Chemical Engineering Science 56 (2001) 1403}1410

Kinetics for benzene#ethylene reaction in near-critical

regions
Yi-feng Shi, Yong Gao, Ying-chun Dai, Wei-kang Yuan*
UNILAB Research Center of Chemical Reaction Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai 200237,
People's Republic of China

Abstract

Based on the determined reaction rates of alkylation of benzene with ethylene to produce ethyl benzene, kinetic expressions are
studied in all the "ve near-critical regions surrounding the critical point: supercritical #uid, low-pressure vapor, vapor}liquid two
phase, high- and low-pressure liquid. Both hyperbolic model and power-law model have been applied for this purpose. Models are
searched to "t all the single-phase regions, and for the four single regions separately. The results are very unsatisfactory. The authors
then worked out the modi"ed models with the aid of a crossover function and have obtained better results. Although the reaction
behaviors are quite complicated in the near-critical regions, a power-law model combined with the crossover function can be used to
"t the experimental data with a much higher regression coe$cient.  2001 Elsevier Science Ltd. All rights reserved.

Keywords: Alkylation; Benzene; Near-critical region; Reaction rate; Ethylene; Kinetics

1. Introduction temperature. The black circle represents the critical

point, which indicates the mole fraction of B, and the
In studying the alkylation of benzene with ethylene corresponding critical pressure. Suppose B is of vapor
over
zeolite to produce ethylbenzene under supercriti- phase under normal conditions. The curve envelops the
cal conditions, the authors do not apply an inert solvent vapor}liquid two-phase region, shown as VL. The super-
to the reaction system such as CO , as have been done by critical (SCF) region is clear, below which is the low-

most researchers. One of the considerations for waiving pressure vapor (LPV) region. To the left of the two-phase
the inert solvent is that in possible applications the pro- region are the high-pressure liquid (HPL) phase and the
cess could be simpli"ed even under the condition of low-pressure liquid (LPL) phase. The phase equilibria
a high ethylbenzene yield. A problem then raised is, since have been determined and published (Shi, Gao, & Yuan,
the system only consists of the reactants and products, 1999). The authors have found that the reaction behav-
with increase in conversion, the system almost inevitably iors in these regions are di!erent and are to some extent
shifts from one phase status to the other, for example, exceeding one's expectation. This paper is concerned
from supercritical to subcritical, or vice versa. There are with the kinetic expressions of the reaction behaviors of
totally "ve near-critical regions in which four are the benzene#ethylene system in these regions.
subcritical close to the critical point. For a binary (or
ternary) system, the phase behaviors of these regions are
usually complicated, and are often in short of available 2. Experimental
data.
Fig. 1 is a schematic depiction of the near-critical Experiments are conducted in all these regions under
regions of a binary system A#B of a certain critical two temperatures: 250 and 2603C. The experimental con-
dition distribution is depicted in Fig. 3, which is also
listed in Table 1 but only for ¹"2503C.
* Corresponding author. Tel.: #86-21-6425-2884; fax: #86-21-
6425-3528. Fig. 2 shows the experimental setup. A tubular reactor
E-mail address: wkyuan@ecust.edu.cn (W. Yuan). which is operated under a di!erential mode, is 6 mm in
 Current address: BASF AG, Engineering R&D, 67056, Germany. inner diameter and 0.6 m high. Ethylene conversion is

0009-2509/01/$ - see front matter  2001 Elsevier Science Ltd. All rights reserved.
PII: S 0 0 0 9 - 2 5 0 9 ( 0 0 ) 0 0 3 6 4 - X
1404 Y.-f. Shi et al. / Chemical Engineering Science 56 (2001) 1403}1410

maintained not higher than 5%, and sometimes much vessel before entering the reactor to prevent from pos-
lower. Reaction products are determined via a GC (HP sible pulses. For the liquid-phase benzene, an HPLC
6890, USA). Ethylene is "rst compressed (NOVA 2514, pump (HP 1100, USA) is installed. Both the gas and
Switzerland) to a certain pressure and kept in another liquid rates are measured through mass #owmeters
(Brooks 5850 TR, USA). The system pressure is precisely
regulated (Tescom 26-1722-44, USA). The bed temper-
ature is measured and controlled through a temperature
controller (No. 3 Shanghai Automatic Instruments,
China), with the aid of an electric coil heater wrapping
the reactor.

