Esterification of fatty acids with ethanol over layered zinc laurate and zinc stearate – Kinetic modeling

Esterification of fatty acids with ethanol over layered zinc laurate and zinc stearate – Kinetic modeling

Fuel 153 (2015) 445–454 Contents lists available at ScienceDirect Fuel journal homepage: www.elsevier.com/locate/fuel Esterification of fatty acids ...

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Fuel 153 (2015) 445–454

Contents lists available at ScienceDirect

Fuel journal homepage: www.elsevier.com/locate/fuel

Esterification of fatty acids with ethanol over layered zinc laurate and zinc stearate – Kinetic modeling Eduardo Jose Mendes de Paiva a,b,c, Stefano Sterchele c, Marcos Lúcio Corazza a,b, Dmitry Yu Murzin c, Fernando Wypych a,⇑, Tapio Salmi c a b c

CEPESQ – Research Center in Applied Chemistry, Department of Chemistry, Universidade Federal do Paraná, P.O. Box 19081, Curitiba, PR 81531-980, Brazil Department of Chemistry Engineering, Universidade Federal do Paraná, Curitiba, PR 81531-980, Brazil Åbo Akademi University, Process Chemistry Centre, Laboratory of Industrial Chemistry and Reaction Engineering, FI-20500 Turku-Åbo, Finland

h i g h l i g h t s

g r a p h i c a l a b s t r a c t

 Modeling of long chain FFA with

ethanol was performed using Eley– Rideal approach.  No diffusional limitations were found with zinc carboxylic salts.  High hydrophobic behavior was observed with zinc laurate.  Ethanolysis of FFA reached 92% and catalytic gain compared to blanks reached 40%.  Structural changes in the catalyst were observed which exchange FFA with the medium.

a r t i c l e

i n f o

Article history: Received 20 January 2015 Received in revised form 2 March 2015 Accepted 10 March 2015 Available online 20 March 2015 Keywords: Esterification Kinetic modeling Zinc carboxylates Ethanol Fatty acids

a b s t r a c t This work is focused on the esterification of fatty acids (commercial oleic mix) with zinc carboxylates (layered metal soap). About 25 experiments were performed, with and without catalyst, yielding a kinetic model based on the Eley–Rideal approach, able to predict fatty acid conversions under different conditions (molar ratio fatty acids/ethanol and temperature). An apparent first order reaction with respect to both reactants with no diffusion limitations was proposed. The activation energy of 80 kJ/mol was found. Fatty acid conversion up to 92% was reached under some conditions and the catalytic yields compared to the blank ones reached 40% in less than 90 min of reaction. This catalyst has shown a unique behavior among all other catalysts available for esterification, acting similarly to a homogeneous catalyst during the reaction but being recovered like a heterogenous catalyst at the end of the process. Ó 2015 Published by Elsevier Ltd.

1. Introduction Organic esters are a very important class of chemicals having wide applications in a variety of areas such as perfumes, flavors,

⇑ Corresponding author. E-mail address: [email protected] (F. Wypych). http://dx.doi.org/10.1016/j.fuel.2015.03.021 0016-2361/Ó 2015 Published by Elsevier Ltd.

pharmaceuticals, plasticizers, solvents and chemical intermediates [1,2]. Besides, esters from alternative sources and nonedible crops are potential candidates to suppress carbon emissions. Low-carbon technologies will have a crucial role to assure future energy supplies and offset the environmental impact. In addition to the energy efficiency, many kinds of renewable energy, carbon capture and storage, nuclear power and new transport technologies must

