Reaction kinetics analysis of branched-chain alkyl esters of palmitic acid and cold flow properties

Renewable Energy 147 (2020) 719e729

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Renewable Energy journal homepage: www.elsevier.com/locate/renene

Reaction kinetics analysis of branched-chain alkyl esters of palmitic acid and cold flow properties Zihao Ni a, b, Yuling Zhai a, b, *, Fashe Li a, b, *, Hua Wang a, b, Kai Yang a, b, Bican Wang a, b, Yu Chen a, b a b

Faculty of Metallurgical and Energy Engineering, Kunming University of Science and Technology, Kunming, Yunnan, 650093, China State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization, Kunming, Yunnan, 650093, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 3 October 2018 Received in revised form 24 June 2019 Accepted 30 August 2019 Available online 4 September 2019

Preparation of methyl palmitate, isopropyl palmitate, isobutyl palmitate, and isoamyl palmitate was carried out using pyridine n-butyl bisulfate ionic liquid as catalyst in a self-designed reactor to catalyze esterification reaction of palmitic acid with methanol, isopropanol, isobutanol, and isoamyl alcohol, respectively. According to the single-factor experimental results, an orthogonal test of four factors and three levels was carried out for branched-chain alkyl esters of palmitic acid under different reaction time, reaction temperature, and catalyst dosage. Verification test was conducted under the optimal conditions, and the conversion in all the cases was up to 97%. Analysis of the reaction kinetics of methyl palmitate, isopropyl palmitate, isobutyl palmitate, and isoamyl palmitate was carried out by the integral method. Reaction order, frequency factor, activation energy, and reaction kinetic model were determined. Compared to methyl palmitate, the kinematic viscosity of the branched-chain alkyl esters of palmitic acid was slightly higher; however, the solidifying point (SP) and cold filter plugging point (CFPP) decreased with increasing degree of branched-chain. The CFPP reduced by up to 15
C. Therefore, the use of branched-chain alcohol instead of methanol ester exchange descaling method can effectively reduce the SP and CFPP of biodiesel to improve its cold flow properties. © 2019 Published by Elsevier Ltd.

Keywords: Ionic liquid Reaction kinetic analysis Integral method Cold flow properties Solidifying point

1. Introduction With shrinking of fossil energy reserves due to increasing global energy demand, biodiesel, as a type of biofuel, has a certain potential to replace petrochemical diesel and meet the energy demand worldwide [1e3]. The quality of biodiesel is regulated by standards, the two most utilized being ASTM D6751 in the United States and EN 14214 in the European Union [4]. However, a critical inherent problem that currently limits the utilization and popularization of biodiesel is its relatively poor cold flow properties. In cold weather, the engine blocks the oil path and cannot guarantee stable output power. Low-temperature crystallization and gelation limit the applications of biodiesel. Therefore, investigation of the cold filter plugging point (CFPP) of biodiesel has always been an

Abbreviations: CFPP, Cold filter plugging point; CP, Cloud point; PP, Pour point; SP, Solidifying point. * Corresponding authors. Faculty of Metallurgical and Energy Engineering, Kunming University of Science and Technology, Kunming, Yunnan, 650093, China. E-mail addresses: [email protected] (Y. Zhai), [email protected] (F. Li). https://doi.org/10.1016/j.renene.2019.08.138 0960-1481/© 2019 Published by Elsevier Ltd.

important research topic [5,6]. Cold flow properties of biodiesel are related to the saturated fatty acid methyl ester content. The presence of saturated fatty acids demonstrate poor cold flow properties. The polyunsaturated fatty acids exhibit better cold flow properties [7e9]. At present, many techniques are used to overcome this problem. Several researchers reported the use of additives to curtail its intermolecular structure and diminish the crystallization temperature. Dunn et al. [10] studied the effects of 12 pour point depressants (PPDs) sold in the market on the low temperature performance of soybean oil biodiesel. Studies have shown that PPD 8500 Winter flow can reduce the pour point by 6
C; however, they do not have any effect on cloud point. Huang et al. [11] experimentally studied the effect of PPD, polyglycerol ester (PGE), and other additives on the low temperature performance of palm oil biodiesel. Makarevi
ciene_ et al. [12] reported the possibility of improving the cold flow properties of biodiesel fuel by mixing with butanol. Ranjan et al. [13] added petrochemical diesel oil and magnesium oxide (MgO) nanoparticles (NPs) to biodiesel, and found that cold flow properties were better after adding MgO NPs.

