tai lieu isolation n-butane

1. Journal of Chemical Engineering of Japan, Vol. 42, Supplement 1, pp. s79–s84, 2009 Research Paper
Discrimination of the Kinetic Models for Isomerization of
n-Butene to Isobutene
Tai-Shang C HEN and Jia-Ming C HERN
Department of Chemical Engineering, Tatung University,
40 Chungshan N. Rd., Sec. 3, Taipei, 10452, Taiwan, R.O.C.
Keywords: Butene, Isomerization, Kinetics, Model, Reaction Network
There has been a considerable interest for long periods in the production of isobutene from n-butene since
it can be used with methanol to produce MTBE. In this study, the general rate equation method that is based
on the Bodenstein approximation and network reduction technique is used to discriminate the kinetic models
for isomerization of n-butene to isobutene. For illustrating the advantages of using the general rate equation
method, two proposed mechanisms from literatures were used as examples to analyze the yield ratio and to
identify the correct mechanism. The experimental data published in literature were used as the test data in
this study. The mechanism with the byproduct polyisobutene produced from product isobutene and adsorbed
isobutene is identified as reasonable mechanism for the isomerization reaction.
Introduction power-law equation and nine Langmuir-Hinshelwood-
type rate equations at different temperatures. However,
Isobutene can be used in the reaction with methanol there was no single suitable rate expression that can
to produce MTBE (methyl tert-butyl ether), which have be used at various temperatures. Byggningsbacka et al.
become a highly demanded material of gasoline (Byg- (1999) investigated the skeletal isomerization of n-butene
gningsbacka et al., 1999). There has been a consider- to isobutene over ZSM-22 zeolite. They proposed three
able interest in the production of isobutene from n-butene different types of mechanisms and solved the system by
over different catalysts (Choudhary and Doraiswamy, numerical method. No explicit rate equation was derived
1971, 1975; Raghavan and Doraiswamy, 1977; Gayubo in the paper. Most types of rate equations published in the
et al., 1997; Byggningsbacka et al., 1999). In the past literatures are either empirical in nature or must assume
fifty years, there were some published literatures inves- some rate-determining steps (LH mechanisms) and thus
tigated on the kinetic modeling of isomerization of n- cannot be used confidently in scale-up design.
butene to isobutene over catalysts or zeolites (Choudhary In this study, we focused on the kinetic models
and Doraiswamy, 1975; Gayubo et al., 1997; Byggnings- for isomerization of n-butene to isobutene. A method-
backa et al., 1999). Though the reaction system seems ology named general rate equation method that is based
not very complex apparently, the real reaction mechanism on the Bodenstein approximation and network reduction
is somehow complicated due to the heterogeneous cat- technique is used to discriminate the reasonable kinetic
alytic reaction. In recent years, continuous studies about models (Chern and Helfferich, 1990; Chern, 2000; Chen
the dimerization of isobutene to produce diisobutenes or and Chern, 2002a, 2002b). For illustrating the advan-
by further oligomerization to produce triisobutenes and tages of using the general rate equation method, two pro-
tetraisobutenes have been also investigated by several re- posed mechanisms modified from the literature (Byggn-
searchers due to environmental concerns (Honkela and ingsbacka et al., 1999) were used as examples to ana-
Krause, 2004; Ouni et al., 2006; Talwalkar et al., 2007). lyze the yield ratio and to identify the more suitable and
The Langmuir–Hinshelwood-type kinetic models were reasonable mechanism. The experimental data from the
derived for the dimerization and trimerization reactions published literature (Choudhary and Doraiswamy, 1975)
to describe the reaction networks. were used as the test data in this study.
Traditionally, the power-law type or the Langmuir–
Hinshelwood-type rate equations are usually adopted to 1. Method
describe the kinetics of heterogeneous catalytic reactions.