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be widely deployed to reach the emission goals [3]. Esterification reactions can be carried out without a catalyst, although the reactions are, in worst cases, extremely slow because the rate is dependent on the autoprotolysis of the carboxylic acid [4]. Typically esterification reactions require days or even months to reach the equilibrium in the absence of a catalyst. To accelerate the reaction rate, catalysts are employed in the liquid-phase esterification and both homogeneous and heterogeneous catalysts are commonly used. Most of the industrial esterification processes around the world are still carried out under homogeneous conditions [5,6]. Despite strong catalytic effects, the use of homogeneous catalysis such as sulfuric and p-toluenesulfonic acids has several drawbacks, such as the existence of side reactions, corrosion of the equipment, and the need to deal with acidic waste [7], which constitutes a real environmental problem. In order to avoid separation problems that arise from the high miscibility of homogeneous catalysis in the reaction medium, such as washing and waste handling, increase of production costs due to increase in the number of separation steps, corrosion and related problems, a lot of studies with heterogeneous catalysis have been carried out. Aranda and co-workers [8–14] employed niobium oxide as a solid catalyst in the esterification of fatty acids from palm oil. The authors reported 80% and 20% of conversion with methanol and ethanol respectively (at 130 °C and 3.2% of catalyst related to the mass of fatty acid), which is lower than the conversions (98% and 90% with methanol and ethanol, respectively) they obtained with sulfuric acid and methanesulfonic acid catalysts at the same conditions. The use of strong acid exchange polymers was reported by Ni and Meunier [15], who employed Nafion/ SAC-13, a fluorosulfonic acid supported on fused silica, in the esterification of palmitic acid in the presence of sunflower oil. The authors reported conversions of 47% after 3 h during the first cycle (at 60 °C under atmospheric pressure and 10% in mass of the catalyst). A considerable decrease of conversions was reported after each reuse and only after 48 h the conversions reached 95%. Zhang and co-workers [16] employed an ionic liquid (N-methyl2-pyrrolidone) in the esterification of oleic acid at 70 °C during 8 h. These authors reported conversions of 95% at molar ratio methanol/fatty/acid of 2:1:0.338. In this context, it is important that most of the work was done with methanol and the majority of the conversions were up to 80% taking considerable time to reach higher conversions. Another class of material has been proposed by some authors as well by our research group. Macierzanka and Szelag [17] studied the esterification of glycerol in the presence of zinc carboxylates and found that this catalyst significantly influenced monoglyceride (MAG) conversion and its presence increased the glycerol-fatty acid interfacial area (increase of microemulsions formation). Di Serio and co-workers [18] described esterification reactions employing layered metal carboxylates or layered metal soaps (zinc acetate and stearate). The authors pointed out that the catalyst has surfactant properties promoting a better contact between the oil and alcoholic phase with the best results achieved with zinc stearate. In our group a significant effort has been put on the understanding of the role of layered metal carboxylates in the esterification reactions. Cordeiro et al. [19] have reported that layered hydroxide nitrate showed a catalytic activity in both esterification and transesterification reactions. An ‘‘in situ’’ transformation occurred in the esterification medium leading to the formation of zinc carboxylates, i.e. the true catalyst in this esterification process. Our group has investigated the activity of this catalyst with several metals and conditions as reported by Lisboa et al. [20]. Layered metal carboxylates were proven to be unique catalysts among all the others available to esterification of fatty acids, the recycle of the catalyst could be done at least 11 times without any loss of

the activity as reported by Cordeiro et al. [19]. In addition, the leaching of this Lewis acid catalyst (zinc laurate) is less than 0.003 wt.% of the original zinc mass, as previously studied [21]. Besides, the catalyst can be recovered as a solid and crystalline catalyst and this behavior in the reaction medium at certain temperatures is assumed to be similar to ionic liquids [20]. Previously, we have studied the esterification of lauric acid in the presence of zinc laurate and compared the results with blanks [21]. The conversion reached 92% in less than 2 h and the gains compared to the blank tests reached 40% at certain conditions. A kinetic model, based on a quasi-homogeneous approach was presented and kinetic data were reported. In this study, conversions compared with the blanks were very high, which was attributed to the auto-catalytic behavior of the reaction. In the literature, the kinetic of esterification reactions has been studied by many authors, although, most of them are focused on the esterification of short chain acids. Anyway, these studies can be used as a background to compare kinetic of long chain fatty acids, since the mechanism is expected to be the same. Altiokka and Citak [22] proposed that esterification reactions of acetic acid and isobutanol catalyzed by cation-exchange resin Amberlite IR120 at temperatures 45–75 °C occur via a single-site Eley–Rideal (ER) pathway in which an adsorbed alcohol molecule reacts with an acid molecule from the bulk phase. Goodwin and co-workers [23] determined through pyridine poisoning experiments that both gas-phase (90–140 °C) and liquid-phase (60 °C) esterification of acetic acid by ethanol and methanol using silica supported Nafion (SAC-13) proceeded through the single-site ER pathway. In one of the few studies carried out with ethanolysis of free fatty acids, Zhang et al. [24] used hybrid catalytic membranes consisting of cation ion-exchange resin particles and polyethersulfone in the esterification of acidic oil (waste oil from cocking) with ethanol and other alcohols. These authors developed an algebraic kinetic equation which was developed based on some assumptions: (i) in this reactive system (oil + free fatty acids) the rate of non-catalyzed reactions is negligible compared to catalyzed ones; (ii) the reaction follows a second order mechanism; (iii) the reaction was assumed to be pseudo-homogeneous. The fitting of parameters was determined by trial and error procedure of the left hand side of the algebraic equation and experimental points. The authors reported higher conversions with butanol (95%) and activations energy values decreasing from butanol to methanol. The present work is focused on establishing an alternative path to free fatty acid (FFA) esterification employing ethanol, a greener and environmental sustainable alcohol, with higher conversions in a shorter time, using a recoverable catalyst the production cost of which is considerably low (less than US$ 2.00/kg). A kinetic model based on a step wise and clear mechanistic route, able to predict fatty acid ethyl ester (FAEE) formation, under different conditions of temperature, molar ratio between fatty acids and ethanol, catalyst amount was proposed and the kinetic parameters were