zeolite for the experiments is o!ered by the Research
Institute of Petroleum Processing (RIPP). Ethylene is
supplied by the Shanghai Research Institute of Chemical
Technology (SRICT) of a purity of higher than 99.95%.
Benzene for experiments is originally produced by the
Shanghai Feida Chemicals and is puri"ed before applica-
tion to guarantee a purity of higher than 99.95%. Ethyl-
benzene is supplied by Shanghai Central Chemicals and
is also puri"ed before the experiments (Fig. 3).
Preliminary experiments have been completed before
the systematic reaction rate determination. These experi-
Fig. 1. Phase states of the "ve near-critical region of a binary system. ments are: tests to verify that the material used for the
experimental setup does not a!ect the reaction results,

Fig. 3. Experimental condition distribution for the ethylene}benzene

Fig. 2. Experimental setup. system.

Table 1
Operating conditions in the near-critical regions at 2503C

Pressure (MPa) Mole fraction of ethylene

0.04 0.08 0.12 0.16 0.22 0.30

¹"2503C 5.9 LPL LPL VL VL LPV LPV

6.4 LPL LPL LPL VL LPV LPV
6.9 HPL HPL HPL HPL SCF SCF
7.4 HPL HPL HPL HPL SCF SCF
 Y.-f. Shi et al. / Chemical Engineering Science 56 (2001) 1403}1410 1405

the minimum #ow rate to ignore the external mass trans- the ethylene fraction (Figs. 4 and 5). Obviously, the
fer resistance, and the suitable catalyst pellet size to observed reaction behaviors are quite unusual. So
neglect the internal di!usion e!ect. we have tried several kinetic expressions to deal
The reaction rates, expressed by benzene disappear- with those data: hyperbolic and power law, separated
ance per unit catalyst weight per unit time, are pre- phase parameter estimation, and uni"ed parameter
sented in the form of "gures and are plotted against estimation.

Fig. 4. Reaction rates at 2503C. Fig. 5. Reaction rates at 2603C.

Table 2
Hyperbolic models derived from reaction mechanisms

Hypothetical reaction mechanics Models Model

no.

kC C
P Surface reaction controlling r" # sq1
(1#K C #K C )
# #
kC
P Both benzene and ethylene P Benzene adsorption controlling r" sq2
1#K C
adsorbed # #

kC
P Ethylene adsorption controlling r" # sq3
1#K C

kC C
P Ethylbenzene desorption controlling r" # sq4
1#K C #K C #K C C
# # ! #
kC C
C H #C H P Ethylene adsorbed without Surface reaction controlling r" # sq5
    1#K C
PC H benzene P adsorbed # #
 
kC
Ethylene adsorption controlling r" # sq6
1#K C
# #

kC C
P Ethylbenzene desorption controlling r" # sq7
1#K C #K C C
# # ! #

kC C
P Benzene adsorbed ethylene P Surface reaction controlling r" # sq8
without adsorbed 1#K C

kC
P Benzene adsorption controlling r" sq9
1#K C
# #
kC C
P Ethylbenzene desorption controlling r" # sq10
1#K C #K C C
! #
1406 Y.-f. Shi et al. / Chemical Engineering Science 56 (2001) 1403}1410