Choudhary and Doraiswamy (1975) studied the reaction 1.1 Network reduction technique
over fluorinated η-alumina catalyst and compared one As shown in the previous papers (Helfferich, 1989;
Chern and Helfferich, 1990; Chern, 2000; Helfferich,
2001), the Bodenstein approximation of quasi-stationary
Received on July 2, 2008; accepted on December 19, 2008. behavior of intermediates permits any simple network to
Correspondence concerning this article should be addressed to
T.-S. Chen (E-mail address: tschen@ttu.edu.tw). be reduced to one with only pseudo-single steps between
Presented at ISCRE 20 in Kyoto, September, 2008.
Copyright ⃝ 2009 The Society of Chemical Engineers, Japan
c s79

2. X0 Xj Xj
Xn Xk
X1
r
Xi
Xi
X2
Fig. 2 Reduce the multi-pathway reaction network to equiv-
… alent single cycle reaction system
Fig. 1 Single loop reaction network with arbitrary number
of intermediates (co-reactants and co-products not
concentration, and Dii can be obtained from a square ma-
shown) (Chern, 2000)
trix of order n by n by tearing the closed network into a
linear one with the intermediate Xi on both ends. For ex-
ample, the D00 in a 4-intermediate cycle X0 –X1 –X2 –X3 –
adjacent nodes and between end members and adjacent X0 is λ12 λ23 λ34 + λ10 λ23 λ34 + λ10 λ21 λ34 + λ10 λ21 λ32 .
nodes. Specifically, the net rate contribution of a multi- If there exist an arbitrary number of parallel paths in
step, reversible simple network segment between adja- between intermediates Xi and X j , the λ coefficient could
cent nodes X j and Xk be replaced by the loop coefficients L (Chern, 1988):
X j ↔ X j+1 ↔ · · · ↔ X j+n ↔ · · · ↔ X k (1) ∑
m
(k)
∑
m
(k)
Li j = ij and L ji = ji (6)
(co-reactants and co-products not shown) is k=1 k=1
r j→k = jk [X j ] − k j [X k ] (2) where m is the number of parallel paths.
1.3 Reduction of multi-pathway to single cycle
where the “segment coefficients” are given by Many enzymatic or catalytic systems contain mul-
tiple sub-reactions and the reaction steps can be con-
∏
k−1 ∏
k−1
λi,i+1 λi+1,i structed as cyclic networks with multi pathways in topol-
i= j i= j ogy. Consider a large cyclic reaction network with two in-
jk = and kj (3)
D jk D jk dependent parallel pathways, as shown in Figure 2. The
parallel pathways between the two node-intermediates
with can be lumped together and the multi-pathway system
  can be reduced to an equivalent pseudo single cycle re-
∑
k ∏
i−1 ∏
k−1
D jk =  λm,m−1 λm,m+1  (4) action network (Chen and Chern, 2002a).
i= j+1 m= j+1 m=i
∏ 2. Results and Discussion
(products = 1 if lower index exceeds upper). The λ
coefficients are the pseudo-first order rate coefficients of The overall isomerization reaction of n-butene to
quasi-single molecular steps and are the products of the isobutene over catalysts or zeolites can be described as
actual rate coefficients and the concentrations of any co- cat.
reactants of the respective steps. For example, for the step A ←→ B −→ P (7)
X0 + A ↔ X1 + B, λ01 = k01 [A] and λ10 = k10 [B].
