Multiscale Modeling of Isobutane Alkylation with Mixed C4 Olefins

Article Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Multiscale Modeling of Isobutane Alkylation with Mixed C4 Olefins Using Sulfuric Acid as Catalyst Piao Cao,† Lin Zheng,† Weizhen Sun,*,† and Ling Zhao†,‡ †

State Key Laboratory of Chemical Engineering, East China University of Science and Technology, Shanghai 200237, China School of Chemistry & Chemical Engineering, XinJiang University, Urumqi 830046, China

Ind. Eng. Chem. Res. Downloaded from pubs.acs.org by UNIV OF CALIFORNIA SANTA BARBARA on 04/08/19. For personal use only.

‡

S Supporting Information *

ABSTRACT: The alkylation of isobutane with mixed C4 olefins catalyzed by sulfuric acid was investigated under conditions of industrial interest. On the basis of previous work, the alkylation kinetic model was improved, in which the fast isomerization between butenes was fully considered and the formation pathways of the heavy ends (HEs) were modified. Satisfactory agreement between experiments and model calculations was achieved with the concentration profiles of three key components in alkylate, i.e. trimethylpentanes (TMPs), dimethylhexanes (DMHs), and heavy ends (HEs). The reliability of the kinetic model was further verified by predicting the isobutane alkylation by mixed C4 olefins with different compositions. In addition, density functional theory (DFT) calculations were performed to confirm the fast isomerization between butenes. MD simulations reveal that butenes can diffuse more easily than isobutane in the H2SO4, facilitating the fast polymerization reaction and the growth of heavy ends (HEs). It is hopeful that the kinetic model developed in this work will provide a fundamental reference for the design and optimization of the industrial alkylation process.

1. INTRODUCTION With the rapid development of automobile industry, automotive exhaust emissions have become one of the major sources of air pollution, drawing worldwide concern.1 Accordingly, the upgrading of gasoline is forced to develop in a more clean-burning direction, such as elimination of lead, limitation of olefins and sulfur, reduction of aromatic content, and increase in oxygenate content. The alkylate, which is produced by the alkylation of isobutane with C3−C5 olefins in the presence of strong acid, has the advantages of high octane number, low vapor pressure, and zero content of olefins and aromatics that allow it to be a desirable blending component for high-quality gasoline.2 Thus, the gasoline upgrading inevitably leads to an increase in the demand for alkylate as a blending component. In China, the alkylate content in the gasoline pool has increased from 3% in China IV (China Gasoline Standard IV) to 6% in China V and is expected to be 8−10% in China VI, which it is still less than the 14% required by the American Gasoline Standard.3 Alkylates will continue to act as a desirable blending component for high-quality gasoline as the quality of gasoline continues to increase.4 To date, the major catalysts for the commercial alkylation process are either sulfuric acid or hydrofluoric acid, which have good selectivity and catalytic activity. Most of the alkylation units tend to employ sulfuric acid as catalyst because of the high toxicity and easy release of hydrofluoric acid.5−7 The alkylation mechanism of isobutane with C3−C5 olefins has been extensively investigated for many years to fully © XXXX American Chemical Society

understand the alkylation mechanism. Schmerling proposed the chain reaction mechanism on the basis of classic carbonium ion mechanism, which could explain the formation of light ends (C5−C7 isoparaffins), dimethylhexanes, and heavy ends; however, several features of alkylation were not adequately explained, i.e., the secondary reactions and the read oil in the acid phase.8 Kramer concluded that the hydride transfer reaction is a key step influencing the alkylation reaction rate.9 Albright proposed a reaction mechanism related to the catalyst used, which explain the startup phenomena, secondary reactions, and role of red oil in the acid phase.5 As is wellknown, the fundamental understanding of the reaction kinetics is not only helpful to provide deeper insight into the reaction mechanism but also plays an important role in the design and optimization of the novel reactor and reaction process. However, because of simultaneous considerable reactions occurring in the alkylation system, including alkylation, polymerization, cracking, disproportionation, and self-alkylation, there exist more than three dozen isoparaffins, as well as the corresponding carbonium cations, which are hard to detect owing to the lack of the effective analysis method. Therefore, only a few publications were devoted to the isobutane alkylation kinetics with sulfuric acid as catalyst to explain the Received: Revised: Accepted: Published: A

