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HUNGARIAN JOURNAL 
OF INDUSTRIAL CHEMISTRY 

VESZPRÉM 
Vol. 35. pp. 39-45 (2007) 

THERMAL CRACKING OF RECYCLED HYDROCARBON GAS-MIXTURES 
WITH HIGH OLEFINS CONCENTRATIONS IN THE FEED:  
OPERATIONAL ANALYSIS OF INDUSTRIAL FURNACES 

1T. GÁL, 2B. G. LAKATOS 

1MOL-Tisza Chemical Works Co. Ltd (TVK), Tiszaújváros, HUNGARY 
2University of Pannonia, Institute of Chemical and Process Engineering, Department of Process Engineering,  

Veszprém, HUNGARY 
 

Simulation studies of thermal cracking of recycled hydrocarbon gas mixtures are presented. Due to their relatively high 
unsaturated content these types of mixtures show behaviour in cracking furnaces different from that of their saturated 
homologues. The detailed mathematical and kinetic model developed was validated by using the process control laboratory 
cracked gas analysis of an industrially operated cracking furnace. The effects of different feed compositions and those of 
operating parameters are also examined. It is shown that the radiant coil temperature profile, online operation period of 
the furnace, and the yield of the main products are different at various unsaturated concentrations in the feed. The influence 
of the radiant section residence time is also presented. Simulation results compared with the experimentally measured 
data of an industrially operated cracking furnace show good agreements. 

Keywords: Pyrolysis, hydrocarbons, gas-mixtures, olefins, modelling, simulation 

Introduction 

Thermal decomposition of hydrocarbons has been studied 
for more than 70 years. Nevertheless, less attention has 
been paid on cracking behaviour of olefins since 
recycling of certain cracked gas-fractions has become 
important only in past one-two decades. While repyrolysis 
of formed ethane and propane has been applied for long, 
recycling of C4 and/or C5 fractions has only been 
introduced into industrial experience parallel with 
decreased market demand for plastics produced from 
butadiene and isoprene.  
 Sundaram and Froment [1-3] developed kinetic models 
for thermal decomposition of gaseous hydrocarbons and 
their mixtures. Kinetic parameters presented in these 
schemes are still applicable for thermal cracking of 
individual hydrocarbons and mixtures up to C4. Van 
Damme et al. [4] and Froment et al. [5] compared the 
results given by their kinetic model with those obtained 
from industrial applications. Ranzi et al. [6], Froment et 
al. [7] and Dente et al. [8, 9] presented the initial 
product distribution when cracking light hydrocarbons 
and prepared the first fundamental pyrolysis simulation 
model, the SPYRO. Willems and Froment [10] presented 
a method of calculation of frequency factors and 
activeation energies, while Dente and Ranzi [11] 

prepared a mathematical model for hydrocarbon pyrolysis 
reactions. More recently, Poutsma [12], Savage [13], 
Sadrameli and Green [14] presented the system of 
fundamental free radical reaction relevant to pyrolysis 
and mechanisms and kinetic modelling systems for 
hydrocarbon pyrolysis, respectively. Zou et al., [15], 
Pleiers et al. [16] and Kopinke et al. [17,18] studied and 
presented coke formation rates that influence the online 
operation period of cracking furnaces. 
 The mentioned C4/C5 fractions are hydrogenated 
upstream the cracking furnaces. Olefin content of 
hydrogenation reactor effluent mainly depends on its 
catalyst performance and can vary between 3 and 30%. 
Yet, unsaturated ratio of the furnace feed can also be 
reduced by mixing fresh, saturated hydrocarbons into 
reactor effluent. These are mainly butanes and/or pentanes 
in practice but, according to our simulation results, 
mixing of ethane also looks to be a promising alternative. 
 This paper examines the effects of unsaturated 
components in the feed on product yields and online 
operation period of the furnace aiming the opportunities 
of harmonizing the operating parameters at different 
feed compositions. Results obtained by numerical 
experimentation using a computer model are compared 
with experimentally measured data of an industrially 
operated cracking furnace. 