where A, B, and P represent n-butene, isobutene and by-
1.2 Single cycle system
product polyisobutene, respectively. After verifying and
Consider the single-cycle reaction network for ho-
analyzing many mechanisms, we proposed two possible
mogeneous catalytic reactions shown in Figure 1. The
mechanisms with reaction steps listed in Table 1 and re-
steady-state rate through the cycle can be expressed by
action network shown in Figures 3(a) and (b). The nota-
the following equations (Chern, 2000):
( n ) tion X0 means the fresh or regenerated catalyst site and
∏ ∏
n X1 to Xn mean the adsorbed reactants or product on cata-
λi,i+1 − λi+1,i [XT ]
i=0 i=0
lyst sites in different forms. The direction of arrow means
r = (5) the addition of reactants or desorption of products from
∑n
Dii catalyst sites. It can be seen in Figure 3(a), the byproduct
i=0 polyisobutene (P) is produced from a pathway with the
(taking index n + 1 = 0 for conveniences) addition of n-butene (A) to intermediate X2 , (X–B). In
where the generalized rate coefficient λi,i+1 is the prod- mechanism Figure 3(b), polyisobutene is produced from
uct of the forward rate constant, ki,i+1 and co-reactant a pathway with the addition of isobutene (A) to interme-
s80 JOURNAL OF CHEMICAL ENGINEERING OF JAPAN

3. 200
Table 1 The reaction steps in two proposed mechanisms of 180 300 oC, r2 = 0.9207
n-butene (n-C4) to isobutene (i-C4) isomerization 335 oC, r2 = 0.8240
160
365 oC, r2 = 0.8934
140 400 oC, r2 = 0.8436
rB/rP, Predicted [ - ]
Reaction step Mechanism (a) Mechanism (b)
435 oC, r2 = 0.8745
Adsorption of n-C4 S + A ⇔ SA S + A ⇔ SA 120
Surface reaction of SA ⇔ SB SA ⇔ SB 100
n-C4 to i-C4 80
Desorption of i-C4 SB ⇔ S + B SB ⇔ S + B
60
Adsorption of n-C4 SB + A ⇔ SP —
Adsorption of i-C4 — SB + B ⇔ SP 40
Desorption of polyisobutene SP ⇔ S + P SP ⇔ S + P 20
0
0 20 40 60 80 100 120 140 160 180 200
rB/rP, Experimental [ - ]
X0
A Fig. 4 Parity plot for the yield ratio derived for mechanism
P in Figure 3(a)
B
X3 X1
where
(2)
(1) L 24 = k24 + k23 PA
L 42 = k42 PB
A ∑ k23
X2 Dii = D00 + D11 + D22 + D22 (9)
k34
X0 D00 = (k12 + k10 )(k24 + k23 PA ) + k10 k21
A D11 = (k24 + k23 PA )k01 PA + k21 k01 PA + k21 k32 PB
P
D22 = k01 k12 PA + (k12 + k10 )k32 PB
B
Note that the index 4 is also expressed as 0 for con-
X3 X1
veniences. The individual reaction rates of product B and
(2) P are
(1) (k24 D22 − k42 PB D00 )[XT ]
rB = ∑ (10)
B Dii
X2
(k23 PA D22 )[XT ]
rP = ∑ (11)
Fig. 3 Two proposed mechanisms for the isomerization re- Dii
action of n-butene to isobutene
The cyclic reaction rate for the mechanism shown in Fig-
ure 3(b) can be derived also by the same procedure and
expressed as
diate X2 Note that the reaction pathway (2), X2 –X3 –X0 ,
(k01 k12 L 24 PA − L 42 k21 k10 )[XT ]
is assumed to be irreversible for both mechanisms. r= ∑ (12)
The systems shown in Figures 3(a) and (b) are clas- Dii
sified as multi-cycle or multi-pathway reaction systems
where
(Chen and Chern, 2002b). The left two reaction path-
ways, (1) and (2), in both Figures 3(a) and (b) can be L 24 = k24 + k23 PB
lumped first by Eq. (6), and then the systems can be L 42 = k42 PB (13)
treated as single cycle systems. It is needless to assume D00 = (k12 + k10 )(k24 + k23 PB ) + k10 k21
any step is a rate-determined step. Taking mechanism
shown in Figure 3(a) for example, the reaction rate can Note the Dii terms in Eqs. (8) and (12) are different be-
be derived by the method (Chen and Chern, 2002a). The cause of the different reactants in the pathways from X2
cyclic reaction rate can be written as to X3 in the two mechanisms.
