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Apparent Kinetic Model of Hydrogenation for Removal of Olefin Impurities from Alkylation Reactor Effluent Mixture Haikuan Yuan, Jie Ren,* and Lian Shen College of Chemical Engineering, Zhejiang University of Technology, Hangzhou 310014, China ABSTRACT: The apparent kinetic model of the hydrogenation of the alkylation reactor effluent mixture for removal of olefin impurities was studied. Hydrogenation experiments over Pd/Al2O3 catalyst were carried out. On the basis of reactor phase structure, the characteristic equation of the reactor was determined. The apparent kinetic model equation of olefin conversion was determined. By thermodynamic analysis, the mathematical models of the hydrogen solubility coefficient and hydrogen solubility were determined through the correlation of hydrogen solubility coefficient with temperature and the molar mass of the liquid medium. The apparent kinetic model of olefin hydrogenation was established through model parameter estimation. The order of hydrogen concentration in liquid was close to 1, and the order of olefin was significantly higher than that of hydrogen. The olefin concentration had greater influence on the hydrogenation reaction rate than hydrogen. There was an hydrogenation activity distribution of olefin mixture. The results of the experimental validation and statistical test showed that the established kinetic model had higher simulation accuracy. The hydrogenation conditions were predicted by the reaction kinetics model. With the decrease of required bromine index of linear alkylbenzene, corresponding hydrogenation conditions needed to be intensified. In the range of the bromine index of hydrogenation feedstock from 100 to 600 mgBr/100 g, the bromine index for linear alkyl benzene should be below 10 mgBr/100 g through hydrogenation under the conditions of 90 °C, 4.0 MPa, and weight hourly space velocity of 0.5 h−1.

1. INTRODUCTION Linear alkylbenzenes (LABs) with appropriate chain length are predominantly used as synthetic detergent intermediates for the manufacture of LAB sulfonate (LAS). Nowadays, most LAB production involves the utilization of hydrofluoric acid catalyst, which is a source of pollution and equipment corrosion. A great deal of effort has been concentrated on the development of solid acid catalysts for the process. Universal Oil Products Company (UOP) and Spanish Petroleum Company (CEPSA) developed the DETAL process for fixed bed alkylation commercialized in 1995 based on solid acid catalyst. The process includes alkylation reaction operation and catalyst washing regeneration operation for each 24 h mutual switching.1 Zeolites have been extensively evaluated for the synthesis of LABs. For example, the dealumination of mordenite or Y zeolite could increase the catalytic stability by opening up the mesoporosity with the zeolite.2,3 SrHY and CeHY prepared through metal cation exchange showed better catalytic performance than HY.4 Beta zeolite and EMT were less active than Y zeolite.5 The catalytic activity and stability of ultrastable Y zeolite (USY) or HY zeolite catalyst could be enhanced with the increase of hydrothermal stabilization temperature.6,7 Through steam dealumination and acid washing, the catalyst activity increased, and catalyst deactivation tendency significantly decreased because of its increased mesoporous surface © 2017 American Chemical Society

area, lower acid site concentration, and less hydrophilic surface.8 The mordenite desilication treatment was found to be more effective than other approaches such as dealumination or metal/zeolite to improve the catalyst stability.9 Mordenite and beta zeolite were desilicated using alkali-metal treatments to create mesporous structure and higher Lewis acidity, improving catalytic stability.10 The coke deactivation of beta zeolite catalyst was caused by bulkier molecules, such as naphthalene, indane, and linear alkylbenzenes.11 The aluminophosphate-5 (AlPO4-5) catalysts with higher acid amount and lower acid strength exhibited better catalytic performance and stability.12 The beta zeolite with a nanosponge-like morphology had high catalytic performance because of the alkylation reactions occurring on external surfaces.13 In addition, the catalytic performances of supported heteropoly acids,14−16 acid-treated bentonite,17,18 and sulfonated magnetic carbon19 have been evaluated for LAB synthesis. To date, the catalytic stability of solid acid catalysts is still a key problem, which needs to be solved for future commercial utilization in LAB production. However, only a few studies have adopted a fixed bed reactor to evaluate the catalyst performance, and most Received: Revised: Accepted: Published: 2407

December 6, 2016 February 13, 2017 February 17, 2017 February 17, 2017 DOI: 10.1021/acs.iecr.6b04727 Ind. Eng. Chem. Res. 2017, 56, 2407−2415

Article

Industrial & Engineering Chemistry Research

hydrogen solubility, the apparent kinetic model equation for hydrogenation was determined. The model parameters for reaction kinetics were estimated by use of hydrogenation experimental data. The hydrogenation conditions were predicted by the reaction kinetics model.

of the previous experiments were carried out in batch reactors, which are inconvenient for testing the catalytic stability. Ren and co-workers investigated the modification of USY zeolite catalyst, the synthesis and catalytic performances of AlPO4-5 molecular sieves and mesoporous molecular sieves, and the reaction kinetics for alkylation and deactivation kinetics of the catalyst.12,20 During the liquid-phase alkylation of benzene with C10−C13 linear olefins in a fixed-bed reactor, the catalyst activity stability expressed with time on stream for olefin conversion greater than 98% and linear alkylbenzene selectivity greater than 93% was more than 3000 h. It was found that the LAB contained phenyl olefin impurities, which might be the reaction products between benzene and a small amount of diolefins in the reaction material. LAB containing unsaturated hydrocarbons affects its storage stability and the color of LAB sulfonate. The olefin impurities in LAB are generally removed with a clay refining method in industry. The clay refining method involves the problem of environmental pollution because of landfill disposal of waste clay. The removal of olefin impurities from LAB through catalytic hydrogenation, improving the quality of LAB products, is an effective development direction. In recent years, some progress has been made in the study of olefin hydrogenation in a three-phase system. During olefin hydrogenation over a polymer-supported palladium-imidazole catalyst, hydrogen solubility in the solvent could influence the rate of hydrogenation, and the reaction follows first-order kinetics in the concentration of olefin or hydrogen.21 The apparent kinetics of olefin hydrogenation followed a heterogeneous-type expression, which was first-order for the hydrogenation of butadiene.22 For the hydrogenation of 1,3butadiene to n-butane, the mathematical model was established, and the performance of the three-phase catalytic reactor has been studied under different operating conditions of the flowing feed stream.23 In the biphasic hydroformylation of the olefin, monoethanolamine increased dramatically the solubility of H2:CO mixture with 1:1 up to 27% compared with pure water, which resulted in a 10-fold increase in the reaction rate.24 The volatility of the hydrocarbon mixture was a paramount factor in the process, because H2 was diluted in the vapor phase; consequently, the amount of H2 dissolved in the liquid stream and the hydrogenation rates decrease significantly.25 During the selective hydrogenation of 1,3-butadiene in liquid phase, an increase of less than 2% in feed temperature increased the selectivity for 1-butene in the fixed bed reactor but decreased them in the slurry reactors.26 During catalytic hydrogenation, the effect of H2 concentration in the liquid phase could enhance the surface coverage of hydrogen on the catalyst surface at a constant H2 partial pressure.27 The masstransfer pathway of hydrogen molecules in a gas−liquid−solid three-phase hydrogenation system under semibatch operation was examined, wherein the hydrogen transported from the bulk gas phase to an intermediate liquid phase and then to the solid polymer phase.28 A kinetic model of the trickle bed pilot reactor was developed, in which mass-transfer resistance was considered in liquid phase and assumed to be negligible in gas phase.29 At present, the related research of catalytic hydrogenation for improving the quality of LAB products is rarely reported. The aim of this work was to develop the apparent kinetic model for the hydrogenation of olefins in the alkylation reactor effluents on Pd/Al2O3 catalysts. Based on the characteristic equation of the reactor and the mathematical models of