Table 3
Estimated parameters for hyperbolic models of the single-phase region

Model Estimated parameters Regression

no. coe$cient
k E K Q K Q K Q K Q RC
  # # ! ! #  #
sq1 70.594 !1E#05 !1.011 61 903 !6.599 60 149 0.7092
sq2 0.0197 427.99 !9E-04 !401.1 *
sq3 1254.6 37691 !2E!04 !7145 0.5832
sq4 2021 2713.9 4832.6 !2993 7644.2 !4653 0.0008 33 133 0.6567
sq5 1.5232 44894 !6E#06 !1E#05 *
sq6 1E#06 68 859 !0.018 !5775 0.8119
sq7 147.84 61 147 !4E#06 !95 841 34 071 !1E#05 0.519
sq8 4E#07 110 569 322 723 !84 795 0.61
sq9 79.597 36 337 !0.042 !9669 *
sq10 425 900 13 317 8298.9 7296.6 1456.2 !14 629 0.6312

3. Kinetic model and preliminary estimation Table 4

Estimated parameters for power-law function for all single-phase
The hyperbolic models we use are based on simulta- regions
neous benzene and ethylene absorption, ethylene ad- Estimated parameters Regression
sorption without benzene adsorption, and benzene coe$cient
adsorption but without ethylene adsorption (Table 2). In k

E b e RC
the table, k and K (subscript i denotes benzene (B), ethy-
G 131.31 64 241 0.1111 0.7583 0.6188
lene (E) or ethylbenzene (EB), respectively) are as follows:


E
k"k exp ! , (1)
 R¹


Q
K "K exp ! G . (2)
G G R¹
K actually symbolizes the ratio of adsorption coe$cient
G
to desorption coe$cient (K "K /K ). A uni"ed para-
G G? GB
meter estimation has been made with these models for
reaction rates of all the four single-phase regions (SCF,
HPL, LPL and LPV). Behaviors of the two-phase region
are supposed to combine those of the two single phases,
i.e., liquid phase and vapor phase. Table 3 gives the
estimated parameters.
Fig. 6. Rate vs. reduced pressure at 2503C.
Obviously, the estimation shows a poor "tness. The
regression coe$cients are low. The &*'s in the table mean
very poor regression. In addition, some of the estimated still unsatisfactory. Some physical contradictions still
parameters, such as activation energy and adsorption exist. A power-law model-based estimation is also done
heat, are physically unreasonable. (Table 6) for comparison. The regression coe$cients are
We then use the power-law model, which is expressed as seemingly better than the uni"ed estimation, though
some of the estimated parameters are still of physically


E
r"k exp ! C@ CC (3) doubtful signi"cance. For example, for the HPL, LPV
 R¹ #
and SCF regions, the activation energies are of negative
and from which the following estimation results (Table 4) values. The above results have persuaded us that the
are obtained. It seems the "tness of the model with the conventional kinetics cannot properly be applied to the
experiments is also poor. near-critical regions.
Considering application of the uni"ed parameter es-
timation to all the four single-phase regions to be inap-
propriate, we estimate the parameters of the hyperbolic 4. Crossover function model
models of the four regions individually. Table 5 presents
some results of the estimation as an example. One clearly Replots of the reaction rate against the reduced pres-
notices from these tables that the estimation results are sure, which are shown in Figs. 6 and 7, remind us that the
 Y.-f. Shi et al. / Chemical Engineering Science 56 (2001) 1403}1410 1407

Table 5
Estimated parameters for hyperbolic models of the supercritical #uid region

Model Estimated parameters Regression

no. coe$eient
k E K Q K Q K Q K Q RC
  # # ! ! #  #
sq1 257 345 !3E#06 12 489 1E#06 242.15 1E#06 0.792
sq2 0.0919 !5.194 0.0004 !8.48 *
sq3 0.1776 41.944 !1E!04 51.221 *
sq4 0.0567 23.578 !0.121 !3.359 0.2764 2.8856 0.0004 24.251 0.592
sq5 0.023 !3E#06 4.646 3E#06 *
sq6 539.22 36 058 !0.025 !5948 0.4318
sq7 0.0956 14.109 0.4736 3.1202 0.0003 11.093 0.6004
sq8 0.0003 950.91 0.0005 761.47 *
sq9 9.3744 20 075 6E#08 !1E#05 0.1617
sq10 0.0555 24.651 !0.15 !7.43 0.0005 32.18 0.3482