Although the Dii terms in Eqs. (8) and (12) for both
(k01 k12 L 24 PA − L 42 k21 k10 )[XT ] mechanisms are complicated to be expressed, we can dis-
r= ∑ (8)
Dii criminate the kinetic models without the Dii terms. For
the purpose of identifying which mechanism is correct,
VOL. 42 Supplement 1 2009 s81

4. 200
300 oC, r2 = 0.9982
Table 2 The fit results of kinetic parame-
175 ters of mechanism (b) for all reac-
335 oC, r2 = 0.9886
365 oC, r2 = 0.9996 tion temperatures
150
400 oC, r2 = 0.9974
rB/rP, Predicted [ - ]
125 435 oC, r2 = 0.9986
Parameter Unit Value
100
ka0 — 1.934 × 102
kb0 — 1.227 × 107
75 Ea kJ/mol −84.83
Eb kJ/mol −15.84
50
25
200
0 300 oC
0 25 50 75 100 125 150 175 200 175
335 oC
rB/rP, Experimental [ - ] 365 oC
150
400 oC
rB/rP, Predicted [ - ]
Fig. 5 Parity plot for the yield ratio derived for mechanism 125 435 oC
in Figure 3(b)
100
75
the yield ratio rB /rP for the two systems can be employed
50
by dividing Eq. (10) to Eq. (11) as
25
k24 D22 − k42 PB D00
rB /rP = (14) 0
k23 PA D22
0 25 50 75 100 125 150 175 200
After inserting both D22 and D00 into Eq. (14), we can re- rB/rP, Experimental [ - ]
arrange the equations, lump all rate coefficients ki j , and
express the yield ratio rB /rP as a simpler form. For mech- Fig. 6 Parity plot for the yield ratio derived for mechanism
anism in Figure 3(a) with two constants, (b) and the kinetic parameters for all temperatures
kb (1 − PB /K PA ) − ka PB
rB /rP = (15)
PA + ka PB
values are shown in Figures 4 and 5. The r-square val-
where ues for mechanism in Figure 3(a) range from 0.8240 to
(k12 + k10 )k42 0.9207 and those for mechanism in Figure 3(b) range
ka = from 0.9886 to 0.9996. From statistical viewpoint, mech-
k01 k12 (16)
k24 anism (b) is more reasonable for the isomerization reac-
kb = tion.
k23
The results shown in Figure 5 were evaluated at
For mechanism in Figure 3(b), five different temperatures simultaneously. Since we have
identified mechanism in Figure 3(b) is more reasonable,
r1 − r2
rB /rP = we can express the two kinetic parameters ka and kb in
r2 Eq. (17) as the Arrenhius forms,
(17)
kb (PA /PB − 1/K ) − ka PB
= −1 ka = ka0 e−Ea /RT (18)
PA + ka PB
where ka and kb are the lumped constants with the same kb = kb0 e−E b /RT (19)
forms as Eq. (16) and K is the equilibrium constant for the Then the yield ratio equation was fitted to all the 30 ex-
isomerization reaction n-butene to isobutene. The value perimental runs with reaction temperatures from 300 to
of K can be evaluated from thermodynamic properties 435◦ C. The results were listed in Table 2 and the r-square
and the values for the lumped constants can be deter- value for the nonlinear regression is 0.972. Note that
mined by nonlinear regression. We used a commercial the four parameters in Table 2 are lumped constants that
software Sigma Plot ver 9.0 to perform the nonlinear re- group the six rate constants together as shown in Eq. (16).
gression and parameter fitting. Both yield ratio equations Therefore, the apparent activation energy for ka gives lit-
were employed to fit the data published by Choudhary tle information about the individual steps. However, the
and Doraiswamy (1975) at five different reaction temper- negative value of Eb shown in Table 2, that is the appar-
atures from 300 to 435◦ C. The results of comparing the ent activation energy for kb suggests that the isobutene
experimental and the predicted yield ratios and r -square
s82 JOURNAL OF CHEMICAL ENGINEERING OF JAPAN

5. Table 3 The fit results of number of
monomers in polyisobutene for
different temperatures of mecha-
nism (b)
Temperature [◦ C] n r -square
300 7 0.9980
365 37 0.9784
400 49 0.9539
435 60 0.9692
comparison of the relationships between the partial pres-
sures of n-butene and isobutene and the yield ratio. It can
be seen in Figure 7 that the yield ratio increases sharply
Fig. 7 Comparison of the relationships between the partial when the partial pressure of n-butene is greater than 0.8
pressures of n-butene and isobutene with the yield atm. This information is useful to help choose the proper
ratio operational parameters for reactor operation conditions.