2. EXPERIMENTAL SECTION 2.1. Feedstocks of Hydrogenation. The feedstock for hydrogenation was the effluent mixture from alkylation reactor. The mixture was produced through the alkylation of benzene with C10−C13 linear olefins over solid acid catalyst in a fixed bed reactor. The effluent mixture contained benzene of 52.47% (m), linear paraffins of 40.25% (m), unsaturated hydrocarbon of 0.44% (m), and LAB of 6.70% (m). The average molar mass and bromine index of the mixture were 102.45 g/mol and 347.61 mgBr/100 g, respectively. The average molar mass of olefins in the mixture was 200.2 g/mol. High-purity hydrogen was used as hydrogen source for hydrogenation. 2.2. Catalyst Preparation. Pseudoboehmite was mixed evenly with the same weight of water and then kneaded into mud ball. The mud ball was extruded into strips. In a muffle furnace, the strips were calcinated for 1 h at 100, 200, 300, and 400 °C, and calcinated for 4 h at 500 °C. After the samples were crushed, 20−40 mesh of Al2O3 was chosen as hydrogenation catalyst support. The impregnation solution was prepared by mixing 2.3990 g of 36% hydrochloric acid, 6.2374 g of distilled water, and 1.0 g of PdCl2. The solution was used to impregnate 12 g of Al2O3 support g by means of incipient-wetness impregnation method. The solid material containing PdCl2 was dried for 24 h at 95 °C, then calcinated for 2 h at 200 and 400 °C in a muffle furnace. The catalyst precursor was obtained through washing for 3 h with distilled water in the ratio of liquid to solid of 50:1 (mL/g) and drying for 24 h at 95 °C. This washing and drying process was repeated five times. The catalyst precursor was reduced into 20−40 mesh catalyst in a fixed bed reactor for 2 h under the conditions of temperature of 200 °C, pressure of 1.0 MPa, and hydrogen flow rate of 0.4 m3/h. The catalyst with the mass fraction of palladium of 5.0% was obtained and expressed as 5.0%Pd/Al2O3, which had a bulk density ρC = 0.48 g/mL. 2.3. Hydrogenation Experimental Method. The hydrogenation reaction was carried out in a down flow fixed bed reactor. The reactor contained a stainless steel tube with inner diameter of 10 mm, outer diameter of 14 mm, and length of 100 cm. The catalyst dosage in reactor was 12 g. The reaction temperature was controlled by a temperature controller, and the pressure was regulated by a back pressure valve. Hydrogenation feedstock and hydrogen were introduced from the top of the reactor. The hydrogenation reaction product flowed out from the bottom of the reactor and entered to the product receiving tank for gas−liquid separation, and excessive hydrogen gas flowed through the flow meter. The liquid product was discharged from the product receiving tank and was analyzed. The flow rate of hydrogen was 17.98 mol/h, and the flow rate of olefin in feedstock was about 8.7 × 10−5 mol/h; therefore, the amount of hydrogen was far in excess. The bromine index of the feedstock or products was measured by using the PRA-100Br type bromine index tester produced by JiangHuan instrument Co. Ltd. (China). The conversion of the olefin hydrogenation was the difference between the bromine indexes of the feedstock and the product, which was divided by the bromine index of the feedstock. 2408

DOI: 10.1021/acs.iecr.6b04727 Ind. Eng. Chem. Res. 2017, 56, 2407−2415

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3. EXPERIMENTAL RESULTS OF HYDROGENATION The hydrogenation reactions of the two kinds of feedstocks were carried out in a fixed bed reactor, exploring the possibility of the removal of the olefin impurities. The first feedstock was the alkylation reactor effluent, mainly containing benzene, C10− C13 linear paraffins, and LAB. The second feedstock was LAB fraction obtained from the first feedstock through vacuum distillation. The reaction temperatures of two kinds of feedstocks were 80 °C for the alkylation reactor effluents and 280 °C for LAB fraction in order to achieve the same conversion of olefins. The olefins contained in the alkylation reactor effluent were more easily saturated by hydrogenation than the olefins contained in LAB fraction. The reason might be that compared with the LAB fraction, the smaller masstransfer resistance of the alkylation reactor effluent made its apparent reaction rate of hydrogenation bigger because of its smaller average molecular size and viscosity. Therefore, alkylation reactor effluent was chosen as the feedstock of the hydrogenation reaction for removal of olefin impurities. The kinetic experiment results under different conditions were listed in Table 1. The Table 1 showed that the conversion

