Alkylation Kinetics of Isobutane by C4 Olefins Using Sulfuric Acid as

(13) The two-step process for the alkylation of isobutane with C4 olefins was investigated, but the rate constants were not given.(10). In this work, ...
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Alkylation Kinetics of Isobutane by C4 Olefins Using Sulfuric Acid as Catalyst Weizhen Sun, Yi Shi, Jie Chen, Zhenhao Xi, and Ling Zhao* State-Key Laboratory of Chemical Engineering, East China University of Science and Technology, Shanghai 200237, China S Supporting Information *

ABSTRACT: The alkylation kinetics of isobutane with butene using sulfuric acid as catalyst was investigated by batch experiments in the conditions of industrial interest. More than 16 alkylates were identified and quantified by GC-MS. On the basis of the classic carbonium ion mechanism, the kinetic model was established, which can predict the concentration change of three groups of key alkylates including trimethylpentanes (TMPs), undesirable dimethylhexanes (DMHs), and heavy ends (HEs). The agreement between experimental and model calculated data was quite satisfactory. The rate constants were found to be constant with the varied temperatures (276.2 to 285.2 K) except those accounting for the addition of H+ to isobutene and its reversible reaction. An anti-Arrhenius behavior was observed for the addition reaction of H+ to isobutene, in which the corresponding rate constant falls with the increasing temperatures. The kinetic model was confirmed by the simulation of the industrial alkylation reactor. Hopefully, the kinetic model developed in this work will be useful to the design and optimization of novel alkylation reactors.

1. INTRODUCTION In early 1990s, the USA refiners had to start changing their strategy on gasoline composition to meet the mandatory CAA (Clean Air Act) specifications.1 Since that time, gasoline was forced to move in a more environmentally friendly direction, such as reducing volatility, limitations in the aromatic content, increased amount of oxygenates, reduction of olefins and sulfur, and elimination of lead. As a desirable blending component, without olefins or aromatics, alkylate exclusively contains isoalkanes with high octane number. Since its commercial production in the last century, alkylate had been the most ideal blending component for a typical refinery gasoline pool. Nearly 70% of the world’s alkylate production is from North America, and over 20% is produced from Europe.2 It was believed that alkylate will continue to be a desirable blending component as long as cars are operated on high octane gasoline.3 The alkylation reaction producing alkylates combines isobutane with light C3−C5 olefins in the presence of a strong acid catalyst. Currently, the only processes of commercial importance use either sulfuric or hydrofluoric acid as catalysts.4 Although the number of established alkylation units using sulfuric acid is almost as much as that using hydrofluoric acid, more new alkylation plants built worldwide chose sulfuric acid as catalyst in the recent past years.5 One of the reasons is that hydrofluoric acid is a highly toxic liquid, and released into the atmosphere, it forms aerosol, which drifts downwind for several kilometers.6 Actually, both acids suffer from certain drawbacks, but it is not the intent of this work to review in detail the pros and cons of sulfuric acid versus hydrofluoric acid but to address the alkylation kinetics using sulfuric acid as a catalyst. It is well-known that the study on reaction kinetics is of fundamental importance not only to the design and optimization of a ripe chemical reactor but also to the development of a novel one. Also, it is helpful in understanding the reaction mechanism. As to the alkylation mechanism of © XXXX American Chemical Society

isobutane with olefins, much classical literature had been published,7−11 in which the formation pathway of the majority of key components and intermediates in alkylate were well formulated although different publications would have different descriptions regarding some specific steps. However, to the best of our knowledge, there was little literature focusing on the alkylation kinetics of isobutane with butene in sulfuric acid to address the formation of several key alkylates such as trimethylpentanes (TMPs), dimethylhexanes (DMHs), and heavy ends (HEs). Using uniform hydrocarbon drops and short contact time, the sulfuric acid catalyzed reaction of isobutane with 1-butene, as well as the oligomerization of 1-butene, was investigated, in which only two key reactions were considered,12 but other important reaction steps in view of the presence of several dozen isoparaffins in commercial produced alkylates are far from being understood.13 The two-step process for the alkylation of isobutane with C4 olefins was investigated, but the rate constants were not given.10 In this work, the alkylation kinetics of isobutane with butene using sulfuric acid as catalyst was measured under the condition of industrial interest. The kinetic model was established on the basis of the carbonium ion mechanism, in which three families of key isoparaffins were considered including TMPs, DMHs, and HEs.