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Joshi et al. [14] added ethyl levulinate diluent to reduce the biodiesel freezing point and cold filter point, improving the cold flow properties. Furthermore, another strategy to improve the cold flow properties of biodiesel has been reported using alcohols with longer carbon chain instead of methanol. The method used branched alcohol instead of methanol ester exchange and found that it can effectively reduce the solidifying point (SP) and CFPP of biodiesel and improve cold flow properties of biodiesel [15,16]. Smith et al. [17] showed that the long-chain alkoxylates in biodiesel were able to lower cold flow properties of oils. Lee et al. [18] reported that branched-chain esters significantly reduced the crystallization onset temperature of neat esters and their corresponding ester diesel fuel blends. Isopropyl and 2-butyl esters of normal (~10 wt% palmitate) soybean oil (SBO) crystallized 7e11 and 12e14
C lower, respectively, than the corresponding methyl esters. Knothe et al. [19] reported that the introduction of longchain alcohols or branched-chain alcohols affected the lowtemperature flow properties of the biodiesel during biodiesel synthesis. The reaction kinetics was used to study the effect of various physical and chemical factors such as temperature, pressure, concentration, medium in the reaction system, catalyst, flow field, temperature field distribution, and residence time distribution on the reaction rate and the corresponding reaction mechanism. It was also used to study the chemical reaction rate and the conditions that affect the reaction rate. The relationship between the material structure and the reaction was investigated to control the chemical reaction. The methods for determination of the reaction orders are as follows: integral method, half-life method, isolation method, and differential method. Bla
z Likozar et al. [20e22] studied chemical equilibrium, and reaction kinetics and mass transfer were modeled for the trans-esterification of oil to biodiesel in a continuous tubular reactor with static mixers. Furthermore, they also presented a model for the transesterification of different oils and alcohols, based on fatty acid composition of tri-(TG), di-(DG), and monoglycerides (MG); and alkyl esters (AE) (biodiesel), acknowledging chemical equilibrium, reaction kinetics and mass transfer. J. M. Encinar1 et al. [23] studied the acceleration that ultrasound causes in the rate of biodiesel transesterification reactions. The transesterification reactions followed a pseudo-first order kinetic model and the rate constants at several temperatures were determined. P.A. Martínez et al. [24] discussed kinetic and thermodynamic parameters of the non-catalytic supercritical methanol transesterification to biodiesel of the vegetable oils. Three different integral kinetic models (pseudo-zero, pseudo-first and pseudosecond order kinetic models) were fitted to the experimental data in order to determine the best reaction order. Methyl palmitate is the main component of biodiesel and also an important chemical intermediate. It has diverse application fields, for example, it can be used as raw material to synthesize various surfactants, detergents, and many other chemicals and an additive for advanced lubricating oils, machined cutting oils, and cooling fluid, etc. [25e27]. Traditional esterification reaction mainly uses strong acid such as sulfuric acid and p-toluenesulfonic acid as catalyst. These catalysts are highly corrosive, demanding on equipment, and the catalyst cannot be reused. The waste liquid generated is expensive to process, and direct discharge results in environment pollution. This has prompted the researchers to explore environmentally friendly catalysts. Ionic liquids (ILs) are a class of low-melting organic compounds composed entirely of anions and cations. Compared to conventional solvents, ILs have solubility similar to that of organic and inorganic solvents and are therefore often used as reaction solvents. Recently, various functionalized ILs have been widely used as catalysts for chemical reactions. In this study, long-chain alcohol containing branched chain