 40

Mathematical model 

The kinetic model 

Starting from the detailed composition of fed hydrocarbons 
and cracked gases a reaction network was built up with 
participation of all theoretically supposed ones in the 
first step of modelling, number of which was closely 
five hundred. As the second step, kinetic parameters were 
assigned to each reaction, source of which was the large 
amount of published literature data. If the published 
system was found to have been similar to the one 
examined by us, these parameters could be directly 
adopted [2, 3, 7]. In cases different from that, parameters 
were collected from other sources then interpolated or 
extrapolated on basis of analogy rules between the 
reactions in the same group [1, 4-6, 8, 9-15]. Of course, 
a comparison was made in the first case as well. The 
aim of these two steps was to build up a ‘first generation’ 
kinetic model that could reproduce measured yield data 
as accurate as possible. 
 Validation of the model was performed by comparing 
the results with those obtained experimentally from 

cracked gas analysis of an industrially operated furnace. 
This means that a set of multiply verified data, among 
stabilized operational circumstances, were collected in 
concert with the sampling schedule and procedure. 
Received yield data were not averaged but those in 
coincidence were taken as reference. Secondly, influence 
of each reaction to the yield-structure was examined. 
Effect of those to the yield structure was negligible 
could be deleted from the system with simplification 
purposes and for the reasons mentioned earlier. Having 
performed these procedures, 239 reactions remained in 
the examined system, kinetic parameters of which were 
fitted to the measured yield data in case of each reaction, 
except those leading to coke formation (coke ‘yield’ 
could not be measured). The fitting was performed in 
such a way that the trend of a product yield or 
consumption of a feed component was drawn as a 
function of modification of parameters (A or E). Table 1 
presents a part of arrangement of frequency factors from 
different sources together with the adopted ones in the 
first phase of modelling and with the ones fitted during 
validation of the model. Fig. 1 shows an example of 
fitting the activation energies to experimentally measured 
yields at reactions of the prepared network. 

 
Table 1: Assigning frequency factors (A, sec-1 or cm3*mol-1*sec-1) to reactions in the system 

Reaction Literature data sources Adopted Fitted 
C3H8 → CH3* + C2H5* 7.1·10

16c 2·1016 h 1.3·1016j --- 3·1016 2.2·1016 
n-C4H10 → 2 C2H5* 5·10

16 c 1.5·1016h --- --- 2·1016 2.5·1016 
C3H8 + CH3* → CH4 + 1(2)-C3H7* 1.5·10

9c 
 

3.4·1010 
(4·109) h 

108 i 4.9·109 
(1.5·109)j 

1.5·109 
(3·109) 

2.2·109 
(4.2·109) 

1-C3H7* → C2H4 + CH3* 5·10
13 c 4·1013 h 5·1013 k 1014 i 5·1013 4.4·1013 

CH3* + C2H5* → C3H8 10
10 c 3.2·109h --- --- 5·109 3.2·1010 

Sources in Table 1 are indicated as follows: c – Dente and Ranzi (1983); d – Zdenek et al. (2003); h – Sundaram and Froment 
(1978); i – Ranzi et al. (1997), j – Willems and Froment (1988); k – Ranzi et al. (1983) 
 
 

10

12

14

16

18

20

22

8,4 25,1 39,8 53,6 62,8 75,4 87,9 125,6

E (kJ/mol)

M
et

ha
ne

 y
ie

ld
 (w

t%
)

18.43%

 
Figure 1: Variation of methane yield as a function of 

activation energy in case of reaction:  
C2H4 + CH3* = C2H3* + CH4 

The reactor model 

The geometry of the furnace coil and high Reynolds-
numbers used in thermal decomposition process enable 
tubular reactor and plug-flow assumptions. As a 
consequence, mass, energy and momentum balances can 
be written as follows [19]. 