2. EXPERIMENTAL SECTION The experiments were carried out in a batch setup with a glass reactor with the volume of 1 L. To keep isobutane and olefin in Special Issue: NASCRE 3 Received: February 4, 2013 Revised: April 2, 2013 Accepted: April 3, 2013

A

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Figure 1. Schematic diagram of experimental setup: 1, cylinder for mixed C4; 2, cylinder for N2; 3, dryer; 4, filter; 5, mass flow meter for liquid; 6, refrigerator; 7, mass flow meter for gas; 8, low temperature salt water; 9, reactor; 10, baffles; 11, sampling cylinder.

liquid phase, the operating pressure was set to be 0.5 MPa. One refrigerant system was employed to obtain cycling salt water, which was used to keep the entire reactor and the hydrocarbons into and out of the reactor at constant temperature ranging from 276.2 to 285.2 K. Inside, the reactor baffles and stirring apparatus were installed, which can be adjusted within 3000 rpm. For a typical experiment, first, the weighed sulfuric acid was put into the reactor, and then, the nitrogen (N2) was introduced to remove air in the reactor, after which the pressure was set to be 0.5 MPa. Next, the refrigerant system started to work to keep the material inside the reactor at the set temperature. When the temperature inside the reactor reached the set temperature, the weighed mixture of isobutane and olefin with certain molar ratio was quickly introduced into the bottom of the reactor. Almost at the same time, the agitator started to work to ensure the good dispersing of hydrocarbon upon contacting the sulfuric acid. According to the alkylation reaction progress, the sampling interval was shorter initially and then longer in the later period. In all of the experiments, the temperature inside the reactor was recorded and controlled to ensure it was within a set range. The schematic diagram of the experimental setup was shown in Figure 1. The gas chromatography−mass spectrometry (GC-MS) was adopted to identify and quantify more than 16 alkylate components. A typical chromatogram of alkylate components is shown in Figure 2. The area normalization method was employed in this work, since all of the correction factors of

different components are very close to 1.0 with respect to the same standard substance benzene on FID detector. The maximum relative analysis deviation was less than 5%, which shown in Table 1. More detailed descriptions about GC-MS can be found in the Supporting Information. Table 1. Reproducibility of Analysis Method mass content, % number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

alkylate components isopentane 2,3dimethylbutane 3-methylpentane 2,4dimethylpentane 2,2,3trimethylbutane 2-methylhexane 2,3dimethylpentane 3-methylhexane isooctane 2,5dimethylhexane 2,2,3trimethylpentane 2,4dimethylhexane 2,3,4trimethylpentane 3,3dimethylhexane 2,3dimethylhexane 2,2,5trimethylhexane

sample 1 sample 2

average, %

relative deviation

1.491 3.475

1.374 3.286

1.433 3.380

0.041 0.028

0.427 2.936

0.403 2.758

0.415 2.847

0.030 0.031

0.348

0.345

0.347

0.004

0.207 1.744

0.227 1.692

0.217 1.718

−0.046 0.015

0.152 21.843 4.054

0.162 21.348 3.982

0.157 21.595 4.018

−0.029 0.011 0.009

2.395

2.377

2.386

0.004

1.100

1.105

1.102

−0.002

9.507

9.276

9.391

0.012

12.174

11.904

12.039

0.011

0.272

0.287

0.280

−0.027

10.083

9.976

10.030

0.005

The intrinsic chemical reaction of alkylation is very fast, leading to a strong mass transfer limitation of olefin into the reaction region when the mass transfer rate is not big enough.14 The experiments showed that when exceeding above 2500 rpm the increasing stirring speeds have no influence on the alkylation rate, which demonstrates the elimination of mass

Figure 2. Chromatogram of all alkylate components. B

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Figure 3. Diagram of the reaction pathways network.