Though we assumed the pathway for polyisobutene
production involves only two steps in Figure 3, the yield
P X0 ratio equation for multi-step isobutene addition can be
Xn+1 A treated by the same way with the general rate equation
B method. Figure 8 shows a revised scheme for mechanism
(b). The product isobutene, (B), would add into reaction
Xn B pathway (2) in Figure 8 step by step. Finally the product
X1 –(isobutene)n –, (P), was desorbed from catalyst.
…
All steps in the pathway (2) of Figure 8 are also as-
X4 sumed to be irreversible. The reaction rate for the path-
(2)
(1) way involving arbitrary number of irreversible reaction
B X3 steps can be treated by the same procedures described
X2 previously. The rate of both pathways in Figure 8 can be
B expressed as,
Fig. 8 A revised mechanism in Figure 3(b) for multi-step (k2,n+2 D22 − kn+2,2 D00 )[XT ]
isobutene addition to produce polyisobutene r1 = (21)
∑
n+1
D00 + D11 + D22 + ( 2k / k,n+2 )
k=3
desorption step has a lower energy barrier than the ad- k23 PB D22 [XT ]
r2 = (22)
sorption of isobutene onto the adsorbed site: ∑
n+1
D00 + D11 + D22 + ( 2k / k,n+2 )
k24 k240 e−E 24 /RT k=3
kb = = (20)
k23 k230 e−E 23 /RT Note that the index 0 in X0 can also be expressed as n + 2
k240 −(E 24 −E23 )/RT for convenience. The yield ratio can be expressed by a
= e = kb0 e−E b /RT similar form as Eq. (17),
k230
for Eb < 0, E24 < E23 . On the other hand, the apparent ac- r1 − (n − 1)r2
rB /rP = (23)
tivation energy for ka gives little information about the in- r2
dividual steps because of more complicated relationship kb (PA /PB − 1/K ) − ka PB
shown in Eq. (16). The parity plot for all the experiments = − (n − 1)
PA + ka PB
is shown in Figure 6. Figure 6 shows a reasonable agree-
ment between the experimental data and the model pre- where n is the number of isobutene for constructing poly-
diction. The slightly higher deviation as shown in Figure isobutene. Equation (23) was used to fit the same data at
6 was due to the significantly error (r-square = 0.9886 five different reaction temperatures from 300 to 435◦ C
as shown in Figure 5) in the experiment for temperature for getting ka , kb and n. The fit results are shown in Ta-
335◦ C. ble 3. The result of 330◦ C is not shown due to lower r-
Equations (17)–(19) can be used to analyze the char- square value (r2 = 0.93) compared with others. Since the
acteristics of the isomerization reaction. The yield ratio degree of polymerization will be affected by the tempera-
r B /r P is the function of P A and P B . Figure 7 shows the ture, it can be seen in Table 3 the extent of polymerization
VOL. 42 Supplement 1 2009 s83

6. of isobutene increases while the reaction temperature in- ka = lumped rate coefficients [—]
creases. The explicit reaction rate for the isomerization kb = lumped rate coefficients [—]
ki j = rate constant of step i → j for path p
reaction can also be easily obtained by using the method-
Li j = loop coefficient of segment i → j defined in Eq. (6)
ology to calculate the Dii terms.
P = polyisobutene [—]
Choudhary and Doraiswamy (1975) and Ragha- PA = pressure of component [atm]
van and Doraiswamy (1977) proposed nine different R = gas constant [J/mol K]
Langmuir–Hinshelwood-type or empirical kinetic mod- r = reaction rate [mol/L s]
els for the system and concluded that different models Xj = reaction species j or intermediate [mol/L]
XT = total catalyst concentration [mol/kg cat]
should be used at different temperatures. The reactions
for multi-step isobutene addition were ignored in their jk = segment coefficient of segment j → k for path de-
studies. Though different model equations were able to fit fined in Eq. (3)
their kinetic data at different temperatures with satisfac- λ jk = pseudo first order rate coefficient of step Xi to X j
tory accuracy, there was no clear connection between the
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