February 14, 2019 March 26, 2019 March 27, 2019 March 27, 2019 DOI: 10.1021/acs.iecr.9b00874 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research Table 1. Mixed C4 Olefin Feeds with Different Compositions and Reaction Conditions components (wt %) exptl run

T (K)

butenes

1-butene

cis-2-butene

trans-2-butene

isobutene

isobutane

pressure (MPa)

time (min)

1 2 3 4 5 6 7 8 9 10 11 12

276.2 279.2 282.2 285.2 276.2 279.2 282.2 285.2 276.2 279.2 282.2 285.2

mixedC4-#1

2.39

5.65

3.44

1.42

87.1

0.5

20

mixedC4-#2

3.4

3.31

5.99

0

87.3

0.5

20

mixedC4-#3

0

3.14

5.66

4.6

86.6

0.5

20

reaction pathways for polymerization of C4 olefins to produce HEs were modified and the isomerization reaction between butenes was fully considered in this model. The reliability of the kinetic model was further confirmed by predicting the batch alkylation process of isobutane with mixed C4 olefins with different compositions. Furthermore, the transition state and activation energy of the isomerization reaction between three C4 olefins were calculated using DFT method and further compared with the predicted results by the kinetic model. Using MD simulation, the diffusion coefficients of three C4 olefins were calculated to demonstrate their fast diffusion and self-assembly at interface before alkylation reaction.

formation pathway of several key components in alkylate. On the basis of uniform hydrocarbon drops and short contact times, the kinetic constants for the alkylation of isobutane with C4 olefins in the presence of sulfuric acid have been researched.10 However, this simplified kinetic model including the main reaction of isobutane with 1-butene and the oligomerization of 1-butene, was established without considering several important isoparaffins in alkylate.11 Also, the isobutane alkylation in terms of a two-step process was studied, although the corresponding kinetic constants were not estimated.12 In our previous work, the kinetic model of the isobutane alkylation with C4 olefins has been established on the basis of the classic carbonium ion mechanism, which can well-predict the concentration profile along time of three key families in alkylate, i.e., TMPs, DMHs, and HEs.13 However, to some extent, the formation pathways of the HEs remained irrational, which leads to an overestimated prediction of the HEs in the isobutane alkylation process. Moreover, the fast isomerization reaction between butenes was not fully considered in the previous model, and the rate constants of the corresponding isomerization were not estimated. In fact, the butene will undergo skeletal isomerization to form isobutylene in the presence of sulfuric acid, which have been widely investigated.14,15 Therefore, the isomerization reaction of butenes should be further considered in the isobutane alkylation with butenes. The DFT calculations have been widely used to study the reaction mechanisms and to solve the chemical ambiguities and to interpret experimental results, which is a useful method to investigate the mechanisms of reaction in a molecule and electronic structure level.16 Moreover, the DFT method can provide more reactivity indices, including activation energy that will provide insights into the mechanism of the isobutane alkylation and butene isomerization.17,18 In addition, MD simulation has proved to be a promising way to investigate the microscopic properties, such as diffusion and solvation of solute molecules in solvents, which can provide the fundamental information at a molecular level to explain and correlate the macroscopic property.19−21 Therefore, in this work the alkylation kinetics of isobutane with mixed C4 olefins using sulfuric acid as catalyst were investigated under conditions of industrial interest. The kinetic model was established on the basis of the carbonium ion mechanism with three key components in alkylate being measured, including TMPs, DMHs, and HEs. Meanwhile, the

