Ammoxidation of acrolein to acrylonitrile over bismuth molybdate catalysts

Ammoxidation of acrolein to acrylonitrile over bismuth molybdate catalysts

Applied Catalysis A: General 520 (2016) 7–12 Contents lists available at ScienceDirect Applied Catalysis A: General journal homepage: www.elsevier.c...

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Applied Catalysis A: General 520 (2016) 7–12

Contents lists available at ScienceDirect

Applied Catalysis A: General journal homepage: www.elsevier.com/locate/apcata

Ammoxidation of acrolein to acrylonitrile over bismuth molybdate catalysts Nguyen Thanh-Binh a , Jean-Luc Dubois b , Serge Kaliaguine a,∗ a b

Department of Chemical Engineering, Laval University, 1065, avenue de la Médecine, G1V 0A6 Québec, Canada ARKEMA, 420 Rue d’Estienne d’Orves, F-92705 Colombes, France

a r t i c l e

i n f o

Article history: Received 21 January 2016 Received in revised form 11 March 2016 Accepted 26 March 2016 Available online 1 April 2016 Keywords: Ammoxidation Acrolein Acrylonitrile Mesostructure Bismuth-molybdate catalysts

a b s t r a c t The present work deals with the potentially significant process converting acrolein of green origin to acrylonitrile using mesoporous bismuth molybdate catalysts. The ammoxidation catalysts were characterized by N2 physisorption, X-ray diffraction, and catalytic tests under various conditions at different temperatures, contact times, and reactant molar ratios. The results indicated a catalytic activity proportional to specific surface area, which depends on bismuth molybdate phases, and concentration of oxygen in the gas feed. The selectivity of the catalysts only depends on reaction temperature. ACN selectivity obtained at 350–400 ◦ C was 100% and reduced to 97% at 450 ◦ C. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Acrylonitrile (ACN) is a key monomer of the polymer industry. Therefore, the global market of ACN is about 6 Mt in 2015 and expected to reach 8 Mt in 2020 [1–3]. However, the major source of ACN is propylene or propane from fossil origin [4]. Current research trends for a greener chemical industry is based on using platform molecules of biological origin such as glycerol. This tricarbon trialcohol is a 10 wt% by-product of biodiesel production. As reported in [5] the annual production of biodiesel increases steadily and reached 27 Mt in 2015. A process was developed by Dubois [6,7] and Takaaki and Minoru [8] to convert glycerol to ACN using direct or indirect processes. For the indirect process, the first step is dehydration of glycerol to acrolein (AC) over acidic catalysts such as WO3 /TiO2 or FePO4 [7,9]. The second one is the ammoxidation of acrolein to acrylonitrile using mixed metal oxides such as bismuth molybdate or antimonate catalysts. For the direct process, both above steps were combined by using catalysts comprising Sb, Nb, and V [9]. This direct process was also previously examined by Guerrero-Pérez et al. both in gas [10–12] and liquid phases [13]. Most importantly the indirect process allows controlling the water content in the acrolein ammoxidation reactor. This is done by using a condenser between the two reactors. A strict control of high water

∗ Corresponding author. E-mail address: [email protected] (S. Kaliaguine). http://dx.doi.org/10.1016/j.apcata.2016.03.030 0926-860X/© 2016 Elsevier B.V. All rights reserved.

to ammonia ratio is suppressing the risk of acrylonitrile hydrolysis to acrylic acid. The indirect method yields an easier control of temperature and higher ACN yields. Therefore, the indirect process seems preferable for the synthesis of ACN from renewable glycerol. Only a few references discussed ammoxidation of acrolein to acrylonitrile [14–21]. Mixed metal oxides based on molybdates, antimonates, tin oxide were used as catalysts for ammoxidation of acrolein. The results showed that the ammoxidation of acrolein is faster than ammoxidation of propylene over the same catalysts. The reaction was carried out at temperatures around 300–500 ◦ C under gas feeds including AC, ammonia, oxygen, and nitrogen. The results showed that molybdate catalysts are better catalysts than antimonate ones. The catalysts have however really low specific surface area of about 1–4 m2 /g. Recently, Hoelderich’s group researched on this reaction [9,20]. SbVO, SbFeO, and MoO3 were investigated for ammoxidation of AC to ACN. The highest ACN yield was however only 40%. This study was conducted in the presence of water vapor and at low AC partial pressure. They demonstrated that higher specific surface area catalysts yield higher activity. Hence, in the present work simple catalysts with high specific surface area were studied. The bismuth molybdate catalysts are the simplest and most promising candidates for ammoxidation of acrolein. In general, the two major factors to achieve a good heterogeneous catalyst for ammoxidation of acrolein are a large active surface area and the right composition yielding not only high activity but also high selectivity [4,22,23]. High surface area oxidation catalysts