Mass balance: 

rc

N

k

i
kki

i

NkNi
x

txc
vTr

t
txc r

→=→=

∂
∂

−=
∂

∂
∑
=

1,1                        

),(
),(

),(

1
cα

 (1) 

where ci is the concentration of reactant i, x is the axial 
distance along the reactor, v denotes the cracked gas 
convective velocity, rk is the rate of the reaction k, and αki 
stands for the stoichiometric coefficient of component i 
in the reaction k. Nc denotes the number of species, 
while Nr stands for the number of reactions. 



 41

Enthalpy balance: 

[ ]),(),(

),()(
),(

1

11

txTTU
x

txT
cCv

TrH
t

txT
cC

fb

N

i
ipi

N

k
kk

N

i
ipi

c

rc

−+
∂

∂
⎟
⎟
⎠

⎞
⎜
⎜
⎝

⎛
−

−−=
∂

∂
⎟
⎟
⎠

⎞
⎜
⎜
⎝

⎛

∑

∑∑

=

==
cΔ

 (2) 

where T is the cracked gas temperature, Cpi is the heat 
capacity of species i, ΔHk denotes the heat of reaction k, 
U denotes the overall heat transfer coefficient from the 
fire box to the cracked gas, dt is the inner diameter of 
the reactor tube, and Tfb stands for the temperature of 
fire box.  

The pressure drop along the radiant pipe: 

2
)(

144

2v
x

gd
L

f
dx
dp

t

t ρξ ⎟⎟
⎠

⎞
⎜⎜
⎝

⎛
+=  (3) 

where p denotes the pressure, ρ is the density of gas 
mixture, Lt the equivalent pipe length, g is acceleration 
due to gravity, ξ(x) is the local resistance coefficient of 
reactor tube junctions or bends, and f denotes the 
friction factor which is calculated using the expression 
for smooth pipes: 

25.0
3164.0

Re
f =  (4) 

The balance equations are solved subject to boundary 
and initial conditions: 

)0()0,(,1)()0,( 00 TxTNixcxc cii =→==  (5) 

)(),0(,1)(),0( . tTtTNitctc incinii =→==  (6) 

The computer model 

The reference furnace consists of a radiant and a 
conection section, as well as of six transfer line 
exchangers (TLE) with one steam drum. Firing in radiant 
section is performed by sidewall and floor burners where 
natural gas is burnt which is also mixed with the methane 
fraction formed in cracking process. Preheating of feed 
and dilution steam as well as preheating and super-eating 
of high-pressure steam takes place in convection section. 
Between the feed preheater and steam super-heater a 
boiler-feed-water preheater is placed. The furnace was 
designed to assure uniform distribution and ‘drive’ of 
different streams to convection-section heat-exchanger 
bundles. Furnace feed streams are collected in two places 
and distributed into 96 radiant coils by Laval-nozzles. 
After a certain length two small-diameter (39 mm) coils 
unify in a bigger one (57 mm). According to this, the 
furnace contains 48 radiant coils connected to one TLE by 
eight as it shown in Fig. 2. The residence time of reaction 
mixture in the radiant section is very short (0.3 sec.). 

 Having identified the kinetic parameters, simulations 
were performed by CHEMCAD computer simulator that 
was chosen for its large thermochemical database as 
well as for the fact that not only molecules but radicals 
can also be created and handled. As a further part of its 
implementation, geometrical data were given according 
to the technical drawings of the examined industrial 
furnace. Data input of parameters and process-variables 
were also performed on basis of industrial circumstances.  
 