was used for transesterification reaction, the biodiesel ester-based structure was changed, and the difference in spatial structure was used to improve the cold flow properties, which provided theoretical and data support for biodiesel industrial preparation and optimization of cold flow properties index. 2. Materials and methods 2.1. Materials and reagents The materials used in this study are as follows: palmitic acid, isobutanol, anhydrous ethanol, ethyl acetate, petroleum ether, potassium hydroxide, potassium hydrogen phthalate, and phenolphthalein were of analytical grade, and sulfuric acid (99.8%). The detailed of suppliers of chemicals are listed in Table 1. 2.2. Test apparatus The following test apparatus was used in the testing process. In addition, the macro programming function in Microsoft Excel 2016 version (16.0.4266.1001)64, ID (00339-10000-00000-AA026) was used. The model and manufacturer of major test apparatus are listed in Table 2. 2.3. Test methods 2.3.1. Preparation method of ionic liquid Pyridine and n-butyl bromide were added to a three-necked flask at a molar ratio of 1:1.5 and magnetically stirred under nitrogen atmosphere for 12 h, until an ionic liquid intermediate was obtained as a white solid. The white solid was dissolved in anhydrous ethanol. To that, activated carbon was added, stirred, and filtered. The filtrate was evaporated under reduced pressure to remove anhydrous ethanol, washed with ethyl acetate and petroleum ether and kept in a vacuum drying oven for 6 h to obtain light yellow viscous liquid as ionic liquid intermediates. The light yellow viscous liquid and concentrated sulfuric acid in equal mass were placed into the flask and magnetically stirred under nitrogen atmosphere for several hours until viscous light yellow was formed. The yellow liquid was washed with ethyl acetate, followed by petroleum ether, and dried in a vacuum drying oven for 6 h, affording yellowish or orange-colored viscous liquid. This liquid was used as the catalyst for the esterification reaction in pyridine n-butyl bisulfate ionic liquid [28]. The synthesis of pyridine n-butyl bisulfate ionic liquids is shown in Fig. 1. 2.3.2. Synthesis of branched-chain alkyl esters of palmitic acid Mechanism of esterification reaction between palmitic acid and branched alcohol is shown in Fig. 2. This esterification reaction is reversible; therefore, in the process, the branched chain alcohol was used in excess for the reaction to proceed in the forward direction for producing more branched-chain alkyl esters of palmitic acid as the target product. Esterification reaction procedure: A certain proportion of palmitic acid, branched alcohol, and catalyst were put into a 250-mL three-necked flask equipped with a thermometer, stirrer, and condensation reflux device. The flask was heated under reflux in a constant temperature oil bath. After the reaction, ethyl acetate and petroleum ether were removed by reduced pressure rotary distillation, and the unreacted branched alcohol was recovered by distillation. Finally, the catalyst was separated from the final product by washing with deionized water, and the reaction product was placed into a vacuum drying oven for drying for several hours to afford branched-chain alkyl esters of palmitic acid and unreacted palmitic acid.

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Table 1 Suppliers of chemicals and their countries. Chemicals

Reagent grade

Supplying company and the Country

Palmitic acid Isopropanol Isobutanol Isoamyl alcohol Pyridine n-butyl bromide Ultrapure water Anhydrous ethanol Ethyl acetate Petroleum ether Potassium hydroxide Potassium hydrogen phthalate Phenolphthalein

Analytical Analytical Analytical Analytical Analytical Analytical Analytical Analytical Analytical Analytical Analytical Analytical Analytical

Sinopharm Chemical Reagent Co., Ltd. Tianjin, China Tianjin Chemical Reagent Technology Co., Ltd. Tianjin, China Tianjin Chemical Reagent Technology Co., Ltd. Tianjin, China Tianjin Chemical Reagent Technology Co., Ltd. Tianjin, China Tianjin Chemical Reagent Technology Co., Ltd. Tianjin, China Tianjin Chemical Reagent Technology Co., Ltd. Tianjin, China PURELAB Classic Ultrapure Water Generator (ELGA Lab Water, UK) Kemiou Pharmaceutical Chemical Co., Ltd. Tianjin, China Kemiou Pharmaceutical Chemical Co., Ltd. Tianjin, China Kemiou Pharmaceutical Chemical Co., Ltd. Tianjin, China Nanjing Chemical Reagent Co., Ltd. Nanjing, China Zhiyuan Chemical Reagent Co., Ltd. Tianjin, China Sinopharm Reagent Group. Shanghai, China

grade grade grade grade grade grade grade grade grade grade grade grade grade

Table 2 The model and manufacturer of major test apparatus. Test apparatus

Model

Manufacturer

Ultrasonic cleaner Petroleum product kinematic viscosity tester Digital temperature oil bath Acid automatic titrator Condensation Cold Filter Point Tester Fourier transform infrared spectrometer Rotary steam evaporator Electric blast drying oven Ultrapure water generator Electronic balance

SK5200HP SYD-256D 602B ZDJ-5 SYD-510F Nicolet iS-10 R-215 101A-1 PURELAB FA604

Shanghai Branch Ultrasonic Instrument, China Shanghai Changji Geological Instrument Co., Ltd., China Jintan Dadi Automatic Instrument Factory, China Shanghai Changji Geological Instrument Co., Ltd., China Shanghai Changji Geological Instrument Co., Ltd., China FTIR, Thermo Fisher Scientific. America BUCHI, Switzerland Shanghai Chongming Experimental Instrument Co., Ltd., China British EL-GA Lab Water Shanghai Balance Instrument Factory

phenolphthalein were added and titrated with KOH-ethanol standard solution. At this time, KOH-ethanol standard solution with volume V2 was added.