2. EXPERIMENTAL AND SIMULATION 2.1. Experimental Methods. In this work, the feedstock compositions and reaction conditions of alkylation experiments were listed in Table 1, and the experiments were carried out at the batch process at the temperature range of 276.2− 288.2 K and 0.5 MPa. On the basis of the proposed kinetic model, the mixed C4-#1 acted as feed butene to estimate the kinetic parameters, and the mixed C4-#2 and mixed C4-#3 were employed for verifying the reliability of the kinetic model and the corresponding rate constants. The batch experiments mean that the sulfuric acid and mixed C4 hydrocarbons were charged into the reactor at the beginning, respectively. For the batch experiments, the experimental setup was in detail introduced in our previous work.13 The introduction of the analytic method to identify and quantify the alkylate was described in detail in our previous work.22 Herein, the brief description concerning the batch experiments is introduced. For the batch alkylation experiments, the sulfuric acid was first introduced into the glass reactor with a volume of 1 L. Afterward, the nitrogen gas (N2) was charged into the reactor to replace the air and then the operating pressure was set at 0.5 MPa to maintain the mixed C4 hydrocarbons in a liquid state. Meanwhile, the temperature was controlled at a set range using the refrigerant system with the salt water as the cycling agent. Once the temperature inside the batch reactor reached the set value, the mixed C4 hydrocarbons were quickly charged into the reactor, and simultaneously the agitator was started at 3000 rpm to well-disperse the sulfuric acid and C4 hydrocarbons. 2.2. Quantum Chemistry Calculations. The structures of all the molecules, including isobutane molecule, 1-butene molecule, 2-butene molecule, isobutylene molecule, H2SO4 molecule, HSO4− molecule, H3O+ molecule, were optimized by the B3LYP/6-311(G) method using Gaussian 09 program, B

DOI: 10.1021/acs.iecr.9b00874 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research

Figure 1. Optimized geometries of molecules in the systems.

isothermal−isobaric (NPT) ensemble to reach fully equilibrium and to calculate the diffusion coefficients. In all simulation systems, a pressure of 1 atm and a temperature of 300 K were maintained by Parrinello-Rahman barostat and Hoover-Nose thermostat, respectively, using a relaxation time of 1 ps. The Lennard−Jones interaction and Coulomb interaction were cut off at a distance of 1.2 nm and all covalent bonds about hydrogen atoms were constrained using LINCS algorithm. The particle-mesh Ewald summation and Lorentz−Berthelot were performed to deal with the longrange electrostatic interaction and periodic boundary conditions were applied in three directions. Diffusion coefficients were calculated from the slope of the mean-square displacement averaged over the trajectories of individual particles.

as shown in Figure 1. It should be noted that the cis−trans isomerization of 2-butene is very easy to occur and the chemical properties of cis-2-butene and trans-2-butene are very close; therefore, the trans-2-butene model is used in this simulation. The energies and geometries of the reactants, transition states and products were calculated using B3LYP density functional theory (DFT) method in DMol3 module in Materials Studio 6.1 package. The valence electrons were described using the double numerical plus polarization (DNP) basis set, which is comparable with the 6-31G** basis set.23 A Fermi smearing of 0.005 Ha (1 Ha = 27.211 eV) was employed and the threshold of the energy convergence and SCF was set to be 2.0 × 10−5 Ha and 1.0 × 10−5 Ha, respectively. The transition state (TS) search was conducted using a combination of the linear synchronous transit method (LST) and the quadratic synchronous transit method (QST). The above computational scheme has been widely used to investigate similar systems and has been demonstrated to be capable of providing excellent structural and energetic information.24 2.3. Molecular Dynamics Simulations. To investigate the diffusion of butenes in the concentrated H2SO4, we conducted molecular dynamics (MD) simulations using the GROMACS 4.5 package. The OPLS-AA force field developed by Jorgensen et al. was employed to describe the interaction between the butene and sulfuric acid molecules.25 In addition, the force field of the sulfuric acid were optimized and confirmed according to our previous work.26 The potential parameters in the force field of the 1-butene, 2-butene, and isobutylene were utilized directly from the OPLS-AA force field while the charge parameters were refitted from the optimized geometry using LMP2/cc-pVTZ(-f)//B3LYP/6311(G) method using Gaussian 09 program to improve the accuracy of the calculation results. The reliability of the parameters has been confirmed in our recent work. Initially, the simulation boxes, consisting of 284 H2SO4 molecules, 28 HSO4− molecules, 28 H3O+ molecules and 38 solutes of 1-butene molecules, 2-butene molecules or isobutylene molecules, were built by Packmol software with the boxes size of 3.5 × 3.5 × 3.5 nm3. Then, an energy minimization of 8000 steps was carried out and all systems were annealed for 8 ns heating from 300 to 500 K and then cooling to 500 K under the canonical (NVT) ensemble. After that a 20 ns production simulation was conducted under the