TMP+ + iC4 = → TMP + C=C(CH3)−C+

transfer limitation. Thus, all of the investigations of alkylation kinetics with varied temperatures were performed with the stirring speeds of 2800 rpm.

C=C(CH3)−C+ + iC4 = → C=C(CH3)−C−C−(CH3)C+−C

3. KINETIC MODEL It is well accepted that the alkylation of isobutane with olefins follows the classic carbonium ion mechanism. Initially the tertbutyl cation is produced by this reaction: k1

iC4 = + H+ → iC4 +

k5

where iC4= is isobutene and iC4+ represents tert-butyl cation. Actually, regardless of whether the feed butene is either 1butene or 2-butene, it tends to give iC4= through fast isomerization, which occurs especially in the presence of sulfuric acid.15 The transform between different butenes proceeds by the following equilibrium reaction, K1

iC4 + + 1‐butene → DMHs+

k6

DMHs+ + iC4 → DMHs + iC4 +

TMPs+ (or DMHs+) + iC4 = (or 2‐butene) → iC12+

(3)

(10)

The tert-butyl cation adds to an olefin to produce the corresponding C8 carbonium cation. For example, when the tert-butyl cation reacts to iC4= or 2-butene, the trimethylpentanes will be formed, k3

iC4 + + 2‐butene (or iC4 =) → TMPs+

+

The iC12 would further add iC4 or 2-butene to give iC16+. For simplification, in this work, we regard iC12+ and iC16+ as the pseudo components iCm+. When these polymer cations iCm+ are contacted with isobutane, the HEs is formed, along with the production of iC4+,

(4)

k4

=

k7

iCm+ + iC4 → iCm + iC4 +

where TMPs is the abbreviation of trimethylpentanes. These C8 carbonium cations tend to isomerize via methyl shifts and hydride transfer reaction to form several isomer cations.4 For simplification, in this work, all these C8 cations are regarded as one pseudo component TMP+. By rapid hydride transfer with isobutane, each TMP+ changes to the corresponding TMP component, regenerating the iC4+ to keep on the chain propagation. TMP+ + iC4 → TMP + iC4 +

(9)

According to the experimental data in this work, it was verified that the formation of DMHs is most likely through the latter pathway, that is, the addition of 1-butene to iC4+. By reactions involving olefins, heavy ends (HEs) are produced, which are primarily polymerization reactions.15 The polymerization of C4 olefins proceeds by the addition of iC4= or 2-butene to TMPs+ or DMHs+,

(2)

Interestingly, it is found that even when isobutane alkylated with olefins rather than butenes, the trimethylpentanes are still generated by so-called self-alkylation. The key step for selfalkylation is the formation of isobutene, which in fact is a reversible reaction of the reaction 1:1 k2

(8)

Similar to TMPs+, the DMHs+ are saturated through the hydride abstraction from isobutane, giving an iC4+ meanwhile,

K2

iC4 + → iC4 = + H+

(7)

Through suitable hydrogen and proton transfer reactions, the unsaturated cation ion forms a DMH molecule. Another possible pathway to give DMHs is through the addition of 1butene to iC4+,11

(1)

1 − C4 H8 ⇄ 2 − C4 H8 ⇄ iC4 =

(6)

(11)

As one of the five groups in alkylated hydrocarbon products, the light ends (LEs) include C5−C7 isoparaffins. The production of LEs is believed to come from the fragmentation of large isoalkyl cations.9 Due to the strong oxidizing capacity of concentrated sulfuric acid, the isoalkyl cation will be generated again from HEs as follows, iCm + H+ → iCm+

(5)

(12)

These heavy isoalkyl cations are fragmentated following the β-scission rule, leading to smaller isoalkyl cations and olefins.1

where iC4 stands for isobutane. The source of undesirable dimethylhexanes (DMHs) with low octane numbers has several possible pathways. One was believed from the addition of iC4= and allylic carbocation, which is the result of a hydride ion abstraction from the allylic position of an olefin molecule.10

k8

iCm+ ⇄ iCx + + iCy = k9

C

(13)

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Figure 4. Concentration profile of key components in alkylation of isobutane with butene. Temperature: (a) 276.2 K, (b) 279.2 K, (c) 282.2 K, (d) 285.2 K. Symbols: experimental data; Line: calculated values by kinetic model.