4. DETERMINATION OF HYDROGENATION KINETIC MODEL EQUATION 4.1. Determination of Characteristic Equation of Reactor. The hydrogenation system included three different phases, namely gas, liquid, and solid catalyst (Pd/Al2O3). The following assumptions were put forward: (1) The gas and liquid were in a gas−liquid phase equilibrium. (2) The gas was an ideal gas, and the liquid was an ideal solution. (3) The gas and liquid synchronously descended through fixed bed reactor in plug flow. (4) The temperature distribution of the catalyst bed was uniform. (5) Because the amount of hydrogen was far in excess and the content of olefin impurities in the feedstock was very small, the volume flow rate change of fluid passing through the catalyst bed was neglected. Based on the material balance for microvolume of the catalyst bed in cross-sectional area of A and a bed height of Δz, the difference in the amounts of olefins leaving and entering the microvolume was equal to the amount of olefin conversion: ′ + vLCAL ′ ) − (vGCAG + vLCAL) = ( −rA )AΔz (vGCAG

where CAG′ = KACAL′; CAG = KACAL; the relative height and volume of the catalyst bed were Z = z/L; and VC = A·L. Equation 1 can be rewritten as

Table 1. Experimental Results of Olefin Conversion under Different Hydrogenation Conditions

a

serial number

ta (°C)

PTb (MPa)

WHSVc (h−1)

ZAd

1 2 3 4 5 6 7

40 40 40 40 40 40 40

1.0 1.0 1.0 1.0 1.0 1.0 1.0

0.330 0.680 0.950 1.310 1.710 2.030 2.330

0.9628 0.9332 0.9134 0.8995 0.8873 0.8797 0.8745

8 9 10 11 12 13

40 40 40 40 40 40

0.5 1.0 1.5 2.0 2.5 3.0

0.330 0.330 0.330 0.330 0.330 0.330

0.9418 0.9628 0.9720 0.9789 0.9825 0.9849

14 15 16 17

20 30 40 50

1.0 1.0 1.0 1.0

0.330 0.330 0.330 0.330

0.8731 0.9366 0.9628 0.9816

b

(1)

−

dCAG VC = rA v dZ vG + KL

(2)

A

It was assumed that the saturated vapor pressure of the olefin was the same as that of the hydrocarbon mixture. The following relationships existed: PTYA = PFSXA

(3)

CAGRT × 10−3 = PFS

CAL C FL

(4)

Because CFL = ρL/MF, the constant relationship in gas−liquid equilibrium of olefins was expressed by eq 5. KA =

PFS −3

RT × 10

MF ρL

(5)

When the small amount of hydrogen dissolved in the liquid phase was ignored, XF = 1. Based on the formula PTYF = PSFXF or nFG =

c

Reaction temperature. Reaction pressure. Weight hourly space velocity. dConversion of olefin.

PFS

n , PT − PFS H 2

the following relationship of the gas flow

containing hydrogen was obtained: ⎛ PFS ⎞ RT × 10−3 ⎟ nH2 vG = ⎜1 + PT PT − PFS ⎠ ⎝

(6)

Because the molar flow of the liquid feedstock was equal to the difference between the total feedstock molar flow and gas feedstock molar flow, the volume flow of the liquid feedstock was expressed as

(ZA) increased with the decrease of weight hourly space velocity (WHSV), increase of reaction pressure (PT) or temperature (t). This was because the increase of reaction pressure and reaction temperature both could improve the reaction rate. Reducing the WHSV of hydrogenation feedstock could prolong contacting time with catalyst bed, which was advantageous to improve olefin conversion. In addition, the gas chromatography analysis for feedstock and products showed that the hydrogenation reaction saturated only the olefin, while the benzene ring was not hydrogenated to cyclohexane, the hydrocarbons did not crack, etc.

vL =

mF0 PFS MF − nH ρL PT − PFS ρL 2

(7)

When eqs 5−7 were combined, the following relationship was obtained: vG + 2409

vL RT × 10−3 = mF0 KA PFSMF

(8) DOI: 10.1021/acs.iecr.6b04727 Ind. Eng. Chem. Res. 2017, 56, 2407−2415

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Industrial & Engineering Chemistry Research 1/1 − α ⎛ 1−α 1 ρL ⎞ β ⎜ ⎟ ZA = 1 − ⎜1 − 1 − α k TC HL ⎟ WHSV ρC ⎠ CAG0 ⎝

Substituting eq 8 into eq 2, the characteristic equation of the reactor was obtained, expressed as eq 9. dC PFSMF 1 1 − AG = rA −3 dZ WHSV RT × 10 ρC

The Arrhenius relationship of the apparent reaction rate constant with reaction temperature was expressed as follows:

(9)

where WHSV = mF0/WC, WC = VCρC, and R = 8.314 mL·MPa· mol−1·K−1. 4.2. Determination of Apparent Kinetic Model Equation for Hydrogenation. The volume flow rate change of fluid passing through the catalyst bed was neglected because the amount of hydrogen was far in excess and the content of olefin impurities in the feedstock was very small. According to the conversion eq 10 of the olefin hydrogenation, the relationship (eq 11) between the olefins concentration of the gas phase and the conversion was determined. ZA =

⎛ E ⎞ k T = k T0 exp⎜ − a ⎟ ⎝ RT ⎠

=1−

vGCAG0 +

vL C KA AG vL C K AG0 A

CAG = CAG0(1 − ZA )

(10) (11)

When nA0 = vGCAG0 + vLCAL0 = (vG+vL/KA)CAG0 was combined with eq 8, eq 12 for the initial concentration of olefins in the gas phase at the entrance to the catalyst bed was obtained. CAG0 = wA0

MF PFS MA RT × 10−3

(12)

where wA0 is the mass fraction of olefins of the hydrogenation feedstock. On the reaction system, the following assumptions were put forward: (1) The phase structure of the gas−liquid−solid threephase reaction system was that the solid catalyst was the core, the solid was surrounded by a liquid layer, and the gas was outside the liquid layer. (2) The gas and liquid was in a gas− liquid phase equilibrium. (3) The apparent hydrogenation was the reaction of α order of olefin concentration and β order of hydrogen concentration in liquid. For the unit volume of catalyst bed, the rate of hydrogenation of olefins was expressed as α β rA = k T′ CAL C HL

where CAL =

CAG , KA

kT =

(13) k T′ K Aα− 1

, and eq 13 was rewritten as

k α β rA = T CAG C HL KA

(14)

When eq 5 was substituted into eq 14 and eq 14 was substituted into eq 9, eq 15 was obtained. −

dCAG 1 ρL α β = k TCAG C HL dZ WHSV ρC

(17)