3. KINETIC MODEL It is well-accepted that the isobutane alkylation reaction proceeds following the classic carbonium ion mechanism.27,28 Considerable efforts have been made to fully understand the alkylation mechanism by Albright et al.,5,29−32 Kramer et al.,9 and Hofmann et al.,33,34 providing the fundamental insights into the isobutane alkylation process. In our previous work, the kinetic model of the isobutane alkylation with C4 olefins catalyzed by H2SO4 has been established based on carbonium ion mechanism. The established model could predict the concentration change of three key groups in alkylate, i.e., TMPs, DMHs, and HEs. However, the formation pathways of the HEs results in an overestimated prediction of the HEs in the alkylation process. In addition, the previous model was lack of complete consideration of the isomerization reaction between butenes. Thus, in this work the formation pathways for the polymerization of C4 olefins to produce HEs were improved and the isomerization between butenes was fully considered. Despite the systematical description of the reaction steps in the earlier work, it is necessary to briefly introduce the main reaction steps to help understand the reaction procedure. Initially, the isobutene is protonated by the strong acid, giving the tert-butyl cation. The protonated reaction is a reversible one k1

iC=4 + H+ F iC+4 k2

(1)

where iC4= stands for isobutylene and iC4+ is the tert-butyl cation. Additionally, there exists a fast isomerization between 1-butene, 2-butene, and isobutylene, especially in the presence C


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Figure 2. Diagram of the reaction pathway network.

of sulfuric acid. The isomerization performs through the following equilibrium reaction k12

k14

k13

k11

1‐butene HoI 2‐butene HoI iC4

In summary, the diagram of the whole reaction pathway network with the full consideration of the isomerization between C4 olefins and the modified formation pathways of the HEs is shown in Figure 2. Because of simultaneous considerable reactions occurring in the alkylation system, there exist more than three dozen isoparaffins, as well as the corresponding carbonium cations. Nevertheless, the alkylation is a fast reaction, with only three or four key groups in alkylate being measured, as the carbonium ions are hard to detect because of the lack of the effective analysis method. To avoid over fitting, the same strategies are followed as our previous model simplification. For instance, TMPs, DMHs, HEs, and LEs, as mentioned above, are considered as one pseudo component, respectively, due to similar molecular weights. However, different from the previous model, the isomerization rates between 1-butene, 2butene, and isobutylene were calculated in detail in the present model. On the basis of the above reaction steps and assumptions, the kinetic model for the isobutane alkylation was built as follows

(2)

The tert-butyl cation reacts to an olefin to generate the corresponding C8 carbonium cation by this reaction k3

c4+ + 2‐butene(or iC=4 ) → TMPs

(3)

In fact, the TMPs possess several isomers due to the isomerization of TMPs+ through methyl shifts and the hydride transfer reaction. Afterward, the TMPs+ reacts to isobutane to produce the TMPs via the hydride transfer, simultaneously giving the iC4+ to continue on the chain propagation k4

TMP+ + iC4 → TMP + iC+4

(4)

where iC4 stands for isobutane. As undesirable components with low octane number, dimethylhexanes (DMHs) are formed in several ways. One possible way of the formation of DMHs is believed from the addition of iC4+ to 1-butene by the following reaction k5

iC4 + + 1‐butene → DMHs+

dc1 = −k1c1 + k 2c3 − k 3c1c3 − k 7c1c 2c4 − k11c1 + k14c11 dt

(5)