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are prone to overheating and require special reactor design to enhance local heat transfer. In 1972, Batist et al. reported several ways for synthesis of Bi-Mo-O based on Bi(NO3 )3 · 5H2 O, (NH4 )6 Mo7 O24 · 4 H2 O, and H2 MoO4 and the method to avoid precipitation of the two precursors by using strong acid HNO3 [24]. Recently, the bismuth molybdates were obtained by several methods such as combining complexation and spray drying [25,26], surfactant assisted hydrothermal treatment [27], hydrothermal treatment [28], reflux and solid state [29], and hard-templating [30]. However, the specific surface area of the bismuth molybdate catalysts are still low (most specific surface areas are around 2–4 m2 /g). Therefore, preparing bismuth molybdate with high surface area requires attention. On the other hand, the different phases of bismuth molybdate also show different effects on catalytic performance [4,31]. Bismuth molybdates have three phases including ˛ (Bi2 Mo3 O12 ), ˇ (Bi2 Mo2 O9 ), and  (Bi2 MoO6 ). For ammoxidation of propylene, the ˛ phase shows good NH3 activation and ˛-H abstraction. The  phase is good for the reoxidation process. Finally, the ˇ phase combines ˛ and  structures, so this phase is the most effective for ammoxidation of propylene. No report has however described the effect of the phase on the ammoxidation of acrolein to acrylonitrile yet. Metal oxides supported on mesostructured silica are widely applied in the catalysis field because of their large specific surface area, high pore volume, large pore size, and high stability [32,33]. The bismuth and molybdate precursors precipitate from their solutions upon mixing, so that a suitable method should be considered. Several reports indicated that in a strong acid, or base, or in glycerol, the mixture remains homogeneous [24,34,35]. However, strong acids or bases will change silica surface properties. In addition, glycerol has high viscosity, making it difficult for the precursors to diffuse into the pores of the mesoporous silica. Yen et al. synthesized mesostructured metal oxides using a hard-templating technique based on a dual-solvent and solid–liquid impregnation method [36]. A non-polar solvent (heptane in our work) was used for pre-wetting, so as to reduce surface tension (surface tensions of solid–gas are larger than surface tensions of solid–liquid) [36,37]. Therefore, metal salts can be easily transported inside the pores of the mesoporous silica. In addition, using this method in absence of water will reduce precipitation of precursors. Hence, the effect of surface area and the phases of the bismuth molybdate catalysts could be studied for ammoxidation of acrolein to acrylonitrile by using Yen et al. one-step impregnation catalyst preparation method. The catalysts including supported on mesoporous 3D KIT-6 and non-supported bismuth molybdate will be investigated in this work.

2. Experimental 2.1. Synthesis of bismuth molybdate catalysts Ordered mesoporous silica KIT-6 with large specific surface area, large pore size (8.1 nm), and 3D mesopore connectivity structure, synthesized, at 100 ◦ C aging temperature, according to a previous report [38] was used as support. The catalysts designed as different mixtures between Bi2 O3 and MoO3 were synthesized based on the method developed by Yen et al. [36]. Specifically, the mixtures Bi2 O3 .nMoO3 with n = 1, 2, and 3 supported on KIT-6 were designated as n1, n2, and n3, respectively. First, 1.25 g evacuated KIT-6 was pre-wetted by n-heptane, and then pre-mixed with 0.94 g of the precursors including calculated weights of bismuth nitrate Bi(NO3 )3 · 5H2 O and ammonium molybdate tetrahydrate (NH4 )6 Mo7 O24 · 4H2 O. The mixture was transferred to a round bottom flask and heated at 85 ◦ C overnight. The solids were filtered and dried at 50 ◦ C, and then calcined at 550 ◦ C for 3 h in air. In order to