Isoalkyl cations generated by fragmentation (iCx+) and protonation of olefins (iCy=) are thought to be the major precursors of LEs. Through the hydride ion transfer, these isoalkyl cations change into the corresponding LEs. According to the experimental observation in this work, the degradation of DMH was found to be obvious. It may be ascribed to the formation of DMH+ from the oxidation of DMH, which is further fragmentated into small LE through scission reaction.16 To simplify this multistage reaction, one single reaction step is used in this work, k10

DMH → LE

c1‐C4H8 = α*cC4H8

(15)

c 2‐C4H8 = β*cC4H8

(16)

ciC4= = (1 − α − β)*cC4H8

(17)

where α and β represent 1/(K1 + K1*K2 + 1), K1/(K1 + K1*K2 + 1) respectively. Following the above reaction steps and assumptions, the kinetic model can be formulated readily as follows, dc1 = −(1 − α − β)k1c1 − (1 − α)k3c1c3 − αk5c1c3 dt

(14)

− (1 − α)k7c1c 2c4 + k2c 3

The diagram of the whole reaction pathway network was shown in Figure 3. The alkylation products are composed of more than two dozen branched−chain paraffinic hydrocarbons. Both TMPs and DMHs have multiple isomers. HE, as well as LE, also refers to one family of isoparaffins with close molecular weight. Including those carbonium components, there will be more than three dozen species in this system. However, only three or four groups of components can be measured due to the limit of analysis method and the faster transform between various species. To avoid the over fit or over parametrization, the number of involved species and pathway should be simplified as much as possible. So first, some species with similar properties are treated as one pseudo component, such as TMPs (or DMHs) mentioned above. HE, as well as LE, is regarded as one single component, respectively, because of close molecular weight. Second, some steps are assumed to be instantaneous, such as reactions 10 and 12, and the reaction 2 is assumed to be under chemical equilibrium control. Accordingly, the concentration distribution for these three butenes can be calculated, respectively, on the basis of the total concentration of butene,

dc 2 = −k4c 2c4 − k6c 2c5 − (1 − α)k7c1c 2c4 dt

(18)

(19)

dc 3 = (1 − α − β)k1c1 + k4c 2c4 + k6c 2c5 − k4c1c3 dt

D

− αk5c1c3 − k2c 3 + (1 − α)k 7c1c 2c4

(20)

dc4 = (1 − α)k3c1c3 − k4c 2c4 − (1 − α)k7c1c 2c4 dt

(21)

dc5 = αk5c1c3 − k6c 2c5 dt

(22)

dc6 = k4c 2c4 dt

(23)

dc 7 = k6c 2c5 − k10c 7 dt

(24)

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Industrial & Engineering Chemistry Research dc 8 = (1 − α)k7c1c 2c4 + k9c 9c10 − k8c 8 dt dc 9 dt