5. DEVELOPMENT OF MATHEMATICAL MODEL OF HYDROGEN SOLUBILITY The knowledge of accurate hydrogen solubility values in hydrocarbons is essential for the kinetic study on olefin hydrogenation in a three-phase system. In recent years, the determination of hydrogen solubility in hydrocarbons and the thermodynamic model have been studied. The hydrogen solubility in bio-oil compound was obtained using a continuous flow synthetic method, which was modeled with the Peng− Robinson equation, and the hydrogen solubility increased with increasing temperature.30 A method based on regular solution theory was proposed for prediction of hydrogen solubility in hydrocarbons, petroleum fractions, and coal liquids with molar mass ranging from 70 to 650 g/mol, and the hydrogen solubility increased both with increasing temperature and/or increasing molar mass of liquid medium.31 The hydrogen solubility in heavy oils was measured. The results showed that increasing the partial pressure of hydrogen and temperature increased the hydrogen solubility, and the Peng−Robinson model overestimated the hydrogen solubility in heavy oils.32,33 Based on experimental data, the adaptive neuro fuzzy inference system (ANFIS) model was developed for prediction of hydrogen solubility in heavy oil fractions, and the hydrogen solubility increased with increasing temperature.34 A simplified perturbed-chain statistical associating fluid theory was chosen to model hydrogen solubility in heavy alkanes and bitumen mixtures, and the hydrogen solubility increased both with increasing temperature and/or increasing molar mass of liquid medium.35 The hydrogen solubility in m-xylene, liquid paraffin, octacosane, and a kind of Fischer−Tropsch wax (FT wax) was measured, which increased with temperature and molar mass of liquid medium.36,37 In this work, the thermodynamic model for hydrogen solubility in hydrocarbons was proposed. Under the conditions of a certain temperature and hydrogen partial pressure, the chemical potentials of the hydrogen in the gas (eq 18) and the hydrogen in the liquid (eq 19) were

(vGCAG0 + vLCAL0) − (vGCAG + vLCAL) (vGCAG0 + vLCAL0) vGCAG +

(16)

0 μHG = μHG + RT ln PH2

(18)

0 μHL = μHL + RT ln C HL

(19)

When the hydrogen was in the phase equilibrium of gas and liquid, μHG = μHL, eq 20 was obtained by eqs 18 and 19. 0 0 −(μHL − μHG ) = −ΔG° = RT ln

(15)

C HL PH2

(20)

B was used to express the hydrogen solubility equilibrium constant or solubility coefficient, and eq 21 was obtained.

Because the amount of hydrogen was far in excess and the change of feedstock composition was very small, the concentration of hydrogen dissolved in the liquid was almost unchanged with the height of the catalyst bed. When eq 15 was integrated in the range of Z = 0−1 in the relative height of the catalyst bed, the apparent kinetic model eq 16 was obtained.

C HL = BPH2

(21)

When ΔG = ΔH − TΔS was substituted into eq 20, eqs 22 and 23 were obtained. 0

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Industrial & Engineering Chemistry Research Table 2. Solubility Coefficients of Hydrogen in Different Liquid Media m-xylene

liquid paraffin

octacosane

FT wax

t (°C)

B × 102 (mol/(L·MPa))

t (°C)

B × 102 (mol/(L·MPa))

t (°C)

B × 102 (mol/(L·MPa))

t (°C)

B × 102 (mol/(L·MPa))

80 100 120 140 160

3.2161 3.2995 3.4635 3.5004 3.5560

100 200 300

3.2870 4.1833 4.8039

100 200 300

2.8567 3.6000 4.2167

100 200 300

3.0500 3.4333 4.0500

Table 3. Model Parameters of Hydrogen Solubility Coefficient in Different Media medium

molar mass (g/mol)

ΔS0a (J/(mol·K))

ΔH0b (J/mol)

m-xylene liquid paraffin octacosane FT wax

106.17 345.00 394.00 730.00

−23.8374 −19.2938 −20.3105 −15.7108

1667.0872 3385.3057 3453.9371 6337.0910

A1c (mol/(L·MPa)) 5.6861 9.8211 8.6906 1.5112

× × × ×

10−2 10−2 10−2 10−1

a

Standardized entropy change of hydrogen solubilization. bStandardized enthalpy change of hydrogen solubilization. cModel parameters of solubility coefficient.

ln B =

ΔS ° ΔH ° 1 − R R T

⎛ ΔH ° ⎞ B = A1 exp⎜ − ⎟ ⎝ RT ⎠

error between the calculated and the measured A1 was EA1 = 6.0613%, and the correlation coefficient was RA12 = 0.9604. The average relative error between the calculated and the measured ΔH0 was EΔH0 = 4.292%, and the correlation coefficient was RΔH02 = 0.9918. The mathematical model of the hydrogen solubility coefficient correlated with temperature and the molar mass of the liquid medium was as follows:

(22)

(23)

The data of hydrogen solubility in m-xylene, liquid paraffin, octacosane, and a kind of Fischer−Tropsch wax (FT wax) have been reported in the literatures.36,37 The hydrogen solubility increased with the increase of hydrogen partial pressure or temperature under the conditions of temperature of 80−300 °C, hydrogen partial pressure of 1.0−5.0 MPa, and molar mass of liquid medium of 106.17−730 g/mol. Based on these data for hydrogen solubility, the solubility coefficients of hydrogen in different liquid media at different temperatures were calculated and are shown in Table 2. The model parameters A1 and ΔH0 of hydrogen solubility coefficient had been estimated by use of data in Table 2, and the results are shown in Table 3. The process of hydrogen dissolving in the liquid medium resulted in an enthalpy increase or endothermic process. The model parameters A1 and ΔH0 increased with the molar mass of liquid medium, and linear correlation results are shown in Figure 1. The average relative

B = (3.9290 × 10−2 + 1.4980 × 10−4MF) ⎛ 756.3191 + 7.5028MF ⎞ ⎟ exp⎜ − ⎝ ⎠ RT

(24)

The hydrogen solubility (CHL) in the liquid medium was the product of the solubility coefficient and hydrogen partial pressure, expressed as eq 25. C HL = (3.9290 × 10−2 + 1.4980 × 10−4MF) ⎛ 756.3191 + 7.5028MF ⎞ ⎟·P exp⎜ − ⎝ ⎠ H2 RT

(25)

The hydrogen solubilities in liquid medium were calculated by eq 25. The average relative error between the calculated and the measured values was ECHL = 11.5444%, and the correlation coefficient was RCHL2 = 0.9418.