 
Figure 2: Radiant coil arrangement 

 
 So as to determine composition of cracked gases at 
the furnace outlet the following input data are needed: 
a.) feed composition by component and its flow-rate  
b.) inlet and outlet temperatures (COT) of the furnace 
c.) pressures at inlet and outlet (to calculate pressure-

drop along the coil) 
d.) hydrocarbon/dilution steam ratio and steam flow-rate 
e.) coil geometry, i.e. the lengths and internal diameters 

of segments 
f.) temperature-profile along the coil or heat-transfer 

coefficient (U), with tube metal temperature (TMT) 
g.) each chemical reaction taking place in the system 

with their kinetic parameters (activation energies and 
frequency-factors, respectively)  

 
Operating parameters of the furnace (points a – d), 

such as temperatures, pressures, flow rates are monitored 
by an Advanced Process Control system (APC) and they 
can be registered in accordance with feed- and cracked 
gas analysis [20].  

The factor of losses depends on convectional 
circumstances dominant in the pipe (Re-number) and its 
shape. According to this, the total pipe length (point e) 
is the sum of straight segments and the equivalent pipe 
length.  

Table 2 presents comparison of measured and 
simulated yield data with fitted kinetic parameters. 



 42

Experimental: Application and presentation of 
simulated results 

Having validated the model, series of simulations were 
performed with the purpose of examining the effect of 
different feed components on product yields. Some 
typical feed compositions are shown in Table 3. 

The influence of the n-butane concentration is shown 
in Table 4.  

As it is seen, 28% higher n-butane concentration is 
needed to achieve 4% increased ethylene yield but the 

relative coke formation rate was decreased by almost 
25%. This decline is also due to the lower relative 
concentration of olefins in the feed, i.e. because of less 
coke precursors. Neither the yield of methane nor that of 
propylene varies significantly but less aromatic compounds 
(BT) are produced. In conclusion, when increased olefin 
content occurs in the feed adding more butane into it 
appears to be economically reasonable since higher 
furnace run-length can be reached in parallel with the 
possible decreased hydrogenation reactor load that also 
leads to depression of olefin content in the feed. 

 
 

Table 2: Comparison of the measured and simulated product yields with fitted kinetic parameters 

Component/ 
Yields (wt %) 

Measured 
1 

Fitted 
1 

Measured 
2 

Fitted 
2 

Measured 
3 

Fitted 
3 

Hydrogen 1.06 0.98 1.05 0.98 0.98 0.96 
CO 0.10 0.11 0.06 0.07 0.05 0.07 

Methane 18.72 18.67 18.53 18.64 18.27 18.52 
Ethane 3.39 3.34 3.56 3.51 3.63 3.53 

Ethylene 30.64 30.58 31.13 31.08 32.30 32.17 
Propylene 19.51 19.64 19.54 19.61 19.26 19.37 
n-butane 8.50 8.58 8.57 8.63 10.08 9.87 

Acetylene 0.51 0.55 0.51 0.56 0.50 0.49 
Benzene 1.34 1.36 1.34 1.36 1.33 1.30 
Toluene 0.22 0.25 0.22 0.25 0.22 0.25 

 
Table 3: Some typical compositions of the furnace feed 

Component (wt%) Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 
Propane 0,8937 0,3251 0,1462 0,4315 0,0880 

Propylene 0,7019 0,9518 0,1881 0,9308 0,3292 
i-butane 12,5453 8,6917 6,5118 6,9339 5,2723 
1-butene 0,8193 0,0716 0,1484 0,0891 0,0891 
n-butane 61,9166 69,5411 67,6253 72,1629 63,9667 
2-butene 2,4412 0,3452 0,3934 0,3899 0,4321 
i-pentane 4,9792 6,4142 8,4320 5,9221 9,4355 

2M-butene-1 0,2211 0 0,0655 0,0473 0,0843 
n-pentane 5,8455 7,0751 8,2326 6,3494 10,8684 
2-pentene 0,2306 0 0 0 0 