(13)

+

The resulting DMHs abstracts a hydride ion from isobutane to generate the DMHs, regenerating iC4+ +

k6

DMHs + iC4 → DMHs + iC4

+

dc 2 = −k4c 2c4 − k6c 2c5 − k 7c1c 2c4 − k15c11c 2c4 dt

(6)

dc 3 = k1c1 + k4c 2c4 + k6c 2c5 − k 3(c1 + c11)c3 − k5c12c3 dt

iC4=

The heavy ends (HEs) are produced by the addition of or 2-butene to TMPs+ or DMHs+ to give the corresponding HEs cation (i-Cm+). By rapid hydride transfer with isobutane, the iCm+ changes to the HEs, along with the formation of iC4+, +

= k7

TMPs + iC4 → i‐Cm

+

k15

+

i‐Cm + iC4 → i‐Cm + iC4

− k 2c3 + k 7c1c 2c4 + k15c11c 2c4

(7)

DMHs+ + 2‐butene → i‐Cm+ +

(8) (9)

The sources of the light ends (LEs), including C5 ∼ C7 isoparaffins, are believed to be attributed to the scission of large isoalkyl cations (i-Cm+). Through the abstraction of the hydride from isobutane, the corresponding LEs are produced i‐Cm + H+ → i‐Cm+

(10)

k8

iCm+ F iCx + + iCy =

(16)

dc5 = k5c12c3 − k6c 2c5 dt

(17)

dc6 = k4c 2c4 dt

(18)

dc 7 = k6c 2c5 − k10c 7 dt

(19)

dc 8 = k 7c1c 2c4 + k15c11c 2c4 + k 9c 9c10 − k 8c8 dt

(20)

dc 9

In addition, one single reaction step is used to simplify the obvious degradation of DMHs observed in the present work

dt

k10

DMH → LEs

= k 8c8 − k 9c 9c10

dc10 = k 8c8 − k 9c 9c10 dt

(12) D

(15)

dc4 = k 3(c1 + c11)c3 − k4c 2c4 − k 7c1c 2c4 − k15c11c 2c4 dt

(11)

k9

(14)

(21)

(22) DOI: 10.1021/acs.iecr.9b00874 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Figure 3. Concentration profiles of key components in the alkylation of isobutane with mixed C4-#1. Temperature: (a) 276.2, (b) 279.2, (c) 282.2, and (d) 285.2 K. Symbols, experimental data; line, calculated values by kinetic model.

dc11 = −k 3c11c3 − k15c11c 2c4 + k11c1 + k12c12 − k13c11 dt − k14c11

dc12 = −k5c12c3 + k13c11 − k12c12 dt

time of alkylation catalyzed by sulfuric acid ranges within 5 min. To fit the kinetic model and estimate model parameters (k1−k15) in eqs 13−24, the nonlinear least-squares fitting method was used as follows

(23)

m

obj =

(24)

∑ (ciexp − cicalcd)2

(25)

i=1

The initial conditions are t = 0, c1 = c10; c2=c20; c3 = 0; c4 = 0; c5 = 0; c6 = 0; c7 = 0; c8 = 0; c9 = 0; c10 = 0; c11=c110; c12 = c120. The corresponding species in eqs 13−24 are 1, iC4H8; 2, iC4, 3, iC4+; 4, TMPs+; 5, DMHs+; 6, TMPs; 7, DMHs; 8, HEs; 9, iCx+; 10, iCy=; 11, 2-C4H8; 12, 1-C4H8.

where ciexp and cicalcd are the experimental and calculated values of i th component, respectively, and m is the number of experimental data. A Matlab function, lsnonlin, was utilized to fit the model parameters k1−k15. Similar to our previous work, the values of the chemical equilibrium constants K1 and K2 were calculated using the RGibbs module in the ASPEN Plus software based on the Gibbs free energy variation of reaction 2. The equilibrium constants as a function of temperature are listed in Table 2.