AV ¼

Fig. 1. Schematic diagram of synthetic pyridine n-butyl bisulfate ionic liquid.

CKOH  V2  56:1 m2

(2)

Acid values of the palmitic acid and the branched-chain alkyl esters of palmitic acid were analyzed and determined. The conversion was calculated according to the following formula:

Conversion ¼

Fig. 2. Chemical equation of esterification reaction between palmitic acid and branched alcohol.

2.3.3. Calculation of conversion First, KOH (6 g) was weighed into a 1000-mL solution of ethanol (95%), sealed, placed until the solution was clarified, filtered, and the filtrate was transferred to a 1000-mL reagent flask. Then KOHethanol standard solution (0.1 mol L1) was formed. Second, potassium hydrogen phthalate (0.4e9.5 g) was weighed at 110
C to a constant weight and dissolved in CO2-free water (50 mL). Further, two drops of phenolphthalein indicator were added, titrated with the configured KOH-ethanol solution until the solution became red, and the consumption volume V1 was noted:

CKOH ¼

m1 V1  204:2

(1)

Third, oil ester (0.4e0.6 g) was added into neutral ethanol (50 mL), it was then shaken to dissolve. Further, three drops of

AV0  AV  100% AV

(3)

where CKOH is the concentration of 0.1 mol L1 KOH-ethanol standard solution; V1 and V2 are volumes of KOH-ethanol standard solution; m1 is mass quality of potassium phthalate, and m2 is the mass of oil ester. AV0 and AV are the acid values of the initial raw material and of the reaction product, respectively.

2.3.4. Method for the cold flow properties Indicators for evaluating cold flow properties of biodiesel generally follow the specifications of diesel fuel, and these indicators include SP, PP, and CFPP. SP refers to the maximum temperature when the oil level of the cooled sample does not move under the specified conditions. If the PP or SP is too high, the cold flow properties of the oil product are poor. The CFPP refers to the maximum temperature when the oil passes through the filter at a rate less than 20 mL min1. The lower the CFPP, the more difficult it is to crystallize biodiesel. In cold weather, the engine will not block oil passages, thus ensuring a stable output power, which has practical guiding significance for the use of diesel [29e31]. SP was detected using GB (GB T510-1983). The CFPP was determined using industry standards (SH/T0248-2006). Kinematic viscosity was determined using GB (GB/T265-1988).

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3. Results and discussion

100

3.1. Single factor test of methyl palmitate

3.1.2. Study on the effect of reaction temperature on conversion Under the following conditions: molar ratio of methanol to palmitic acid 50:1, catalyst dosage 6%, and reaction time of 90 min, effect of reaction temperature on conversion was investigated, and the results are shown in Fig. 4. With a gradual increase in temperature, the conversion gradually increases, mainly because the conversion is slower at lower reaction temperature and the reaction temperature can increase the conversion. However, when the reaction temperature reaches 70
C, the conversion reaches the maximum. Further, with the continuous increase in the reaction temperature, the conversion decreases Boiling point of methanol is 64.7
C. When the reaction temperature is 70
C, i.e., the temperature reaches the boiling point of methanol, then methanol is released from the reaction solution and partially stays in the upper portion of the flask, thus leading to a decrease in the methanol concentration in the reaction solution. Rate of the reaction decreases, and conversion is lowered. Therefore, the optimum reaction temperature is 70
C. 3.1.3. Study on the effect of molar ratio of methanol to palmitic acid on conversion The effect of molar ratio of methanol to palmitic acid on conversion was investigated under the optimal reaction conditions

95

Conversion(%)

3.1.1. Study on the effect of reaction time on conversion Under the following conditions: molar ratio of methanol to palmitic acid 50:1, catalyst dosage 6%, and reaction temperature 65
C, effect of reaction time on the conversion was evaluated and shown in Fig. 3 conversion increases with the reaction time and reaches equilibrium at 110 min. With increasing extent of reaction, the conversion remains basically unchanged, because the reaction time is the main factor affecting the conversion of the reversible reaction. When the reaction time is shorter, the conversion increases rapidly with the reaction time. However, after the reaction time reaches a certain level, the esterification reaction gets completed. When the reaction time is 110 min, the conversion reaches 96.54%, and the reaction time is prolonged. The effect on the conversion of the esterification reaction is not obvious. Therefore, the optimum reaction time for the esterification reaction is 110 min.