2M-butene-2 1,7299 0,4041 0,5704 0,4425 0,7475 
Cyclopentene 0,0874 0 0 0 0,0735 
Cyclopentane 5,9247 5,4214 6,7055 5,7778 7,7222 
2M-pentane 0,5752 0,6778 0,6036 0,4434 0,8912 
∑ other C6 1,0885 0,0808 0,3773 0,0794 0 

 
Table 4: Variation of product yields as a function of n-butane concentration in the feed 

n-butane conc., wt%→ 
product yields, wt% ↓ 

65.95 
simulated 

65.95 
measured

72.35 
simulated

72.35 
measured

79.55 
simulated

79.55 
measured 

86.71 
simulated 

93.89 
simulated

Hydrogen 0.88 0.92 0.89 0.94 0.91 0.99 0.95 0.98 
Methane 18.54 18.71 18.14 19.32 18.11 19.18 18.02 17.96 
Ethylene 30.58 30.61 31.02 31.21 32.21 32.42 33.43 34.43 

Propylene 19.34 19.74 19.28 19.53 19.16 19.34 19.09 19.01 
n-butane (residual) 8.92 8.77 9.28 9.17 9.75 9.68 10.07 10.38 
Benzene + Toluene 1.78 1.73 1.61 1.58 1.41 1.37 1.28 1.19 
Coke (theoretical) 0.0087 ------ 0.0084 ------ 0.0081 ------ 0.0075 0.0069 

 
Further simulations were carried out at five different 

unsaturated concentrations in such a way that 
concentration of each component in the feed was varied 
proportionally. Rest of independent variables (COT, 
ST/HC) was kept constant. Simulated results are 
presented in Fig. 3. As Fig. 3 shows, trend of methane 

yield and that of propylene shows a linear decline with a 
rising unsaturated rate. Rising conversion of n-butane is 
only ‘virtual’ since its relative concentration in the feed 
also declines when the unsaturated concentration is 
higher. Nevertheless, variation of ethylene yield shows 
a slightly rising trend which, for the first sight, looks to 



 43

be surprising. To find the explication, it was examined 
how the concentration of some key unsaturated feed 
components vary along the radiant coil. Parallel with 
this, their kinetic route was also followed. Variation of 
three feed components concentration, that are present in 
the highest amount in the feed, is shown in Fig. 4. 
Concentrations of 2M-butene-2, butane-1 and butane-2 
are the most elevated in the feed so their kinetic routes 
were examined. All of them take part in chain-initiation, 
hydrogen-abstraction, chain-forwarding and recombination 
reactions [3] 
 

0

5

10

15

20

25

30

35

0 2,83 5,51 10,51 15,27

Olefins in the feed, w/w%

pr
od

uc
t y

ie
ld

s,
 w

/w
%

methane ethylene propylene n-butane coke*1000  
Figure 3: Variation of product yields as a function of 

olefin concentration in the feed 
 

0

0,01

0,02

0,03

0,04

0,05

0,06

0

2,8
26

5

5,6
52

9

8,4
79

4

11
,30

6

14
,13

2

16
,95

9

19
,78

5

22
,61

2

25
,43

8

28
,26

5

31
,09

1

33
,91

7

36
,74

4
39

,57

42
,39

7

Reactor volume, liter

M
as

s 
fr

ac
tio

n

2M-burene-2 butene-1 butene-2  
Figure 4: Variation of some olefins concentration along 

the radiant coil 
 
 Fig. 5 shows the temperature profiles in the first part 
of the radiant coil revealing the differences between 
those in case of cracking a C3-C6 mixture in a furnace 
with short residence time (0.3 sec) when the feed is free 
of olefins and when it contains 15% unsaturated 
components. This examination was initiated by some 
operational experiences observed in industrial plants 
according to which higher coke deposits were realized 
in the first part of radiant coil, causing a very short 
online operation time as well as cracking of coils in 
certain cases. The theoretical explication of this 
phenomenon is that unlike saturated hydrocarbons, all 
the olefins and diolefins contribute more to coke 
deposits in the first part of cracking coil. This is more 

pronounced the higher the reactivity of the component 
is. It is a question of profitability to operate the furnace 
at the lowest possible steam/hydrocarbon ratio since a 
lower steam rate reduces specific energy consumption 
of the production unit. Basically, one thing has to be 
decided: up to what extent this ratio can be reduced 
without having a significant negative effect on product 
yields and on furnace online period. Table 5 shows that 
reducing the ratio by 20% practically has no influence 
on product yields but a shorter runtime can be expected 
because of higher coke formation rate. 
 