6. ESTIMATION OF KINETIC MODEL PARAMETERS FOR HYDROGENATION Based on the composition of hydrogenated feedstock, the saturated vapor pressure (PTS) and liquid density (ρL) were calculated by use of the mixture of benzene and dodecane as model compounds. Based on the average molar mass data of the feedstock (MF = 102.45 g/mol), the hydrogen solubility coefficient (B) was calculated by eq 24. By use of the data of the molar mass and saturated vapor pressure of hydrogenated feedstock and the mass fraction and molar mass of olefins, the initial concentration of olefin in gas phase at the entrance to the catalyst bed was calculated by eq 12. These calculated results are listed in Table 4. Assuming that the gas in the reaction system was an ideal gas, the liquid was an ideal solution, and hydrogen dissolved in liquid was ignored, the hydrogen partial pressure of hydrogenation reaction was equal to the difference of reaction pressure with saturated vapor pressure of the feedstock. The

Figure 1. Variation of the model parameters of hydrogen solubility coefficient with the molar mass of the liquid medium. 2411


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7. EXPERIMENTAL VALIDATION OF THE KINETIC MODEL Hydrogenation experiments were carried out under the conditions of 30 °C, 1.0 MPa, and different WHSV values. The experimental data of olefin conversion were used to validate the established kinetic model. The experimental values (ZA) of olefin conversion and calculated values (ZAC) by model eq 16 are listed in Table 6. Table 6 shows that the experimental

Table 4. Properties, Hydrogen Solubility Coefficients, and Initial Concentrations of Olefin in Gas Phase ta (°C)

PFS × 102 (MPa)b

ρL × 10−3 (g/L)c

B × 102 (mol/(L·MPa))d

CAG0 × 105 (mol/L)e

20 30 40 50 60 70 80 90

0.7187 1.1407 1.7477 2.5949 3.7461 5.2738 7.2587 9.8000

0.8139 0.8055 0.7969 0.7883 0.7796 0.7708 0.7618 0.7533

2.9224 2.9833 3.0415 3.0971 3.1505 3.2014 3.2503 3.2971

0.6640 1.0191 1.5115 2.1747 3.0453 4.1623 5.5666 7.3085

Table 6. Comparison of Experimental Values of Olefin Conversion and the Calculated Values of the Model

a

Temperature. bSaturated vapor pressure of feedstock. cLiquid density. d Hydrogen solubility coefficient. eInitial concentration of gaseous olefins.

WHSVa (h−1)

ZAb

ZACc

0.300 0.648 1.068 1.325 1.747

0.9372 0.9017 0.8650 0.8559 0.8363

0.9372 0.9007 0.8669 0.8492 0.8233

a Weight hourly space velocity. bOlefin conversion. cCalculated value of olefin conversion.

parameters of the kinetic model were estimated with the Gauss−Newton iteration method by use the sum (QZA) of squared residuals of model-calculated values with experimental values of olefin conversion as the objective function. Based on the reaction experimental data from serial numbers 1−7 in Table 1 and data at 40 °C in Table 4, the kinetic model parameter α in eq 16 was estimated. Kinetic model parameter β and reaction rate constant at 40 °C were estimated by use of the reaction experimental data from serial numbers 8−13 in Table 1, shown in Table 5. The frequency factor of reaction rate constant and apparent activation energy were also calculated by use of the reaction experimental data from serial numbers 14−17 in Table 1, shown in Table 5. When the model parameters in Table 5 were substituted into eq 16, the olefin conversions under conditions of Table 1 were calculated by eq 16. The sum of squared residuals of the modelcalculated values with experimental values of olefin conversions was QZA = 1.5155 × 10−3; the average relative error was EZA = 0.706%, and the correlation coefficient was RZA2 = 0.9350. This showed that the model eq 16 had higher simulation accuracy. In Table 5, the orders of hydrogen and olefins concentration in liquid were β = 1.2446 (close to 1) and α = 2.6584, respectively. The order of olefin was significantly higher than that of hydrogen. This showed that the olefin concentration had greater influence on the hydrogenation reaction rate than hydrogen. The order of olefin being obviously larger than 1 indicated that the distribution of hydrogenation activity from low to high existed in olefin mixtures. In the vicinity of the catalyst bed entrance, olefin concentration was higher, and the distribution of olefin with higher activity was larger; consequently, the olefin hydrogenation rate was higher. Near the catalyst bed exit, olefin concentration was lower, and the distribution of olefin with higher activity was smaller; consequently, the olefin hydrogenation rate was correspondingly lower.

values of olefin conversion were consistent with the model calculation values; the average relative error of the calculated value and the experimental value was EZA = 0.5336%, and the correlation coefficient was RZA2 = 0.9734.

8. PREDICTION AND ANALYSIS OF HYDROGENATION CONDITIONS Because the activity of diolefins is higher than that of olefins, the alkylation of aromatic compounds with diolefins was carried more easily.38,39 During benzene alkylation with C10−C13 linear olefins, the bromine index of the LAB product increased with the increase of diolefins content in alkylation feedstock.40,41 In the production of LAB, the amount of monoalkylbenzene was very high because of the size selectivity of zeolites.1 In benzene alkylation of diolefin-containing dodecene over modified mordenite, the effect of diolefins on catalyst activity stability was notable, while the consecutive alkylation of diolefins was not observed.9 Because of the size selectivity of the zeolite, very little diphenyl alkanes could be produced through consecutive alkylation. Because of the small amount of diolefins contained in alkylation feedstock, the phenyl olefins might be produced through the alkylation of benzene with the diolefins, which resulted in the effluent mixture from alkylation reactor containing unsaturated hydrocarbons. Because the linear olefins were completely alkylated with benzene, the mass fraction of LAB in the effluent mixture from alkylation reactor was 6.7%. If the feedstock of the bromine index of 347.61 mgBr/100 g was hydrogenated to reach the bromine index of the LAB of 10.00 mgBr/100 g, the required conversion of olefin hydrogenation should be (347.61 − 10.00·6.7%)/347.61 = 0.9981. The fixed bed reactor of the catalyst dosage of 12 g was used, whose cross-sectional area was 0.7144 cm2, and the hydrogen flow amount was 17.98 mol/h. For the model parameters in

Table 5. Results of Parameter Estimation for Kinetic Model Equation αa 2.6584

βb 1.2446

kT40c ((mol/L)−2.903·h−1) 2.3292 × 10

11

kT0d ((mol/L)−2.903·h−1) 2.0577 × 10

16

Eae (J/mol) 29651.51

Order of olefin concentration in liquid. bOrder of hydrogen concentration in liquid. cOlefin hydrogenation reaction rate constant at 40 °C. dRate constant frequency factor. eReaction activation energy. a