Table 6
Estimated parameters for power-law model of the single-phase regions

Phase region Estimated parameters Regression

coe$cient
k E b e RC

Low-pressure liquid 2E!09 312 763 8.168 4.41 0.9903
High-pressure liquid 0.1221 !7002 !0.055 0.9358 0.9118
Low-pressure gas 7E!05 !1274 1.4587 0.5429 0.8948
Supercritical #uid 0.0019 !68 627 0.3946 !1.101 0.8075

Table 7
Uni"ed estimated parameters for power-law-crossover function model
of all the single-phase region

Estimated parameters Regression

coe$cient
k E b e n RC

3.461464 12 624.81 0.139617 0.773204 !0.21546 0.91337

crossover function to be good for "tting:


y L
f (y)" (4)
1#y
Fig. 7. Rate vs. reduced pressure at 2603C.
in which

 
P!P
y" A. (5)
reaction behaviors may have some similarity with the P
A
physical properties in the near-critical regions, because
both are related to the critical conditions. Dating back to The power-law model becomes

  
the 1940s, Guggenheim (1944) discussed the possible !E y L
existence of some power-law rule near the critical point. r"k exp C@ CC . (6)
 R¹  # y#1
Later Fox (1983) suggested the crossover theory which
could be applied to the near-critical regions. For the A uni"ed estimation of the parameters are listed in
conditions far from critical, the crossover function Table 7.
reduces to unity. The authors have compared several The regression gives better results, though still un-
crossover functions via experimentally measured data satis"ed. We have also tried the hyperbolic models
regression and "nally would suggest a very simple to compare with the power-law model. To combine
1408 Y.-f. Shi et al. / Chemical Engineering Science 56 (2001) 1403}1410

Table 8
Estimated parameters for hyperbolic model combined with the crossover function of the single-phase region (the "rst kind)

Model Estimated parameters Regression

no. coe$cient
k E K Q K Q K Q K Q n RC
 C  # # ! ! #  #
fsq1 0.0019 !981.1 0.0031 !4687 0.0047 !821.9 !0.206 0.945
fsq2 0.1660 15 809 !29.87 !45 046 !0.394 *
fsq3 2.5193 12 669 !1.9E!05 !214.1 !0.216 0.754
fsq4 5.3102 12 771 1.2483 299.10 1.6218 46.635 0.0004 !192.3 !0.213 0.636
fsq5 244.54 12 672 821.36 864.97 !0.267 *
fsq6 0.6019 12 311 !0.015 !2046 0.0275 *
fsq7 115.07 12 621 !4.963 !1.147 0.0999 !0.333 !0.263 0.328
fsq8 0.0045 12 768 0.0014 !34.97 !0.238 0.917
fsq9 2.5881 22 886 !0.046 !10 299 !0.131 *
fsq10 0.0198 1131.4 0.0250 3689.1 0.0015 !13 189 !0.212 0.770

the hyperbolic model with the crossover function,

we would choose two formats. Take model sq1 as an
example:
Format 1 (written as fsq1):

 
kC C P!P L
r" # A . (7)
(1#K C #K C ) P
# #
Format 2 (written as ssq1):

kC C (P!P )/PL
r" # A .
(1#K C (P!P )/PL #K C (P!P )/PL )
A # # A
(8)
Fig. 8. Reaction rate simulation results at 2503C.

The estimation can be seen in Tables 8 and 9.

We notice that in Table 8 only model fsq5 gives
physically reasonable parameters, however, in Table 8
we "nd that models ssq4, ssq6}ssq8, and ssq10 o!er
`gooda parameters. Model ssq6 seemingly gives better
results than others. So only from this point, our impres-
sion is that Format 2 combination may be better than
Format 1. This may be explained that in the near critical
regions, both kinetics and adsorption play the role.
Model ssq6 implies that the mechanism may be that
the reaction is ethylene adsorption control without hav-
ing the benzene adsorbed. This point coincides with Zeng
(1994) who reported that benzene was very weakly
adsorbed.
We use Model ssq6 to correlate the reaction rates
which are compared with the measured (dots), as depic-
Fig. 9. Reaction rate simulation results at 2603C.
ted in Figs. 8 and 9.
Although the hyperbolic models are of physical im-
plications, we would suggest, for better "ttings, a power-
law model with a crossover function could be considered:
where x and x are, respectively, simple mole fraction of
#