4. RESULTS AND DISCUSSION 4.1. Estimation of Rate Constants. Four runs of alkylation experiments of isobutane with mixed C4-#1 were carried out in the temperature range of 276.2−285.2 K. The concentration of three key groups in alkylate along time is shown in Figure 3. At the beginning, the HEs are produced by the addition of isobutylene or 2-butene to TMPs+ or DMHs+ followed by hydride transfer with isobutene, thus initially the TMPs and DMHs content is small and the HEs increase sharply to the maximum value in tens of seconds. Then the HEs cations will convert to LEs under scission reaction and hydride transfer, corresponding to the rapid decrease of the HEs content. This observation corresponds to the rapid consumption of olefins and also demonstrates the nature of very fast reaction of the isobutane alkylation. The DMHs are mainly produced at the initial stage of the reaction and subsequently go down slightly. However, the TMPs go up gradually with increased time. In general, the reaction reaches to a steady state after 5 min, indicating the optimized reaction

Table 2. Equilibrium Distribution and Constants of Butenes T (K)

1-C4= (%)

cis-2C4=(%)

trans-2C4= (%)

i-C4= (%)

K1

K2

276.2 279.2 282.2 285.2

0.003529 0.003798 0.004080 0.004376

0.03410 0.03554 0.03700 0.03847

0.09163 0.09383 0.09602 0.09820

0.8707 0.8668 0.8629 0.8589

35.63 34.06 32.60 31.23

6.925 6.700 6.487 6.285

There are three key groups of observables in the alkylation system, whereas 15 parameters need to be estimated in the kinetic model. Thus, if we directly fit this kinetic model, over fitting or over parametrization will occur due to so many parameters. From previous results, it was found that some of the rate constants were independent of temperature, such as k4, E


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Industrial & Engineering Chemistry Research Table 3. Estimated Rate Constants with 95% Confidence Intervals T (K) 276.2 279.2 282.2 285.2

k7,10 (kg mol−2 min−2) 9.99 10.54 11.04 11.59

± ± ± ±

0.72 1.22 0.46 0.36

k11 (min−1) 7.95 9.59 11.41 13.30

± ± ± ±

1.89 0.41 1.84 0.22

k12,102 (min−1) 2.54 3.17 3.84 4.69

± ± ± ±

0.01 0.01 0.10 1.54

k6, and k8−k10, which indicated small or very small activation energy in these reaction steps. Hence, we assumed that these rate constants kept constant with the variation of temperature in the experimental range to reduce the number of adjustable parameters. As a result of this, the above-mentioned kinetic constants were directly taken from the earlier results of parameter estimation for same carbonium ion mechanism and catalyst. In addition, it was found that the rate constants k1, k2, k3, and k5 depend on the temperature.25,26 Similarly, for simplification we directly employed the parametrized rate constants of k1, k2, k3, and k5 from the previous model fitting, in order to focus on the aim of our present work. By doing this, we fixed the values of k1−k6 and k8−k10, that is, the parameters that need to be estimated are decreased, and simultaneously this strategy can keep the rate constants more definite. As a result, the rest of adjustable parameters are k7 and k11−k15, corresponding to modified reaction pathway of the HEs and the transformation rates between butenes, respectively. On the basis of experimental data, the fitting results over the temperature range of 276.2−285.2 K are plotted in Figure 3. Evidently, the fitting data related to the TMPs, DMHs, and HEs agrees well with the experimental one. Furthermore, it can be captured successfully that the HEs are produced dramatically in a short time due to the fast polymerization of butenes and then go down shortly. The estimated parameters of k7 and k11−k15 are listed in Table 3 with 95% confidence intervals. The whole list of the rate constants is presented in Table S1. It can be seen that most of the confidence intervals are about 1 order of magnitude less than the corresponding rate constants, which confirms the reliability of the kinetic model and estimated parameters. The rate constants k12 and k14, are two and one order of magnitudes larger than that of the correspondingly reversible reaction, k13 and k11, respectively, indicating that the isomerization rates of 1-butene into 2-butene and 2-butene into isobutylene proceeds much faster than that of their reversible reactions. The observation is comparable to the fact that either 1-butene or 2-butene tends to transform into isobutene via fast isomerization in the presence of sulfuric acid. Also, the Arrhenius relationships of k7 and k11−k14 can be obtained through the variation of ki against temperature. The fitting results are plotted in Figure 4, showing good linear relationships (R2 = 0.99). The calculated activation energies and pre-exponential factors are shown in Table 4. The fitting activation energies corresponding to k11−k14 are 37.54, 44.33, 53.92, 30.48, respectively. Compared to k13 and k11, k12 and k14 show a lower activation energy, which means the isomerization of 1-butene to 2-butene and 2-butene to isobutylene are easier than their reversible reactions. 4.2. Validation of Kinetic Model. The estimated rate constants in this work should be independent of the ratio of butenes in the feed. In order to confirm this view, another eight runs of the isobutane alkylation experiments with different ratios of butenes in the feed, i.e., mixed C4-#2 and mixed C4-#3, are carried out under the temperature range of