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Industrial & Engineering Chemistry Research Table 5 and the corresponding data in Table 4 to be substituted into the model eq 16, the reaction conditions of hydrogenation for different bromine index required of LAB were predicted by the kinetic model eq 16 of olefin hydrogenation. 8.1. Effects of Reaction Temperature and Pressure. If the feedstock of the bromine index of 347.61 mgBr/100 g was hydrogenated to reach the bromine index of the LAB of 10.00, 15.00, 20.00, and 30.00 mgBr/100 g, the required conversion of olefins hydrogenation should be 0.9981, 0.9971, 0.9961, and 0.9942, respectively. With the decrease of the required bromine index of LAB, the olefin hydrogenation conversion increased. Under the condition of WHSV = 0.5 h−1, the required reaction temperature and pressure were predicted to reach the corresponding hydrogenation requirement by the hydrogenation kinetic model, shown in Figure 2.

Figure 3. Variation of LAB bromine index with bromine index of feedstock or WHSV under the conditions of temperature of 90 °C and pressure of 4.0 MPa.

As shown in Figure 3, if a bromine index of LAB was reached, WHSV should decrease with the increase of the bromine index of the feedstock. If the bromine index of hydrogenated feedstock was determined, WHSV should decrease with the required bromine index of LAB from 30 mgBr/100 g to 10 mgBr/100 g. This indicated that if the bromine index of hydrogenated feedstock increased or the required bromine index of LAB decreased, the hydrogenation condition needed to be intensified. Above all, in the range of the bromine index of hydrogenation feedstock from 100 to 600 mgBr/100 g, the bromine index for LAB should be below 10 mgBr/100 g through hydrogenation under the conditions of 90 °C, 4.0 MPa, and WHSV of 0.5 h−1.

Figure 2. Variation of LAB bromine index with hydrogenation temperature or pressure in WHSV of 0.5 h−1.

9. CONCLUSIONS By use of the effluent mixture from alkylation reactor as a hydrogenation feedstock, which was mainly composed of benzene, linear paraffins, and LAB, the hydrogenation over Pd/Al2O3 catalyst in a down flow fixed bed reactor was carried out for removal of olefin impurities in the mixture. Considering that the hydrogenation system included three phases, namely, an ideal gas and ideal liquid as reactants and a solid catalyst; that the gas and liquid was in gas−liquid phase equilibrium; and that the volume flow rate changes of the gas and liquid synchronously descending through fixed bed reactor in plug was neglected, the characteristic equation of the reactor was obtained. The phase structure of the reaction system was considered as that the solid catalyst was the core, the solid was surrounded by a liquid layer, and the gas was outside the liquid layer. Based on the α order of olefin concentration and β order of hydrogen concentration in liquid, the apparent kinetic model equation of olefin conversion was determined. By thermodynamic analysis, the hydrogen solubility in the liquid medium was the product of the solubility coefficient and hydrogen partial pressure, and the relationship between the hydrogen solubility coefficient and the reciprocal of temperature was exponential. Based on the solubility data, the mathematical models of the hydrogen solubility coefficient and hydrogen solubility were determined through the

As shown in Figure 2, under the condition of WHSV = 0.5 h−1, if a bromine index of LAB was reached, reaction pressure should decrease with the increase of reaction temperature. With the required bromine index of LAB from 30 mgBr/100 g reducing to 10 mgBr/100 g, the reaction pressure should increase from 0.62 to 2.41 MPa at 90 °C or from 1.82 to 7.88 MPa at 70 °C, and the reaction temperature should increase from 56 to 79 °C at a pressure of 5.0 MPa. With the decrease of required bromine index of LAB, the hydrogenation reaction temperature or pressure needed to rise, namely, the hydrogenation reaction conditions needed to be intensified. Under the conditions of reaction temperature of 80 °C, pressure of 4.2 MPa, and WHSV of 0.5 h−1, the olefin conversion of feedstock should be 99.81% through the hydrogenation reaction, and the bromine index of LAB should be 10 mgBr/100 g. 8.2. Effects of Bromine Index of Feedstock and WHSV. In the case of different bromine index or olefin mass fraction of hydrogenation feedstock, if the required bromine index of the LAB was determined, olefin hydrogenation conversion should change, and the hydrogenation condition should be adjusted accordingly. If the required bromine index of the LAB was 10.00, 15.00, 20.00, or 30.00 mgBr/100 g, the corresponding WHSV for different bromine index of hydrogenation feedstock was predicted by the reaction kinetic model under the conditions of 90 °C and 4.0 MPa (Figure 3). 2413


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Industrial & Engineering Chemistry Research correlation of hydrogen solubility coefficient with temperature and the molar mass of the liquid medium. The apparent kinetic model of olefin hydrogenation was established through model parameter estimation by use of the experimental data of hydrogenation. The order of hydrogen concentration in liquid was close to 1, and the order of olefin was significantly higher than that of hydrogen. The olefin concentration had a greater influence on the hydrogenation rate than hydrogen. The hydrogenation activity of olefins were distributed from higher to lower. The results of experimental validation and statistical tests showed that the kinetic model had higher simulation accuracy. The reaction conditions were predicted by the reaction kinetic model. With the decrease of required bromine index of LAB, corresponding hydrogenation conditions needed to be intensified. In the range of the bromine index of hydrogenation feedstock from 100 to 600 mgBr/100 g, the bromine index for LAB should be below 10 mgBr/100 g through hydrogenation under the conditions of 90 °C, 4.0 MPa, and WHSV of 0.5 h−1.