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parameters and make the estimated rate constants more definite. So, in the refitting of experimental data, the values of k3 through k10 are kept fixed with temperatures, and the only adjustable parameters are k1 and k2. The fitting results are shown in Figure 4, compared with the experiments. It can be seen that the agreement between experimental and calculated data is quite satisfactory. In particular, the dramatic change of HEs in short time is captured successfully by the model. The estimated k1 through k10 are listed in Table 2 with 95% confidence intervals. We can see that most of the confidence intervals are one magnitude smaller than the corresponding parameters except k3 and k6, which confirms the reliability of the estimated rate constants. However, an anti-Arrhenius behavior can be found for k1; that is, the value of k1 falls as the temperature increases. In fact, this phenomenon is not unusual or abnormal for hydrocarbon reaction with the presence of free radical molecules.18 The observations of antiArrhenius kinetics are usually ascribed to an entropic contribution to the free energy of activation. This antiArrhenius behavior is believed to be caused by a decrease of the equilibrium constant of a multistep reaction.19 The Arrhenius relationships of k1 and k2 are obtained by plotting ln(ki) against 1/T shown in Figures 5 and 6, respectively, both of which have good linear relationships. The activation energies of k1 and k2 are computed to be −58.3 and 173.2 kJ/mol, and the corresponding pre-exponential factors are 5.23 × 10−11 and 6.87 × 1031 min−1 respectively. According to the fundamental principle of physical chemistry, in a reversible reaction, the difference of activation energy between the forward and backward reaction should be equal to the heat of the reaction. So, in this sense, the heat of reaction for the addition of H+ to the iC4= can be calculated to be −231.5 kJ/mol, which indicates that this is a strong exothermic reaction. Using uniform hydrocarbon drops, L. Lee et al. studied the sulfuric acid catalyzed reaction of isobutane with 1-butene and the 1-butene oligomerization.12 Kinetic constants for a simplified model were calculated, in which only the primary reactions were considered. When using sulfuric acid of 98%, the rate constants for alkylation of isobutane with 1-butene and 1butene oligomerization at 298 K were calculated to be 2.25 × 108 and 9.5 × 108 cm3/mol/s, respectively. However, in this work, there are no such reaction steps exactly corresponding to those in the literature.12 This is because the kinetic model in this work was developed on the basis of the carbonium ion reaction mechanism which used elementary steps, while L. Lee et al. dealt with the alkylation and oligomerization reactions by the empirical method on the basis of power exponent. Even so, it is found that one elementary step in our model is similar to the alkylation reaction of isobutane with 1-butene, which is the addition of 1-butene to iC4+ (eq 8). The rate constant for this step was estimated to be 1.26 × 104 kg/mol/min, which equals 1.17 × 105 cm3/mol/s. It seems much smaller than the alkylation reaction rate constant of isobutane with 1-butene reported by L. Lee et al., but it should be noted that our experiments were carried out at the temperatures from 276.2 to 285.2 K, which are 13 to 22 K smaller than that reported by L. Lee et al. (298 K). According to L. Albright et al.’s work,10 at the temperature of 259 K, the alkylation reaction rate slowed down dramatically, in which “hour” was used as the unit of time. Thus, taking into consideration the sensibility of alkylation reaction to temperature, the difference of the rate

(25)

= k8c 8 − k9c 9c10

(26)

dc10 = k8c 8 − k9c 9c10 dt

(27)

These ordinary differential equations (ODEs) are completed with specifications of the following initial conditions at time t = 0, c1 = c10 ; c6 = 0;

c2 = c20; c 7 = 0;

c3 = 0;

c4 = 0;

c8 = 0; c 9 = 0;

c5 = 0; c10 = 0

(28)

In eqs 18 to 28, the relationship between the numbers of 1 through 10 and the corresponding species is as follows: 1, butene; 2, iC4; 3, iC4+; 4, TMP+; 5, DMH+; 6, TMP; 7, DMH; 8, HE; 9, iCx+; 10, iCy=.

4. RESULTS AND DISCUSSION The concentration profiles of three groups of key components in alkylation of isobutane with butene were plotted in Figure 4. It shows that all of three species have dramatic changes within 2 min. Initially, the HEs go up sharply and then come down shortly. This demonstrates that the alkylation of isobutane with butene is a very fast reaction. Almost after 5 min, each of the species reaches to a platform individually, although the DMHs still continue to go down slightly. To fit the experiments and estimate k1 through k10 in eqs 18−28, the nonlinear least-squares fitting method was employed by the following object function, m

obj =

∑ (ciexp − cical)2 i=1

cexp i

(29)