k13 (min−1) 7.13 9.31 11.76 15.02

± ± ± ±

0.02 0.03 0.31 4.92

k14, 10 (min−1)

k15 (kg mol−2 min−2)

± ± ± ±

32.62 ± 19.80

5.50 6.42 7.40 8.36

1.31 0.27 1.19 0.14

Figure 4. Arrhenius relationship between ln(ki) and T−1.

276.2−285.2 K, as shown in Figures 5 and 6, respectively. The predictions of concentration profiles of key components in alkylate with mixed C4-#2 and mixed C4-#3 as the feed butene are also plotted. Clearly, the agreement between the experiment and model prediction is quite satisfactory, which confirms the good transferability of the model parameters regardless of the species of butenes in the feed when the sulfuric acid is used as catalyst. 4.3. Transition State of Butene Isomerization Reaction. Density functional theory (DFT) method has been employed to investigate the alkylation reaction mechanisms of isobutane and 2-butene catalyzed by Brønsted acids and phosphotungstic acid, the isomerization reaction mechanism of 1-butene to cis-2-butene, respectively, which proved to be a useful method to further understand reaction mechanism in a molecule level.18,35,36 To better understand the isomerization reaction of butenes, we calculated the energies and geometries of the reactants, transition states, and products for the isomerization between 1-butene, 2-butene, and isobutylene using the quantum chemical based on density functional theory (DFT) method, as shown in Figure 7. The transition states of the 1-butene isomerize to form 2-butene, 2-butene isomerize to form isobutylene and 1-butene isomerize to form isobutylene were searched, and the corresponding energies were calculated. The activation energies for the isomerization of 1-butene to 2-butene, 2-butene to isobutylene and 1-butene to isobutylene are 63.65, 63.43, and 64.42 kcal mol−1, respectively. It is clear that the activation energy between the three butenes is comparable, which explains the fact that the C4 olefins can be isomerized to each other. It should be noted that the difference between the results obtained from DFT method and calculated by kinetic model can be attributed to the vacuum environment and no proton provided by the sulfuric acid in the simulations. The result is reasonable when considering the difference between the real reaction environment and the simulation conditions. Although the results of the DFT calculations have considerable F


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Industrial & Engineering Chemistry Research Table 4. Calculated Activation Energies (Ea) and Pre-exponential Factors (k0) for Each Reaction Ea(kJ mol−1) k0

k7

k11

k12

k13

k14

10.69 1.05 × 104 (kg mol−2 min−2)

37.54 1.01 × 108 (min−1)

44.33 6.18 × 1010 (min−1)

53.92 1.13 × 1011 (min−1)