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AUTHOR INFORMATION

vL = Liquid flow, L·h−1 VC = Volume of catalyst bed, L wA0 = Olefin mass fraction of feedstock WC = Catalyst mass in reactor, g XA = Molar fraction of olefins in liquid XF = Molar fraction of feedstock in liquid YA = Mole fraction of olefins in gas z = Catalyst bed height, dm Z = Relative height of catalyst bed μHG = Gas hydrogen chemical potential, J·mol−1 μHG0 = Gas hydrogen standardized chemical potential, J· mol−1 μHL = hydrogen chemical potential in liquid, J·mol−1 μHL0 = hydrogen standardized chemical potential in liquid, J· mol−1 ρC = Catalyst bulk density, g·L−1 ΔG0 = Standardized Gibbs free energy change of hydrogen solubilization, J·mol−1

REFERENCES

(1) Kocal, J. A.; Vora, B. V.; Imai, T. Production of linear alkylbenzenes. Appl. Catal., A 2001, 221, 295−301. (2) Meriaudeau, P.; Ben, T. Y.; Thangaraj, A.; Almeida, J. L. G.; Naccache, C. Zeolite based catalysts for linear alkylbenzene production: Dehydrogenation of long chain alkanes and benzene alkylation. Catal. Today 1997, 38, 243−247. (3) Sasaki, Y.; Suzuki, T.; Takamura, Y.; Saji, A.; Saka, H. Structure analysis of the mesopore in dealuminated zeolite Y by high resolution TEM observation with slow scan CCD camera. J. Catal. 1998, 178, 94−100. (4) Thomas, B.; Das, B. B.; Sugunan, S. Rare earth exchanged (Ce3+, La3+ and RE3+) H−Y zeolites as solid acid catalysts for the synthesis of linear alkyl benzenes. Microporous Mesoporous Mater. 2006, 95, 329− 338. (5) Cao, Y.; Kessas, R.; Naccache, C.; Ben, T. Y. Alkylation of benzene with dodecene. The activity and selectivity of zeolite type catalysts as a function of the porous structure. Appl. Catal., A 1999, 184, 231−238. (6) Yuan, X. D.; Park, J. N.; Wang, J.; Lee, C. W.; Park, S. E. Alkylation of benzene with 1-dodecene over USY zeolite catalyst: effect of pretreatment and reaction conditions. Korean J. Chem. Eng. 2002, 19 (4), 607−610. (7) Lovás, P.; Hornácek, M.; Hudec, P.; Jorík, V. Preparation of an active and regenerable catalyst for liquid-phase alkylation of toluene with 1-decene. Appl. Catal., A 2014, 475, 341−346. (8) Boveri, M.; Marquez-Alvarez, C.; Laborde, M. A.; Sastre, E. Steam and acid dealumination of mordenite characterization and influence on the catalytic performance in linear alkylbenzene synthesis. Catal. Today 2006, 114 (2−3), 217−225. (9) Lin, J. S.; Wang, J. J.; Wang, J. S.; Wang, I.; Balasamy, R. J.; Aitani, A.; Al-Khattaf, S.; Tsai, T. C. Catalysis of alkaline-modified mordenite for benzene alkylation of diolefin-containing dodecene for linear alkylbenzene synthesis. J. Catal. 2013, 300, 81−90. (10) Aslam, W.; Siddiqui, M. A. B.; Rabindran Jermy, B.; Aitani, A.; Č ejka, J.; Al-Khattaf, S. Selective synthesis of linear alkylbenzene by alkylation of benzene with 1-dodecene over desilicated zeolites. Catal. Today 2014, 227, 187−197. (11) Han, M. H.; Cui, Z.; Xu, C.; Chen, W.; Jin, Y. Synthesis of linear alkylbenzene catalyzed by Hβ-zeolite. Appl. Catal., A 2003, 238, 99− 107. (12) Yuan, H. K.; Liu, X. R.; Ren, J.; Shen, L. Surface acidity of aluminum phosphate and its catalytic performance in benzene alkylation with long chain olefin. Chin. J. Chem. Eng. 2013, 21 (6), 627−632. (13) Kim, J. C.; Cho, K.; Ryoo, R. High catalytic performance of surfactant-directed nanocrystalline zeolites for liquid-phase Friedel−

Corresponding Author

*E-mail: [email protected]; [email protected]. ORCID

Jie Ren: 0000-0003-0625-9016 Notes

The authors declare no competing financial interest.

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NOMENCLATURE A = Reactor cross-sectional area, dm2 BrF = Bromine index of feedstock, mgBr·(100 g)−1 BrLAB = LAB bromine index, mgBr·(100 g)−1 CAG = Gaseous olefin concentration, mol·L−1 CAL = Liquid olefin concentration, mol·L−1 CAL0 = Initial concentration of liquid olefin, mol·L−1 CFL = Liquid feedstock concentration, mol·L−1 CHL = Hydrogen concentration in liquid, mol·L−1 EB = Average relative error of solubility coefficient, % ECHL = Average relative error of hydrogen solubility, % EZA = Average relative error of olefin conversion, % KA = Olefin gas−liquid phase equilibrium constant kT = Olefin hydrogenation reaction rate constant, (mol/ L)−2.903·h−1 L = Total height of catalyst bed, dm mF0 = Feedstock mass flow, g·h−1 MA = Olefin molar mass, g·mol−1 MF = Feedstock molar mass, g·mol−1 nF0 = Feedstock molar flow, mol·h−1 nFG = Feedstock gas molar flow, mol·h−1 nFL = Feedstock liquid molar flow, mol·h−1 nH2 = Hydrogen molar flow, mol·h−1 PH2 = Hydrogen partial pressure, MPa QZA = Sum of squared residuals of olefin conversion rA = Olefin reaction rate, mol·L−1·h−1 R = Gas constant, R = 8.314 mL·MPa·mol−1·K−1 R2 = Correlation coefficien RB 2 = Correlation coefficient of hydrogen solubility coefficient RCHL2 = Hydrogen solubility correlation coefficient RZA2 = Olefin conversion correlation coefficient T = Temperature, K vG = Gas flow, L·h−1 2414