  
E P!P L ethylene and benzene. The estimated parameters are
r"k exp ! (Px )C(Px )@ A , (9)
 R¹ # P available in Table 10.
A
 Y.-f. Shi et al. / Chemical Engineering Science 56 (2001) 1403}1410 1409

Table 10

Regression
Estimated parameters of Eq. (9)

coe$cient

0.90282

0.73792
0.69361

0.94101
0.37759

0.67763
0.87855
Regression parameters of models Regression

RC

*
coe$cient
k E b E N RC


!180.627 !180.67

n 3E#09 71441 1.4292 !1.223 !0.586 0.9915

!55.0496

!180.92

!180.67

n

!54.8248
!0.14135

!0.23142
!168.045

!180.733
!0.0226
!180.77

5. Conclusions
5.04218

0.51518
1.49020


1. After trying 10 hyperbolic models representing vari-

n

ous supposed reaction mechanisms, we have found that

!110.084
!0.23253
!0.33981
!180.688
!0.36234
!0.06397
!181.009

!180.697
!201 725 !69 961.7 !0.4072

no one from the ten can be used to "t the experimental

1.01211

results satisfactorily. The power-law model also gives



unsatisfactory results.
n

2. The "tness with the experimental results can be

Estimated parameters for hyperbolic model combined with the crossover function of the single-phase region (the second kind)

318.737

greatly improved after the models are combined with

a proper crossover function. A regression coe$cient of
#
Q

0.99 can be obtained when a power-law crossover func-

tion model is applied.
0.00196
# 
K

0.00156 9.91801

0.00121 23.7618

0.00194 8.15269
!

Notation
Q

C concentration
!
K

E activity energy
0.01655 !3582.39
!0.00063 !145.917

¹ temperature
!0.00264 38 373.9
1.24808

1.49063

P pressure
Q adsorption activity energy
#
Q

r reaction rate
k rate constant
0.56879

3.75361

K the ratio of adsorption coe$cient to desorp-

#
K

tion coe$cient
!16 306.8

!2.89E!05 !138.225

17 464.0
11.4354

8.15148
Q

Subscripts

B, E, EB benzene, ethylene, ethylbenzene

0.52457
0.13674

0.00332

0.46722

c critical state

K

!9781.75

!2479.24
Estimated parameters

48 102.1
45 129.0
22.3995

25.1592
9349.66

16.2055
71.0941
113.886

Acknowledgements
E

This work is supported by the National Natural

0.46757
0.09335

1.38895
4629.24
0.13630
0.12359

0.45219
0.00102
0.00840

0.00321

Science Foundation of China, and the China

Petrochemical Corporation (Contract No. 29792077).

k

The
zeolite applied for the experiments was developed

Table 9

Model

and supplied by the Research Institute of Petroleum

ssq10
ssq1
ssq2
ssq3
ssq4
ssq5
ssq6
ssq7
ssq8
ssq9
no.

Processing.
1410 Y.-f. Shi et al. / Chemical Engineering Science 56 (2001) 1403}1410

References Shi, Y. F., Gao, Y., & Yuan, W. K. (1999). High-pressure vapor}liquid
equilibrium for ethylene#benzene. Journal of Chemical Engineer-
Fox, J. R. (1983). Method for construction of nonclassical equations of ing Data, 44, 30}31.
state. Fluid Phase Equilibria, 14, 45}55. Zeng, Zh. H. (1994). Shape selective catalysis. Beijing: China
Guggenheim, E. A. (1944). Statistical thermodynamics of mixtures with Petrochemical Press.
zero energies of mixing. Proceedings of the Royal Society A, 183,
203}277.