85

80

55

60

65

70 Temperature

75

80

85



Fig. 4. Effect of reaction temperature on conversion.

(reaction temperature 70
C, catalyst dosage 6%, and reaction time 90 min), and the results are shown in Fig. 5. The conversion increases with increasing molar ratio of methanol to palmitic acid and reaches the maximum at the molar ratio of 50:1. When the molar ratio of methanol to palmitic acid was higher than 50:1, the conversion decreased with increasing molar ratio of methanol to palmitic acid. This is mainly attributed to the fact that the esterification is a reversible reaction, and the concentration of reactants increases with increasing molar ratio of methanol to palmitic acid, increasing the progress of the forward reaction, and thus increasing the conversion. However, when excess methanol was added, the concentration of palmitic acid reactant decreased to a certain extent, inhibiting the forward reaction, thus decreasing the conversion. Therefore, the molar ratio of methanol to palmitic acid should be maintained at 50:1. 3.1.4. Study on the effect of catalyst dosage on conversion The effect of catalyst dosage on the esterification reaction was investigated under the following optimum conditions: molar ratio

100

100

90

90

80

Conversion(%)

Conversion(%)

90

70

80

70 60

50

50

70

90

110 130 150 Time min

170

Fig. 3. Effect of reaction time on conversion.

190

210

60

10

20

30

40

50

60

The molar ratio of methanol to palmitic acid Fig. 5. Effect of molar ratio of methanol to palmitic acid on conversion.

70

Z. Ni et al. / Renewable Energy 147 (2020) 719e729

increasing catalyst dosage, the conversion gradually increased. However, when the catalyst dosage was >6%, the conversion started to decrease. Use of polar adjustable feature of IL can increase the mutual solubility of IL, methanol, and palmitic acid, thus leading to the enhancement in the conversion. However, excessive use of catalyst led to the gradual decrease in the conversion, making the process more complex, handling of products difficult, and causing greater environmental pollution [32]. Therefore, the optimal catalyst dosage was maintained at 6% in the subsequent experiments.

100 95

Conversion(%)

90 85 80 75

3.2. Orthogonal test

70

According to the single-factor experimental results, an orthogonal test of four factors and three levels was carried out for molar ratio of methanol to palmitic acid, reaction time, reaction temperature, and catalyst dosage. The test design of optimized reaction conditions is presented in Table 3. The test results and analysis are summarized in Table 4. By analyzing the size of the extreme R from Table 4, the factor order is as follows: C > D > A > B, indicating that the catalyst dosage is the main factor affecting the conversion, followed by the reaction time and reaction temperature, and finally the molar ratio of methanol to palmitic acid. The optimized level was C3D3A2B2; optimum catalyst dosage was 8%, reaction time was 130 min, molar ratio of methanol to palmitic acid was 50:1, and reaction temperature was 70
C. The test according to this condition did not appear in the nine tests of the orthogonal test Table. By conducting a supplementary verification test, the conversion was 98.63%, which was greater than the maximum value of 97.37% in the orthogonal test results. At the same time, the optimal reaction conditions for isopropyl palmitate, isobutyl palmitate, and isoamyl palmitate were also obtained under the effects of reaction temperature, reaction time, molar ratio of alkyl alcohol, and catalyst dosage. The test results are presented in Table 5.

65 60

0

2

4

6

8

10

12

Catalyst dosage(%) Fig. 6. Effect of catalyst dosage on conversion.