0
0,002
0,004
0,006
0,008

0,01
0,012
0,014
0,016
0,018

0,02

0

3,
53

31

7,
06

61

10
,59

9

14
,13

2

17
,66

5

21
,19

8

24
,73

2

28
,26

5

31
,79

8

35
,33

1

38
,86

4

42
,39

7

Reactor volume, liter

C
ok

e,
 w

t%

0% unsaturated
15% unsaturated

 
Figure 5: Formation rate of coke along the radiant coil 

 
 Fig. 6 shows the variation of formation rates of some 
undesired products, such as CO, coke and acetylenes 
along the radiant coil. As it is seen, formation of MAPD 
starts first and rate of coke formation increases 
exponentially at the last part of reactor pipe. 
 

0

0,001

0,002

0,003

0,004

0,005

0,006

0
2,4

1 9,2 7,2
4

18
,8

12
,1

28
,6

16
,9

37
,4

21
,7

42
,4

Reactor volume, liter

Y
ie

ld
s 

of
 s

ec
on

da
ry

 
pr

od
uc

ts
, w

/w
%

CO
Coke
acetylene
MAPD

 
Figure 6: Variation of formation rates of some 

undesired products along the radiant coil 
 
 It should be noted that the effects of the dilution 
steam reduction cannot be simulated with high accuracy 
since catalytic effect of tube metals are not described by 
any known kinetics. Though the literature survey [15-
18] shows a clear classification of coke precursors (such 
as olefins, acetylenes and aromatics) but there are no 
detailed discussions on dilution steam effect. Nevertheless, 
practical experience also confirms the data shown in 
Table 5.  
 



 44

Table 5: Simulation at different steam/hydrocarbon ratios 

Steam reduced by...% 
Temperature (COT), ºC → 

Product yields, wt% 

5 
835 

5 
840 

10 
835 

10 
840 

15 
835 

15 
840 

20 
835 

20 
840 

Methane 18.22 18.75 18.32 18.72 18.43 18.83 18.53 19.06 
Ethylene 32.22 33.73 32.07 33.18 31.92 33.07 31.78 33.25 
Propylene 20.63 20.15 20.68 20.34 20.74 20.38 20.79 20.32 
Butadiene 3.97 3.85 3.97 3.89 3.98 3.89 3.98 3.86 

n-butane (residual) 8.74 7.58 8.72 7.88 8.70 7.82 8.68 7.56 
Benzene + toluene 1.61 1.63 1.71 1.64 1.75 1.66 1.81 1.69 

Coke 0.016 0.019 0.017 0.018 0.017 0.018 0.018 0.019 
 
 According to the daily operational experience, for 
the relatively high unsaturated-content of the feed, 
online operation period of the furnace became shorter 
than the designed value, especially at the end of radiant 
coil lifetime. This is mainly due to the higher coke 
formation rate, which is caused by the elevated olefin 
content (coke precursors) in the feed and by those 
formed during the decomposition process. For these 
reasons, further alternatives were searched for to 
process the mixture in question more efficiently. 
Simulations with variation of radiant coil geometry, i.e. 
alteration of residence time were carried out to compare 
yield data and coke formation rate. Geometrical data of 
two existing furnaces (CF2 and CF3) were taken as 
reference so that the calculated residence times could be 
in real domain, i.e. 0.65 sec and 1.1 sec, respectively. It 
was supposed that a higher key-conversion and a higher 
ethylene yield could be reached, parallel with a reduced 
coke formation rate, when cracking these mixtures in 