ccal i

where and represent the experimental and calculated values of ith component, respectively, and m is the number of experimental data. An lsnonlin function in Matlab was used for the regress of the set of k1 through k10. Equations 18−28 were resolved by the Runge−Kutta method in each iteration. Before the fitting was performed, the values of α and β should be determined first; that is, the equilibrium constants in reaction 2 should be computed. According to thermodynamics, K1 and K2 are the functions of temperature and can be calculated on the basis of the Gibbs free energy variation of reaction 2. As we know, the ASPEN Plus software is a useful tool in chemical process modeling and has a reliable thermodynamic database. The RGibbs module in ASPEN Plus was used to obtain the average values of K1 and K2 at the temperatures between 276.2 and 285.2 K, which is 28.39 and 6.433, respectively. Accordingly, the values of α and β can be calculated to be 0.004718 and 0.1340, respectively. Preliminary fitting results show that with the variation of temperature most of the rate constants change a little, except k1 and k2. It indicates that those reaction steps corresponding to the rate constants of k3 through k10 have small or even no activation energy. A similar finding has been reported by Langley et al. in the alkylation kinetics of isobutane with propylene.17 In this work, these rate constants including k3 through k10 are assumed to be constant with varied temperatures in the range from 276.2 to 285.2 K. One of the advantages of such an assumption is to reduce the adjustable E

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5.48 ± 0.82

2.61 ± 0.85

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Figure 5. Arrhenius relationship between k1 and 1/T.

4.36 ± 2.48

Figure 6. Arrhenius relationship between k2 and 1/T.

constant of isobutane alkylation reaction with 1-butene between L. Lee et al.’s and ours should be reasonable. In L. Albright et al.’s work,10 an S-shaped curve of alkylation yield versus time for a batch run can be noticed. The author believed that the increasing rates of alkylate formation during the initial stages were ascribed to the increasing acidity of the acid phase because acid was regenerated, but this S-shaped curve can be easily understood if we illustrate this phenomenon from the point of view of reaction mechanism. In this work, eq 1 is a chain initiation step. By the subsequent addition of iC4+ and olefin, the precursor of alkylates are generated. Thus, in the initial stage, the alkylation rate increases due to the continuous accumulation of the concentration of iC4+. At the last period, the alkylation rate slows down with the decrease of olefin concentration. This is similar to the free radical chain reaction of hydrocarbon, in which the existence of induction period is very common in the oxidation of hydrocarbon, especially at low temperature. To confirm the reliability of the kinetic model developed in this work, we simulated the alkylation reactor operated at industrial conditions. Table 3 listed some basic conditions of the typical industrial alkylation reactor. The industrial alkylation

± ± ± ± 6.37 5.06 4.15 2.79

0.72 0.57 0.50 0.71

0.15 0.45 1.00 1.59 ± ± ± ±

0.06 0.20 0.38 0.56

8.33 ± 1.86

1.03 ± 0.22

1.26 ± 0.42

88.46 ± 6.78

0.63 ± 0.06

min−1 kg·mol−1·min−1 min−1 kg·mol−1·min−1 min−1

Table 3. Operating Conditions for Industrial Alkylation Reactor

276.2 279.2 282.2 285.2

K

min−1

kg·mol−1·min−1

kg·mol−1·min−1

kg·mol−1·min−1

kg2·mol−2·min−1

k9 k6, 103 k3, 102 k2 k1 temperature

Table 2. Estimated Rate Constants with 95% Confidence Intervals

k4

k5, 104

k7

k8

k10, 10−2

Industrial & Engineering Chemistry Research

A/H, m3/m3a

I/O, mol/molb

temperature, K

pressure, MPa

1.1:1

8:1

279

0.45

a Ratio of sulfuric acid to hydrocarbon (isobutane + olefin) based on volume. bRatio of isobutane to olefin based on mole.

F

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reactor of isobutane with olefin is a well mixed flow reactor.1 For this type of reactor, the material balance equation can be written as follows: xi 0 − xi = τ *( −ri)

5. CONCLUSIONS The alkylation kinetics of isobutane with butene was measured in the condition of industrial interest. The kinetic model was established on the basis of the classic carbonium ion mechanism. The agreement between experiments and model fitting is quite satisfactory. Except the addition of H+ to isobutene and its reversible reaction, other reaction steps’ rate constants were found not to change with the varied temperatures from 276.2 to 285.2 K. An anti-Arrhenius behavior was observed for the addition of H+ to isobutene. Both of them also can be found in other hydrocarbon reactions. By the kinetic model, the successful simulation of industrial alkylation reactor was achieved. We hope that the alkylation kinetics reported in this work will be useful for the reactor design and optimization of isobutane alkylation with butene.