compare supports, catalyst C3 was synthesized using commercial porasil silica (Milipore Corporation, 34 Maple Street, Milford, MA 01757) as support and same elemental composition as catalyst n3 active phase. In preparing the non-supported catalyst a similar impregnated silica was prepared and the KIT-6 silica support was then removed by digestion in 2M NaOH solution at room temperature (three times over one day). A total amount of 4.5 g of the mixed precursors was impregnated on 1.25 g of KIT-6. The resulting solids were filtered and calcined at 500 ◦ C for 3 h before silica removal. The final bismuth molybdate mixed oxide was then washed for several times in water and aqueous ethanol and dried at 100 ◦ C. 2.2. Characterization N2 physisorption isotherms at 77 K were measured using a Quantachrome Nova 2000 series instrument. The samples were preliminarily degassed in vacuumn at 150 ◦ C for 6 h. Specific surface area of the catalysts was calculated using the linear part of the BET plot (0.05–0.2 in relative pressure). The pore size distribution is calculated from the adsorption branch following the NLDFT (nonlocal density functional theory) method for cylinder shape. The pore volume is taken as the adsorbed nitrogen volume at 0.99 relative pressure. Wide-angle X-ray diffraction (XRD) analysis was performed with a Siemens 80 Model D5000 diffractometer using CuK˛ radiation ( = 0.15496 nm). In addition, the catalysts phases were monitored by Raman spectroscopy LABRAM HR800 (Horiba Jobin Yvon, Villeneuve d’Ascq, France) coupled with an Olympus BX30 fixed stage microscope using Ar+ laser (514.5 nm) as an excitation light source (Coherent, INNOCA 70C Series Ion Laser, Santa Clara, CA). The chemical composition of the samples was established by Inductively Coupled Plasma-Optical Emission Spectroscopy (ICPOES) using a Perkin Elmer Optima 4300DV spectrometer. 2.3. Catalysts test 50 mg of the catalysts was loaded in a fixed-bed quartz reactor (inner diameter and length 8 mm and 420 mm, respectively) at atmospheric pressure, on-line connected with a gas chromatograph (GC, HP 5890). The low catalyst mass allows avoiding hot spots. The reactants and products were analyzed using a TCD detector and Haysep P and molecular sieve 13X columns. The reactor system is shown in Fig. 1. Gas feeds including acrolein, air, ammonia, and nitrogen enter the quartz reactor through two separate inlets in order to avoid polymerization at the contact between ammonia and acrolein. One feed comprises air, ammonia (0.47 cc/min), and nitrogen diluent. Acrolein is vaporized from a 95% aqueous solution at 0 ◦ C. The acrolein vapor diluted in 25 cc/min nitrogen is fed separately. In order to investigate the effect of total flow rate (contact time) on catalytic reaction, reactant molar ratio (AC/NH3 /O2 ) was fixed whereas the diluent nitrogen flow rate was varied. All inlet gas compositions were selected outside of the flammability region (see Figs. S1 and S2 in supporting information). On the other hand, studying the effect of reactant molar ratio on catalytic performance, the flow rates of air and diluent nitrogen were changed to keep total flow rate constant (detail information in Table S1). In order to avoid condensation of polyacrolein and polyacrylonitrile, the system lines are heated (red-lines) to 180 ◦ C and several three way valves (V1, V3, V4, V5) were used. After each catalytic test, methanol is flown through part of the system for cleaning. In order to protect the GC sampling loop, the reactor exhaust is send to the vent using valves V3 and V4 between samplings. A carbon balance was calculated based on all detected products including carbon dioxide, acrolein, acetonitrile (ACE), and acrylonitrile (carbon monoxide was never detected). The reported

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Fig. 1. Schematic diagram of the catalytic ammoxidation reactor system. MFC, mass flow controller; P, pressure gauge; T, thermocouple; V2, two way ball valve, the other valves: three way ball valves.

conversion and selectivity values were obtained by averaging 3–6 measurements made at carbon balance better than 94–95%. Conv.(%) = Sel.(%) =

nAC,in − nAC,out ∗ 100 nAC,in

(1)

nACN ∗ 100 nAC,in − nAC,out

Carbon balance(%) =

(2)

3nACN + 3nAC,out + 2nACE + nCO2 3nAC,in

∗ 100

(3)