30.48 3.22 × 107 (min−1)


significance to the advancement of the alkylation process and the improvement of the alkylate properties. The equilibration snapshots of different systems were shown in Figure 8. It can be clearly seen from the equilibration snapshots of various systems with different butenes in H2SO4 that the three C4 olefins all have a certain assembly behavior in the sulfuric acid phase due to the strong interaction between themselves, which will hinder their distribution in the catalyst phase and facilitate the polymerization of C4 olefins. The results of diffusion coefficients were listed in Table 5. It should be noted that the diffusion coefficients of the isobutane and 2-butene were taken from our previous work.37 From Table 5, the diffusion coefficients of butenes are about two times larger than that of isobutane, which means that butenes can diffuse more easily than isobutane in the H2SO4. The easier diffusion of butenes at interface or in the catalyst phase facilitates the fast polymerization reaction and results in the growth of heavy ends (HEs) at the beginning of the isobutane alkylation reaction. The polymerization of C4 olefins is detrimental to the production of high quality alkylates, therefore a high ratio of isobutane to C4 olefins (I/O) is always preferred under experimental and industrial conditions to inhibit the side reaction.

deviations from the real reaction, the essential reaction characteristics revealed by the DFT calculation can provide valuable insights into the understanding of the isomerization between butenes. Accounting for the comparable energy barrier of isomerization between butenes, it can be believed that either 1-butene or 2-butene tends to transform into isobutene via fast isomerization, supporting the rationality of the consideration of the fast isomerization in the established model. In addition, comparing the results calculated by the established kinetic model in Table 4 and the DFT method in Figure 7, it can be concluded that the presence of sulfuric acid as a catalyst greatly reduces the energy barriers of the isomerization and facilitates the reaction, which further facilitates the acquisition of alkylate products. 4.4. Diffusion of Butenes in H2SO4. The isobutane alkylation is a typical liquid−liquid heterogeneous reaction. Promoting the mass transfer of isobutane in the catalyst phase facilitates the hydride transfer from isobutane to C8+ ions, which contributes to a faster reaction rate. However, the mass transfer of butenes at liquid−liquid interface or in the catalyst phase accelerates the fast polymerization reaction which is detrimental to the production of high quality alkylates. Therefore, the quality and the composition of the alkylate are determined in great part by the ratios of the isobutane to olefin at the interface or in the sulfuric acid phase, and thus the diffusion of C4 reactants in the catalyst phase is of considerable

5. CONCLUSION The alkylation experiments of isobutane with different mixed C4 olefins in the presence of sulfuric acid were carried out G


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Figure 7. Optimized geometries and potential-energy profile of the reactants, transition states, and products for the isomerization in butenes. The energy of 1-butene is set to zero.

under conditions of industrial interest. According to the previously established kinetic model, the alkylation kinetics was improved, where the isomerization reaction between butenes was fully considered and the reaction pathways for polymerization of C4 olefins to produce HEs were modified. The concentration changes of three key components in alkylate, i.e., TMPs, DMHs, and HEs, were well-predicted by the kinetic model with satisfactory agreement between experiments and model calculations. The rate constants of transformation rate

of 1-butene into 2-butene and 2-butene into isobutene are two and one order of magnitudes larger than that of the corresponding reversible reaction, respectively. The reliability of the kinetic model was verified by the isobutane alkylation experiments with mixed C4 olefins with different compositions, confirming the good transferability of the model regardless of the species of butenes in the feed. Furthermore, MD simulations show that butenes can diffuse more easily than H


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Table 5. Diffusion Coefficients of C4 Hydrocarbons in the Concentrated H2SO4 at 1 atm and 300 K system 1-butene 2-butenea isobutylene isobutanea

D (× 10−5 cm2/s) 0.30 0.21 0.20 0.12

± ± ± ±

0.05 0.02 0.06 0.03

a

These data are taken from a previous work.37

isobutane in the H2SO4, facilitating the fast polymerization reaction and the growth of heavy ends (HEs).

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.9b00874. Table S1 (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +86-21-64253027 (W.S). ORCID

Weizhen Sun: 0000-0002-9957-3620 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support by the National Natural Science Foundation of China (91434108) is gratefully acknowledged. REFERENCES

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Multiscale Modeling of Isobutane Alkylation with Mixed C4 Olefins

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