furnaces with longer residence time. Simulations at 
similar feed compositions, total olefin content of which 
was 15.27%, were carried out with three values of COT 
and yield data were compared with those obtained from 
reference furnace. ST/HC ratio was adjusted similarly in 
all three furnaces. Results are shown in Fig. 7. As it was 
expected, a higher conversion of n-butane could be 
achieved both in CF2 and CF3 furnace than in the 
reference (CF1) furnace. Yield of ethylene is by 7% 
higher in CF2 and by 11.1% in CF3 at same COT. 
Though the coke formation rate is much bigger in both 
furnaces, by 21% and 32% respectively, this quantity of 
coke will be deposed on a five times higher surface in 
CF2 and on a ten times higher one in CF3. Taking into 
consideration the differences in residence times as well, 
it can be concluded that a 35-40% longer online 
operation period is expectable in case of both CF2 and 
CF3. 

 

0

10

20

30

40

50

60

p
ro

d
u

ct
 y

ie
ld

s,
 m

/m
%

CF1 CF2 CF3 CF1 CF2 CF3 CF1 CF2 CF3

n-butane

propylene

ethylene

COT=83 COT=840 COT=845
 

Figure 7: Yield comparison at furnaces with different residence time 
 

Conclusions 

When thermal cracking of recycled hydrocarbon gas 
mixtures occurs in industrial furnaces, the feedstock 
contains a relatively large amount of unsaturated 
components such as olefins and diolefins, a special 
attention has to be paid on coke formation since these 
compounds are coke precursors. The simulation study, 
carried out by means a computer model developed for 
examining thermal cracking of recycled gas mixtures, 

confirmed that variation opportunities originating from 
very different feed compositions can be harmonized 
well with operating parameters of the furnaces, with the 
purpose of achieving a maximum profitability. As it was 
shown, coke formation rate can significantly be reduced 
by decreasing olefin content of the feed. This can be 
done by mixing fresh hydrocarbons into the recycled 
streams like ethane and/or n-butane. According to 
industrial practice, recycled ethane is always available 
and n-butane is also worth to be purchased for this 
purpose. In conclusion, recycled streams cracking in 



 45

furnaces with longer residence time looks to be a good 
alternative for olefin producers. Of course, the 
hydrogenation reactor upstream the cracking furnace as 
well as its catalyst has a main role in this complex 
process.  

NOMENCLATURE 

ΔHk  – heat of reaction k [J/mol]  
A  – surface area per unit axial distance [m2]  
ci  – concentration of reactant i [mol/m

3]  
Cpi – heat capacity of species i [J/kg/K]  
d  – diameter of pipe/fitting [m] 
ƒ  – friction factor [-]  
gc  – acceleration of gravity [m/s

2] 
L  – equivalent pipe length [m] 
Nc  – number of species 
Nr – number of reactions 
rk – rate of the reaction k [mol/m

3/s] 
T  – temperature of cracked gas [K] 
t  – time [s] 
t  – mean residence time [s] 
Tfb  – temperature of firebox [K]  
U  – overall heat transfer coefficient from the firebox 

to cracked gases [W/m2/K] 
V – convective velocity of cracked gas [m/s] 
x  – axial distance along the reactor [m] 
αki – stoichiometric coefficient of component i in the 

reaction k 
Δp – pressure drop [MPa] 
ρ  – density of cracked gas [kg/m3]  

ACKNOWLEDGEMENT  

Support provided by TVK Olefin Unit operational and 
laboratory staff is gratefully acknowledged.  
 

REFERENCES 

1. SUNDARAM K. M., FROMENT G. F.: Chemical 
Engineering Science, 1977, 32, 601-608 

2. SUNDARAM K. M., FROMENT G. F.: Chemical 
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