3. Results and discussion The Mo/Bi atomic ratio of the catalysts was established by ICP. The results are displayed in Table 1. They show Mo/2Bi ratios rather close to the target values. 3.1. N2 physisorption As shown in Table 1, the specific surface area of the supported catalysts are the highest reported so far [25–30]. The hysteresis loops of the supported catalysts (n1–n3) are similar to the hysteresis loop of KIT-6 as presented in Fig. 2. This indicates that the pore structure of the supported catalysts are similar to the bi-continuous pore structure of KIT-6. The supported catalysts have however no

micropore and the mesopore size was shifted to slightly smaller sizes compared to the KIT-6 template as shown in Fig. 3. This data indicates that metal oxides fill all micropores and cover the mesopore walls KIT-6. As discussed above, specific surface area (SSA) plays a key role for catalysts performance. Hence, the n1–n3 and C3 catalysts are suitable candidates for ammoxidation of acrolein to acrylonitrile. There are not much SSA difference between the supported catalysts. On the other hand, the non-supported catalyst has low SSA and pore volume. After the silica template removal, the non-supported catalyst has crystal domain size of about 15 nm (based on X-ray diffraction data). The pores of the non-supported catalyst are likely to be external pores between nanoparticles.

3.2. X-ray diffraction X-ray diffraction patterns of the catalysts are shown in Fig. 4. The non-supported, n3, and C3 catalysts have ˛ (JCPSD 21-0103) and  (JCPSD 72-1524) phases. The n2 and n1 catalysts have only  phase. The phase composition of the catalysts was confirmed by Raman spectroscopy (Fig. S3) showing same result as X-ray diffraction. Le at al. showed that obtaining the three phases of bismuth molybdate depends not only on the weight ratio of the precursors but also on calcination temperature [39]. For example, ˛ phase is created at temperature 500–650 ◦ C, whereas 600–660 ◦ C is required

Table 1 Texture properties and structure of the catalysts, * determined by ICP. Catalysts SiO2 KIT-6 Non-supported n1 n2 n3 C3 n3 (used) O2 /AC = 16.5 O2 /AC = 0.5 O2 /AC = 0

Catalyst components

SBET (m2 /g)

Pore size (nm)

Bi2 O3 · 2MoO3 Bi2 O3 · MoO3 /KIT-6 Bi2 O3 · 2MoO3 /KIT-6 Bi2 O3 · 3MoO3 /KIT-6 Bi2 O3 · 3MoO3 /SiO2

269 823 17 389 360 378 183

13.9 8.1 7.0 7.6 7.6 7.6 13.9

330 280 270

7.3 7.0 7.0

Bi2 O3 · 3MoO3 /KIT-6

Pore volume (cc/g)

XRD

Mo/2Bi*

˛+   ˛+ ˛+

1.57 0.82 1.64 2.48 2.42

1.04 1.09 0.13 0.61 0.62 0.63 0.73 0.53 0.50 0.50

˛+  + MoO2 + Bi MoO2 + Bi2 O3 + Bi

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Fig. 2. N2 physisorption isotherms of the catalysts and support KIT-6. Fig. 5. Influence of temperature on catalytic activity when reactant molar ratio AC/NH3 /O2 /N2 =1.0/1.25/16.5/158.3, F = 66 cc/min, TOS = 3.5 h.

3.3. Catalytic tests

Fig. 3. NLDFT pore size distributions (adsorption branch).

Fig. 4. X-ray patterns of the catalysts.

for ˇ phase, and 500–600 ◦ C for  phase. As mentioned above, the ˇ phase would be the best performing catalyst, but it is also known to be too fragile under ammoxidation conditions [4,31]. It may thus be expected that the n3, C3, and non-supported catalysts would perform better in the ammoxidation of acrolein.

Blank tests (glass wood instead of catalyst) were performed at temperatures from 250 to 450 ◦ C and no product was obtained. Acrolein is thermally stable at these temperatures. Some acrolein was however consumed (2%) because acrolein or polyacrolein reacts with ammonia. The effect of temperature on the catalysts activity was tested from 300 to 450 ◦ C as shown in Fig. 5. At 300 ◦ C, however the carbon balance was low (about 60–80%). There are two reasons for this phenomenon: (i) coke condenses on catalyst surface, (ii) unknown products that could not be separated by Haysep P column or yield very small peaks are obtained under these conditions. Conversion of AC continuously increases with temperature. As shown in supporting information, ACN selectivity decreases from 100% to 96–98% when the temperature rises up to 450 ◦ C and acetonitrile (ACE) and CO2 are the only by-products (Table S2). The non-supported catalyst yields only 5% AC conversion at 450 ◦ C and no conversion of AC at temperature 350 ◦ C. The n1 and n2 catalysts show similar trends for conversion and selectivity variation with temperature. AC conversion varies from 13% to 39% and 18% to 33% with n1 and n2, respectively. C3 catalytic activity is better than those of n1, n2, and non-supported catalysts. However, its activity is significantly lower than that of n3 catalyst, which has high AC conversion increasing from 30% to 84% as temperature increases from 350 to 450 ◦ C. This catalyst n3 yields the highest conversion and selectivity compared to the other catalysts reported here or in literature [20]. For example, the best SbFeO catalyst reported in [9,20] shows an ammoxidation conversion of 80% at 400 ◦ C and 0.11 s contact time, but a selectivity of 30–40% to ACN. Using catalyst n3 we observed a 84% conversion at 0.16 s contact time (calculated as GHSV−1 ) but the selectivity was 97–98%. The results shown in Fig. 5 indicate that both surface area and bismuth molybdate phase play key roles for catalytic activity. The flow rate or space velocity affects directly catalytic conversion and selectivity as well. As expected, increasing contact time will decrease selectivity and increase conversion. The results shown in Fig. 6 were obtained at 400 ◦ C and reactant molar ratio AC/NH3 /O2 = 1.0/1.25/16.5 (oxygen being fed as air). The AC conversion reduces gradually with increasing flow rate from 56 cc/min to 76 cc/min but the ACN selectivity remains 100% (Table S3). This result indicates that the reaction is limited to the primary reaction with no secondary ACN conversion (Eq. (4)). At 400 ◦ C, the

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Fig. 6. AC conversion as a function of flow rate at 400 ◦ C and molar reactant ratio AC/NH3 /O2 /N2 = 1.0/1.25/16.5/y (y values as reported in Table S1), TOS = 3.5 h.

selectivity is not dependent on contact time. As discussed above only increasing temperature to 450 ◦ C affected selectivity. CH2 CH − CHO + NH3 +

1 O2 → CH2 CH − C N + 2H2 O 2

(4)

The influence of oxygen concentration on AC ammoxidation was investigated over catalyst n3 at 450 ◦ C and 66 cc/min total flow rate. The molar ratio of the gas feed is AC/NH3 /O2 /N2 = 1.0/1.25/x/y (see Table S1 for y values). Nitrogen flow rate was adjusted to keep the volume flow rate constant. Then the GHSV remains constant but the WHSV changed slightly from 304 to 309 h−1 due to slight differences in gas density with composition as molar ratio of O2 /AC was varied from 0 to 21.5 (Tables S1 and S4). As shown in Fig. 7, AC conversion showed a sharp increase with x ranging from 0 to 2.5. It then increased slowly when x got higher than 2.5 and it was almost unchanged with x above 9.5. The results indicate that oxygen concentration has a strong effect on catalytic reaction rate. Catalyst n3 is still active in absence of oxygen in the gas feed and the observed conversion was constant over 3.5 h. This activity was found equal to the one obtained at stoichiometric ratio x = 0.5. It is therefore likely that the reaction makes use of the catalyst oxygen atoms (MarsVan Krevelen mechanism) and that the role of gaseous oxygen is to reoxidize the catalyst. A quick calculation of the number of atoms of oxygen consumed over 3.5 h yields an estimate of 1.4 ×10−3 O

Fig. 7. Effect of oxygen on AC conversion at 450 ◦ C and F = 66 cc/min over catalyst n3.

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Fig. 8. Effect of oxygen in gas feed on catalyst structure. The numbers below patterns indicate molar ratio of the O2 /AC, TOS = 3.5 h.

atoms. The total number of oxygen atoms in the 50 mg of catalyst n3 (15 mg of Bi2 Mo3 O12 ) is estimated to 0.2 ×10−3 O atoms. It is therefore likely that the traces of water present in the feed contributed to catalyst reoxidation. It was also observed that at low oxygen content (x ≤ 0.5) the color of the catalyst turned to black over 30 min. This change may be due either to catalyst reduction or coking. The presence of coke is also accompanied by a decrease in SSA and pore volume of the catalyst as observed experimentally (see Table 1). X-ray diffraction patterns of the fresh catalyst and the ones used at different O2 /AC ratios are shown in Fig. 8. The pattern of the fresh (n3) catalyst is same as the one obtained after a test at high amount of oxygen in feed (x = 16.5). However, reducing oxygen in feed to the stoichiometric value of 0.5, bismuth molybdate was partly reduced to MoO2 (JCPDS 76-1807) and Bi (JCPDS 44-1246). In absence of oxygen, the solid contains only Bi, Bi2 O3 (JCPDS 27-0050), and MoO2 , and no mixed bismuth molybdate phases. These results demonstrated that the mixed ˛ and  phases are necessary for catalytic activity. The stability of the n3 catalyst was tested at 450 ◦ C and 66 cc/min with molar ratio AC/NH3 /O2 /N2 = 1.0/1.25/16.5/158.3 (GHSV = 22,500 h−1 ) (Fig. 9). Catalyst n3 reaches steady state after about 1 h on stream. AC conversion and ACN selectivity keep constant to about 84% and 97%, respectively. After 12 h, n3 catalyst showed no sign of deactivation.

Fig. 9. Catalytic activity stability test; reactant AC/NH3 /O2 /N2 = 1.0/1.25/16.5/158.3, 450 ◦ C, F = 66 cc/min.

molar

ratio

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4. Conclusions In summary, simple bismuth-molybdate supported on KIT-6 catalysts were synthesized showing high activity, selectivity, and stability compared to previously reported catalysts such as SbVO4 , AsFeO, and SbMoO. The n3-supported catalyst with large specific surface area and mixed phases, showed the highest AC conversion (84%) and ACN selectivity (97%). This demonstrated that the surface active and synergistic phases play a vital role for catalytic ammoxidation of AC to ACN. In addition, the reaction temperature also has some influence on catalytic activity and selectivity. Other factors such as contact time and molar ratio of reactants affect only reaction rate as expected. Acknowledgments The authors gratefully acknowledge financial support of The Consortium de Recherche en Biotechnologie Industrielle du Québec and MITACS. We also thank Dr. Hoang Vinh-Thang and Mr. Gilles Lemay for help in setting up the system and for interesting discussions. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.apcata.2016.03. 030. References [1] The Sohio acrylonitrile process: BP Chemicals Inc., Warrensville Heights, Ohio: A National Historic Chemical Landmark, September 13, 1996, American Chemical Society, Washington, DC, 1996. [2] The Sohio Acrylonitrile Process: INEOS in League City, Texas: A National Historic Chemical Landmark, November 14, 2007, American Chemical Society, League City, TX, 2007. [3] World petro chemical analysis acrylonitrile, 2014 https://www.ihs.com/ (Retrieved products/world-petro-chemical-analysis-acrylonitrile.html October 2014). [4] R.K. Grasselli, M.A. Tenhover, Ammoxidation, Wiley-VCH Verlag GmbH & Co. KGaA, 2008, http://dx.doi.org/10.1002/9783527610044.hetcat0178. [5] B. Katryniok, S. Paul, F. Dumeignil, ACS Catal. 3 (8) (2013) 1819–1834, http:// dx.doi.org/10.1021/cs400354p. [6] J.-L. Dubois, Method for the synthesis of acrylonitrile from glycerol, 2007, February, US 8829223 B2. [7] J.-L. Dubois, Method for the synthesis of acrylonitrile from glycerol, 2010, February, US 20100048850A1. [8] K. Takaaki, K. Minoru, Method of producing acrylonitrile, 2012, February, JP5761940B. [9] C. Liebig, Indirect Ammoxidation of Glycerol into Acrylonitrile Via the Intermediate Acrolein, Diss. RWTH Aachen University, 2013. [10] M.O. Guerrero-Pérez, J.M. Rosas, J. Bedia, J. Rodriguez-Mirasol, T. Cordero, Recent Patents Chem. Eng. 2 (1) (2009) 11–21 (2009-01-01T00:00:00). http:// www.ingentaconnect.com/content/ben/cheng/2009/00000002/00000001/ art00002.

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