Table 3 Factor level table of orthogonal test. Level

1 2 3

723

A

B

C

D

Temperature/
C

Molar ratio of methanol to palmitic acid

Catalyst dosage/%

Time/min

65 70 75

40:1 50:1 60:1

4 5 6

90 110 130

Table 4 Analysis and computation table of orthogonal test. Test number

A

B

C

D

conversion/%

1 2 3 4 5 6 7 8 9 K1 K2 K3 k1 k2 k3 R Optimization

1 1 1 2 2 2 3 3 3 275.82 284.79 283.60 91.94 94.93 94.53 8.97 A2

1 2 3 1 2 3 1 2 3 278.01 285.14 281.06 92.67 95.05 93.69 7.13 B2

1 2 3 2 3 1 3 1 2 269.64 283.32 291.25 89.88 94.44 97.08 21.61 C3

1 2 3 3 1 2 2 3 1 273.16 283.46 287.59 91.05 94.49 95.86 14.43 D3

84.14 94.51 97.17 96.50 96.71 91.58 97.37 93.92 92.31

3.3. Infrared characterization of branched-chain alkyl esters of palmitic acid Fig. 7 exhibits the infrared (IR) spectrum of methyl palmitate. The absorption peaks at 2916.63 and 2848.60 cm1 correspond to the asymmetric and symmetric telescopic vibrations ofeCH2e, respectively. The absorption peak at 1739.39 cm1 is the characteristic absorption peak of carboneoxygen double bond in the ester, indicating the presence of ester bond in the product, and confirming the esterification reaction between the alcohol and palmitic acid. The absorption peak at 1462.86 cm1 corresponds to the methylene bending vibration and methyl asymmetric bending vibration. The peak at 1381.40 cm1 can be j attributed to the stretching vibration absorption peak of H3 C  CHCH2 CH3 . The absorption peak at 1170.45 cm1 is attributed to the asymmetric stretching CeOeC vibration. The absorption peak at 719.68 cm1 is assigned to the oscillation of e(CH2)ne. Thus, the IR spectrum confirms the product to be methyl palmitate. The IR spectra of isopropyl palmitate, isobutyl palmitate, and isoamyl palmitate are shown in Fig. 8.

of methanol to palmitic acid 50:1, reaction temperature 70
C, and reaction time 90 min. The results are shown in Fig. 6. The catalyst dosage was found to positively correlate with the conversion. With

Table 5 Optimum reaction conditions of branched-chain alkyl esters of palmitic acid. Esters

Time

Temperature

Molar ratio of alkyl alcohol

Amount of catalyst

conversion

Methyl Palmitate Isopropyl Palmitate Isobutyl Palmitate Isoamyl Palmitate

130 120 60 60

70 80 100 90

50:1 8:1 5:1 20:1

8% 6% 5% 6%

98.63% 97.12% 98.79% 98.35%

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Z. Ni et al. / Renewable Energy 147 (2020) 719e729

1.0

0.8

Conversion



 

0.4

    

0.2



 

  

0.6

0.0 4000

3500

3000

2500

2000

1500

1000

500

0

-1

Wavenumber( cm )

10

20

30

40

50

60

WPLQ

Fig. 7. FTIR spectrum of methyl palmitate. Fig. 9. The relationship between reaction time t and conversion of methyl palmitate.

Isopropyl Palmitate A Isobutyl Palmitate B Isoamyl Palmitate C

1 2

C

[) Q

3

B

A

4

    

5 6 7

4000

3500

3000

2500

2000

1500

1000

500

8

-1

Wavenumber( cm )

0

10

Fig. 8. IR spectra of branched palmitic acid esters.

3.4.1. Determination of reaction orders and reaction rate equation The integration method was used to determine the chemical reaction orders of esterification of methyl palmitate. Esterification Equation (4) is represented as follows: catalysts

⇔

CH3 ðCH2 Þ14 COOCH3 þ H2 O (4)

t¼0 t¼t

CB0

CA0 CA

CB

0 CC

30

WPLQ

40

50

60

Fig. 10. The relationship between ð1  XÞð1nÞ and reaction time t at different reaction temperatures.

3.4. Analysis of reaction kinetics

CH3 ðCH2 Þ14 COOH þ CH3 OH

20

Table 6 Chemical reaction orders、rate constant and correlation coefficient of esterification reaction. Temperature/
C Reaction Orders n Rate Constant K Correlation Coefficient R2 60 65 70 75 80

1.730 1.797 1.821 1.856 1.881

0.0541 0.0691 0.1216 0.2105 0.2621

0.9810 0.9898 0.9903 0.9940 0.9944

0 CD

The rate equation for methyl palmitate formation can be expressed as follows:

rA ¼ k1 C aA C bB  k2 C cC C dD

(5)

where k1 and k2 are the rate constants of the forward and backward reactions, respectively; a and b are the number of the reaction

Z. Ni et al. / Renewable Energy 147 (2020) 719e729

-1.0

orders of the forward reaction of palmitic acid and methyl, respectively; c and d are the number of reaction orders of the backward reaction of methyl palmitate and water, respectively. Owing to the presence of excess amount of methanol in the reaction, the reaction can be considered as a negligible reaction and thus can be expressed as follows:

0HWK\O 3DOPLWDWH

rA ¼ k1 C aA C bB

5 

rA ¼ KC nA

-2.5

(7)

among K ¼ k1 C bB The conversion of methyl palmitate is defined as X; the initial concentration is CA0 , the concentration of palmitic acid in the reaction system at any time is CA , then CA ¼ CA0 ð1  XÞ 2,840

2,880

2,920

2,960

7( h.)