(30)

xi0

where and xi stand for the inlet and outlet concentration of ith component in alkylates with the unit of mol/kg and τ and −ri represent the mean residence time of sulfuric acid in reactor and formation or consumption rate of the ith component with the unit of min and mol/kg/min. In the eq 30, −ri is determined by the kinetic model in this work and xi0 is calculated through the operating conditions listed in Table 3. Thus, xi can be solved only if τ is given. The conversion of olefin and alkylate yield versus mean residence time is shown in Figures 7 and 8, respectively. It can

■

ASSOCIATED CONTENT

S Supporting Information *

Mass spectrogram of key alkylates and retention time of alkylate products in GC. This information is available free of charge via the Internet at http://pubs.acs.org/.

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: +86 21 64253175. Fax: +86 21 64253528. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

Figure 7. Conversion of olefin versus mean residence time.

ACKNOWLEDGMENTS The authors gratefully acknowledge the financial support from the Joint Funds of the National Natural Science Foundation of China (U1162202), the Fundamental Research Funds for the Central Universities, the China Postdoctoral Science Foundation (2012M512055), and the 111 Project (B08021).

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REFERENCES

(1) Corma, A.; Martínez, A. Chemistry, catalysts, and processes for isoparaffin−olefin alkylation: Actual situation and future trends. Catal. Rev.: Sci. Eng. 1993, 35 (4), 483−570. (2) Shorey, S. W. In Motor-Fuel Alkylation with CDAlky Process Technology. 103rd NPRA Annual Meeting, San Francisco, CA, March 13−15, 2005; pp 1−16. (3) Hommeltoft, S. I. Isobutane alkylation: Recent developments and future perspectives. Appl. Catal., A: Gen. 2001, 221 (1), 421−428. (4) Kranz, K. Intro to Alkylation Chemistry: Mechanisms, operating variables, and olefin interactions; DuPont STRATCO Clean Fuel Technology: Leawood, 2008; pp 1−29. (5) Albright, L. F. Alkylation of isobutane with C3−C5 olefins: Feedstock consumption, acid usage, and alkylate quality for different processes. Ind. Eng. Chem. Res. 2002, 41 (23), 5627−5631. (6) Feller, A.; Zuazo, I.; Guzman, A.; Barth, J. O.; Lercher, J. A. Common mechanistic aspects of liquid and solid acid catalyzed alkylation of isobutane with n-butene. J. Catal. 2003, 216 (1−2), 313− 323. (7) Schmerling, L. The mechanism of the alkylation of paraffins. II. Alkylation of isobutane with propene, 1-butene and 2-butene. J. Am. Chem. Soc. 1946, 68 (2), 275−280. (8) Schmerling, L. Reactions of hydrocarbons: Ionic mechansims. Ind. Eng. Chem. 1953, 45 (7), 1447−1455. (9) Hofmann, J. E.; Schriesheim, A. Ionic reactions occurring during sulfuric acid catalyzed alkylation. II. Alkylation of isobutane with C14labeled butenes. J. Am. Chem. Soc. 1962, 84 (6), 957−961.

Figure 8. Alkylate yield versus mean residence time.

be seen that the conversion of olefin will be greater than 99.5% when the mean residence time (τ) is above 10 min, but the yield of alkylate is under 200% even when τ reaches 20 min. Usually, the alkylate yield is required to be more than 200%, so the τ should be kept greater than about 21 min according to Figure 8. It also indicates that when τ exceeds 30 min the alkylate yield will approach its theoretical value (203.6%). It was reported that in the industrial unit the mean residence time ranges from 20 to 30 min.1,20 Clearly, the simulation results show that the kinetic model developed in this work can predict the mean residence time of the industrial alkylation reactor successfully. As we all know, the mean residence time determines the reactor size when the scale of production is known and vice versa. Thus, using the kinetic model developed in this work, we will be allowed to design and optimize the novel alkylation reactors. G

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dx.doi.org/10.1021/ie400415p | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX