ
k
½CH ꢄ½C H ꢄ ꢁ k ½CH ꢄ½C H ꢄ ꢁ k ½CH ꢄ½C H ꢄ ð18Þ
C12
3
2
5
C13
3
3
7
C14
3
4
ꢀ
d½C2H ꢄ
5
ꢀ
ꢀ
ꢀ
13
¼
k ½C H ꢄ þ k ½C H ꢄ þ k ½C H ꢄ þ k ½C H ꢄ
kH62½C6H14ꢄ½C2H ꢄ ꢁ kC12½CH ꢄ½C2H ꢄ ꢁ kC22½C2H ꢄ½C2H ꢄ
0
2
6
14
b42
4
9
b53
5
11
b64
6
ds
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ð19Þ
ꢁ
ꢁ
5
3
5
5
5
ꢀ
ꢀ
7
k
½C H ꢄ½C H ꢄ
C23
2
5
3
123

D.Li, Y. Zhao
ꢀ
d½C3H ꢄ
7
ꢀ
ꢀ
ꢀ
7
¼
2k ½C H ꢄ þ k ½C H ꢄ þ k ½C H ꢄ ꢁ k ½C H ꢄ
0
3
6
14
b52
5
11
b63
6
13
b32
3
ds
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢁ
kH63½C H ꢄ½C H ꢄ ꢁ k ½CH ꢄ½C H ꢄ ꢁ k ½C H ꢄ½C H ꢄ ð20Þ
6
14
3
7
C13
3
3
7
C23
2
5
3
7
ꢀ
d½C4H ꢄ
9
ꢀ
ꢀ
ꢀ
¼
k02½C6H14ꢄ þ kb62½C6H ꢄ ꢁ kb42½C4H ꢄ ꢁ kb43½C4H ꢄ
1
3
9
9
ds
ꢀ
ꢀ
ꢀ
ꢁ
kH64½C6H14ꢄ½C4H ꢄ ꢁ kC14½CH ꢄ½C4H ꢄ
ð21Þ
ð22Þ
9
3
9
ꢀ
d½C5H ꢄ
1
1
ꢀ
ꢀ
ꢀ
¼
k ½C H ꢄ ꢁ k ½C H ꢄ ꢁ k ½C H ꢄ ꢁ k ½C H ꢄ
01
6
14
b52
5
11
b53
5
11
b54
5
11
ds
ꢀ
ꢁ
kH65½C H ꢄ½C H ꢄ
6
14
5
11
ꢀ
d½C6H ꢄ
1
3
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
9
¼
ðkH60½H ꢄ þ kH61½CH ꢄ þ kH62½C2H ꢄ þ kH63½C3H ꢄ þ kH64½C4H ꢄ
3
5
7
ds
ꢀ
ꢀ
ꢀ
þ kH65½C5H ꢄ þ kH66K66½C6H ꢄÞ½C6H14ꢄ ꢁ kb62½C6H ꢄ
1
1
13
13
ꢀ
ꢀ
ꢀ
13
ꢁ
k
½C H ꢄ ꢁ k ½C H ꢄ ꢁ k ½C H ꢄ
ð23Þ
b63
6
13
b64
6
13
b65
6
Therefore, the steady-state assumption for radical concentration gives the
following group of RPP equations for balance between production and consumption
of each individual radical:
X01 ¼ Xb52 þ Xb53 þ Xb54
X01 þ Xb32 þ Xb43 þ Xb54 þ Xb65 ¼ XH61 þ 2XC11 þ XC12 þ XC13
X02 þ Xb42 þ Xb53 þ Xb64 ¼ XH62 þ XC12 þ 2XC22
ð24Þ
ð25Þ
ð26Þ
ð27Þ
ð28Þ
ð29Þ
2
X03 þ Xb52 þ Xb63 ¼ Xb32 þ XH63 þ XC13
X02 þ Xb62 ¼ Xb42 þ Xb43 þ XH64
X00 þ XH60 þ XH61 þ XH62 þ XH63 þ XH64 ¼ Xb62 þ Xb63 þ Xb64 þ Xb65
Obviously, the sum of RPP for n-hexane conversion must equal unity, that is:
X00 þ X01 þ X02 þ X03 þ XH60 þ XH61 þ XH62 þ XH63 þ XH65
ð30Þ
þ X þ X
þ X
¼ 1
H64
coke
H66
According to a literature report [3] on the relative rates b-cracking for the same
radical, we have:
0
0
:164
:419
0:164
0:276
0:164
0:141
Xb62 ¼
Xb63 ¼
Xb64 ¼
Xb65
ð31Þ
ð32Þ
0
0
:164
:276
0:164
0:141
Xb52 ¼
Xb53 ¼
Xb54
Also, the following conditions must be satisfied:
Xcoke ¼ Scoke
SC H ¼ 0 ) XH65 ¼ 0; XC14 ¼ 0; XC23 ¼ 0
ð33Þ
ð34Þ
ð35Þ
5
12
Xij ꢃ 0
1
23

Radical reactions in n-hexane pyrolysis
Finally, by using the experimental product molar selectivity data in Table 2 to
solve the above equations, we obtain the RPP data presented in Table 3.
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2
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123