3,000

rA ¼ 

Fig. 11. Relationship between ln (K) and.1 =T

dCA d½C ð1  XÞ dX ¼ CA0 ¼ KC nA ¼  A0 dt dt dt

Then:

1.0

1.0 1.2

0.6

1.4

[ Q

0.8

    

0.4

0.2

1.6

    

1.8 2.0

0.0

2.2 0

10

20

30

40

50

0

60

10

20

30

(a) Relationship between t and conversion

50

60

and t at different temperatures

(b)

Isopropyl Palmitate

-2.7

-3.0

5  Q 

-3.3

-3.6

-3.9 270

40

WPLQ

WPLQ

,Q .

-3.0 2,800

(6)

where k1 C bB is a constant. Equation (6) can be transformed into:

Q 

Conversion

OQ .

-1.5

-2.0

725

280

290

300

310

320

7h.

(c) Relationship between ln (K) and Fig. 12. Analysis of reaction kinetics of isopropyl palmitate.

(8)

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Z. Ni et al. / Renewable Energy 147 (2020) 719e729

dX K ¼ ½C ð1  XÞn dt CA0 A0

in Fig. 9. ð1  XÞð1nÞ values at different reaction times were obtained, and the obtained data are plotted in Fig. 10. Calculate the reaction orders, rate constant, and correlation coefficient at different temperatures for methyl palmitate. The chemical reaction orders, rate constant, and correlation coefficient of esterification reaction are listed in Table 6.

(9)

dX K ¼ dt ð1  XÞn C 1n A0

(10)

Integrating both sides of Eq. (10) leads to the following equation:

ð1  XÞ1n ¼

Kðn  1Þ C 1n A0

t

3.4.2. Esterification activation energy Arrhenius equation can be expressed as follows: Ea

K ¼ AeRT

(11)

Eq. (11) shows that ð1  XÞð1nÞ is linear with t. When n ¼ 1, lnð1 XÞ and t have a linear relationship; when n s 1, ð1  XÞð1nÞ is linear with t. The correlation coefficient can be calculated for different values of n. At maximum correlation coefficient, n is the reaction order. Herein, the macro programming function in Microsoft Excel 2016 version (16.0.4266.1001)64, ID (0033910000-00000-AA026) was used. The maximum correlation coefficient R2 was determined as the target in the solution. The reaction order n is variable. Based on this function, the optimal value of n can be determined to make two sets of data with a maximum linear correlation. According to the experimental data, the conversion of methyl palmitate at different temperatures was plotted, as shown

(12)

where K is the reaction rate constant; A is the frequency factor; Ea (kJ mol1) is the activation energy; and R is the universal gas constant 8.314 J mol1 K1 [33]. Taking the logarithm of both sides of Eq. (12) leads to the following equation:

lnðKÞ ¼ 

Ea þ ln A RT

(13)

Eq. (13) shows that relationship between ln (K) and 1 =T is linear. According to the reaction rate constant at different temperatures, the corresponding ln (K) values can be obtained, and the relationship between ln (K) and 1 =T can be plotted, as shown in Fig. 11.

1.0 1.5 3.0

0.6

4.5

0.2

(1-x)

0.4

1-n

    

    

6.0 7.5 9.0

0.0 0

10

20

30

t/min

40

50

10.5

60

0

10

20

30

40

50

t/min

(a) Relationship between t and conversion

and t at different

(b)

temperatures -0.5

Isobutyl Palmitate -1.0

-1.5

,Q .

Conversion

0.8

5  Q 

-2.0

-2.5

-3.0 2600

2650

2700

2750

2800

2850

2900

2950

7h.

(c) Relationship between ln (K) and Fig. 13. Analysis of reaction kinetics of isobutyl palmitate.