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Industrial & Engineering Chemistry Research Crafts alkylation of benzene due to external surfaces. Appl. Catal., A 2014, 470, 420−426. (14) Zhang, J. C.; Chen, B. H.; Li, C. Y.; Zhu, Z. G.; Wen, L. Y.; Min, E. Z. Kinetics of benzene alkylation with 1-dodecene over a supported tungstophosphoric acid catalyst. Appl. Catal., A 2003, 249, 27−34. (15) Hernandez-Cortez, J. G.; Martinez, L.; Soto, L.; Lopez, A.; Navarrete, J.; Manriquez, M.; Lara, V. H.; Lopez-Salinas, E. Liquid phase alkylation of benzene with dec-1-ene catalyzed on supported 12tungstophosphoric acid. Catal. Today 2010, 150, 346−352. (16) Hafizi, A.; Ahmadpour, A.; Koolivand-Salooki, M.; Heravi, M. M.; Bamoharram, F. F. Comparison of RSM and ANN for the investigation of linear alkylbenzene synthesis over H14[NaP5W30O110]/ SiO2 catalyst. J. Ind. Eng. Chem. 2013, 19, 1981−1989. (17) Faghihian, H.; Mohammadi, M. H. Surface properties of pillared acid-activated bentonite as catalyst for selective production of linear alkylbenzene. Appl. Surf. Sci. 2013, 264, 492−499. (18) Faghihian, H.; Mohammadi, M. H. Acid activation effect on the catalytic performance of Al-pillared bentonite in alkylation of benzene with olefins. Appl. Clay Sci. 2014, 93−94, 1−7. (19) Liang, X. Z. Novel magnetic carbon based solid acid for alkylation of benzene and dodecene. Chem. Eng. J. 2015, 264, 251− 257. (20) Jin, Y. J.; Yuan, X. D.; Ren, J.; Zhou, J. L. Solid acid catalysts for alkylation of benzene with long chain olefins II. The composition, acidity and properties of SiW12/HAlMCM-41 catalysts. Petrochem. Technol. (Beijing, China) 2000, 29 (8), 557−560. (21) Velu, U.; Stanislaus, A.; Virupaiah, G.; Balasubramanian, S. V. Hydrogenation of olefins catalyzed by polymer-supported palladiumimidazole. Chin. J. Catal. 2011, 32 (2), 280−285. (22) Tailleur, R. G.; Hernandez, J.; Rojas, A. Selective hydrogenation of olefins with mass transfer control in a structured packed bed reactor. Fuel 2008, 87, 3694−3705. (23) Tohidian, T.; Dehghani, O.; Rahimpour, M. R. Modeling and simulation of an industrial three phase trickle bed reactor responsible for the hydrogenation of 1,3-butadiene: A case study. Chem. Eng. J. 2015, 275, 391−404. (24) Baricelli, P. J.; Melean, L. G.; Alonso, M. M.; Rodríguez, A.; Rosales, M.; González, Á . Advances in the aqueous-phase hydroformylation of olefins from a refinery naphtha cut: The effect of monoethanolamine in the catalytic activity of the Rh/TPPTS system. Catal. Today 2015, 247, 124−131. (25) Bressa, S. P.; Alves, J. A.; Mariani, N. J.; Martı ́nez, O. M.; Barreto, G. F. Analysis of operating variables on the performance of a reactor for total hydrogenation of olefins in a C3−C4 stream. Chem. Eng. J. 2003, 92, 41−54. (26) Pérez, D.; Olivera-Fuentes, C.; Curbelo, S.; Rodríguez, M. J.; Zeppieri, S. Study of the selective hydrogenation of 1,3-butadiene in three types of industrial reactors. Fuel 2015, 149, 34−45. (27) Singh, U. K.; Vannice, M. A. Kinetics of liquid-phase hydrogenation reactions over supported metal catalysts  a review. Appl. Catal., A 2001, 213, 1−24. (28) Wang, H.; Rempel, G. L. Organic solvent-free catalytic hydrogenation of diene-based polymer nanoparticles in latex form: Mass transfer of hydrogen in a semibatch process. J. Ind. Eng. Chem. 2015, 25, 29−34. (29) Ahmadigoltapeh, S.; Mehranbod, N.; Halimejani, H. Z. Propylene hydrogenation through structured and conventional catalyst beds: Experiment and modeling. J. Nat. Gas Sci. Eng. 2015, 27, 822− 830. (30) Qureshi, M. S.; Touronen, J.; Uusi-Kyyny, P.; Richon, D.; Alopaeus, V. Solubility of hydrogen in bio-oil compounds. J. Chem. Thermodyn. 2016, 102, 406−412. (31) Riazi, M. R.; Roomi, Y. A. A method to predict solubility of hydrogen in hydrocarbons and their mixtures. Chem. Eng. Sci. 2007, 62, 6649−6658. (32) Saajanlehto, M.; Uusi-Kyyny, P.; Alopaeus, V. Hydrogen solubility in heavy oil systems: Experiments and modeling. Fuel 2014, 137, 393−404.

(33) Uusi-Kyyny, P.; Pakkanen, M.; Linnekoski, J.; Alopaeus, V. Hydrogen solubility measurements of analyzed tall oil fractions and a solubility model. J. Chem. Thermodyn. 2017, 105, 15−20. (34) Nasery, S.; Barati-Harooni, A.; Tatar, A.; Najafi-Marghmaleki, A.; Mohammadi, A. H. Accurate prediction of solubility of hydrogen in heavy oil fractions. J. Mol. Liq. 2016, 222, 933−943. (35) Ma, M. X.; Chen, S. N.; Abedi, J. Modeling the solubility and volumetric properties of H2 and heavy hydrocarbons using the simplified PC-SAFT. Fluid Phase Equilib. 2016, 425, 169−176. (36) Bai, L.; Zhao, Y. L.; Zhang, B. J. Solubilities and mass transfer coefficients of hydrogen and carbon monoxide. Chem. React. Eng. Technol. 1996, 12 (2), 189−195. (37) Zhao, L. F.; Zhao, Y. L.; Bai, L.; Zhang, B. J. Investigation on solubilities and volumetric mass transfer coefficients of H2 and CO in m-xylene. J. Fuel Chem. Technol. (Beijing, China) 2000, 28 (1), 80−84. (38) Ke, M.; Tang, Y. T.; Cao, W. Z.; Peng, H. P.; Zhou, A. G. Study on alkylation reaction of diolefin with thiophene. J. Xi’an Shiyou Univ., Nat. Sci. Ed. 2008, 23 (5), 75−80. (39) Tian, L.; Cao, F. H.; Fang, D. Y.; Guo, S. Z. Alkylation of toluene with 1,3-pentadiene over [bupy]BF4-A1Cl3 ionic liquid catalyst. Chin. J. Chem. Eng. 2007, 15 (5), 680−682. (40) Xu, Y.; Wu, P. C.; Wang, Y.; Liu, D.; Huang, X. L. Industrialization of long-stright diolefins selective hydrogenation catalyst and process. China Surfactant Deterg. Cosmet. 2002, 32 (1), 62−64. (41) Li, J. Industrial application of long-chain di-olefin selective hydrogenation process. Adv. Fine Petrochem. 2009, 10 (6), 27−30.

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