60

Z. Ni et al. / Renewable Energy 147 (2020) 719e729

methyl palmitate was 1.82. The reaction kinetic model of the reaction can be expressed as follows:

From the graph,

ln ðKÞ ¼ 

727

10039:96 þ 27:16 T

(14)

83:47 dc  A ¼ 6:27  1011 e RT c1:82 A dt

The activation energy was calculated as Ea ¼ 10039:96; R ¼ 83:47KJ=mol from the slope of the equation, and the frequency factor can be obtained from the intercept as A ¼ 6:27  1011 . By taking the average of the reaction orders under each condition, the reaction orders of the esterification reaction of

(15)

Similarly, the reaction kinetic analyses of isopropyl palmitate, isobutyl palmitate, and isoamyl palmitate are shown in Figs. 12e14, respectively. The reaction orders, activation energy, and reaction kinetic model of branched-chain alkyl esters of palmitic acid are

1.0 1.5

0.8

0.6

    

0.4

0.2

[ Q

Conversion

3.0

4.5

    

6.0

7.5

0.0 0

10

20

30

40

50

9.0

60

0

10

20

30

40

50

60

WPLQ

WPLQ

(a) Relationship between t and conversion

and t at different

(b)

temperatures

-1.2

Isoamyl Palmitate

,Q .

-1.5

-1.8

5  Q 

-2.1

-2.4

-2.7 270

280

290

300

7h.

310

(c) Relationship between ln (K) and Fig. 14. Analysis of reaction kinetics of isoamyl palmitate.

Table 7 Reaction orders, activation energy, and reaction kinetic model of branched-chain alkyl esters of palmitic acid. Esters

Reaction Orders

Activation Energy(kJ mol1)

Correlation Coefficient (R2)

Reaction kinetic Model

Methyl Palmitate

1.817

83.472

0.9885

83:47 dCA ¼ 6:27  1011 e RT C 1:82 A dt 28:26 dCA ¼ 801:22e RT C 1:23  A dt 56:84 dCA ¼ 2:70  107 e RT C 1:49  A dt 38:62 dCA ¼ 7:72  104 e RT C 1:58  A dt 

Isopropyl Palmitate

1.232

28.259

0.9924

Isobutyl Palmitate

1.491

56.844

0.9907

Isoamyl Palmitate

1.576

38.62

0.9959

728

Z. Ni et al. / Renewable Energy 147 (2020) 719e729 25

4.8

Kinematic Viscosity SP CFPP

(U1602272) and Research Fund from State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization (No. CNMRCUTS1704).

35 30

20

25

4.4

4.2

10

5

4.0 0 3.8

References

15

Methyl Palmitate Isopropyl Palmitate Isobutyl Palmitate Isoamyl Palmitate

20 15

CFPP

4.6

SP



Kinematic ViscosityPPV

5.0

10 5 0

Fig. 15. Comparison of cold flow properties of branched-chain alkyl esters of palmitic acid.

listed in Table 7. Similarly, the analysis of reaction kinetics of isoamyl palmitate is shown in Fig. 11. 3.5. Measurement and analysis of the cold flow properties Fig. 15 shows that the SP and the CFPP of branched-chain alkyl esters of palmitic acid gradually decrease with increasing length of the branch chain under the same carbon chain length. Compared to methyl palmitate, the cold flow properties of branched-chain alkyl esters of palmitic acid are better. Kinematic viscosity of branchedchain alkyl esters of palmitic acid is slightly higher, however, does not exceed the Chinese national standard. The kinematic viscosity (40
C) standard as per the national standard for biodiesel in China is in the range 1.9e6.0 mm2 S1. Therefore, the branched-chain alkyl esters of palmitic acid can be used as a component of biodiesel alone with good flow performance. 4. Conclusion (1) According to the single-factor experimental results, orthogonal test was carried out for branched-chain alkyl esters of palmitic acid. Verification test was conducted under the optimal conditions, and conversion for all the samples was up to 97%. (2) Analysis of the reaction kinetics of the branched-chain alkyl esters of palmitic acid was determined by the integral method, for obtaining the frequency factor, and activation energy, and reaction kinetic model. (3) Under the same carbon chain length, with increasing branch chain length, the SP and CFPP of branched-chain alkyl esters of palmitic acid gradually decreased. It can be used as a component of biodiesel alone with good flow performance. Acknowledgments *Corresponding author: Yu-ling Zhai (1986-), doctor of engineering, mainly engaged in energy conversion and utilization. Kunming, Yunnan 650093, China. E-mail: [email protected]. Fa-she Li (1978-), Kunming University of Science and Technology, professor, mainly engaged in energy and power research. Kunming, Yunnan 650093, China. E-mail: [email protected]. The authors sincerely acknowledge funding from the National Natural Science Foundation of China (51766007), Natural Science Foundation of Yunnan Province (2018FB092), NSFC-Yunnan Joint Fund Project

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