Table 1 Contact angle and surface energy measurements performed with ZnL tablets. Liquid

Surface tension total (mN/m)

ST (dispersive) (mN/m)

ST (polar) (mN/m)

Contact angle (measured)

Diiodomethane Water Formamide Ethanol Oleic mix 90%

50 72.10 56.90 22.10 38.51

47.40 19.90 23.50 17.5 –

2.60 52.20 33.40 4.60 –

77.5 98.3 87.6 33.6 43.7

Surface energy (mN/m)

Dispersive (mN/m)

Polar (mN/m)

Correlation

18.94

15.65

3.29

0.9993

ZnL calculated by Van Oss, Chaudhury and Good method [27].

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2. Experimental section The catalyst preparation and characterization has been described in our previous work [19,20]. Zinc laurate (coded as ZnL) was prepared by neutralization or metathesis in an alcoholic medium of lauric acid with sodium hydroxide followed by precipitation with a zinc salt (ZnCl2). The powder produced was analyzed by Fourier Transform Infrared spectroscopy (FTIR) and X-ray diffraction (XRD) confirming the layered structure and binding between the zinc metal cations and carboxylate anions by a bidentate bridge [19]. Commercial zinc stearate (coded as ZnS) was kindly provided by SIM Estearina Indústria e Comércio Ltda. (Curitiba, state of Paraná/Brazil). Commercial zinc stearate is a single crystallographic phase where the anions stearate and palmitate are simultaneously intercalated between the layers and the basal distance is determined by the longer carbonic chains (stearate) as will be shown further in SM1. Esterification of oleic, linoleic and stearic acid, a commercial mixture of 90% of oleic acid (Sigma–Aldrich – SM2) with anhydrous ethanol was carried out in an isothermal batch stainless steel Parr reactor (300 mL) equipped with a heating jacket and coupled with a parallel chamber also equipped with a reacting jacket to ensure that both alcohol and fatty acids could reach the reaction temperature at the same time right before the kinetic measurements. The reaction was started by pouring the preheated alcohol into the reactor vessel filled with fatty acids and the catalyst as powder. All the chemicals were of reagent grade and used without any further treatment. The stirring speed was 500 rpm, transferred by a four pitched blade impeller with internal channels to enhance mixing and temperature was kept within 0.2 °C. Samples (1.4 mL) were withdrawn at defined time and quenched with pure acetone to accelerate the catalyst precipitation, thereafter the samples were centrifuged at 7000 rpm for 10 min, the upper layer was extracted followed by evaporation of the solvent under reduced atmosphere (200 mbar) at 65 °C. Then the samples were filtered with PTFE

Ac. ZnS Ac. ZnL EE. ZnS EE. ZnL

0.14

Concentration [mol/L]

0.12 0.1 0.08 0.06 0.04 0.02 0 0

50

100

150

200

Time [min] Fig. 1. Comparative plot between oleic acid esterification with ethanol catalyzed by 5 wt.% of ZnL and ZnS (165 °C MR8).

0.16 Ac. ZnS

0.14

Concentration [mol/L]

determined by fitting the model with the experimental results. These data and discussion will help to enhance the gap in the literature concerning the kinetics of ethanolysis of long chain fatty acids. One of the main goals in this work is to model simultaneously fatty acid (oleic, linoleic and stearic acids) conversions employing a commercial oleic mixture, which is similar to tall oil, and provide parameters and kinetic data needed for the process development.

blank Ac. EE. ZnS

0.12

blank EE.

0.1 0.08 0.06 0.04 0.02 0 0

50

100

150

200

250

Time [min] Fig. 2. Comparative plot: blank reactions vs. catalyzed by 5 wt.% of ZnS in the ethanolysis of oleic acid (165 °C and MR8).

micro-filters (45 lm) and analyzed by gas chromatography (GC). It is important to point out that both catalyzed and blanks experiments were conducted following the same procedure, as described in this section. The total liquid volume in the experiments was kept constant in approximately 50% of the reactor vessel. Different initial molar ratios (MR) between fatty acids (oleic mix 90% Sigma–Aldrich) and ethanol (coded as MR followed by the ratio number) were employed (i.e. 1:3, 1:7 and 1:12). The amount of the catalyst was 0.7 and 5 wt.% of zinc laurate (ZnL) and commercial zinc stearate (ZnS) related to the fatty acid mass, respectively. The temperature was set at 135 °C, 150 °C and 165 °C. The pressure inside the reactor corresponded to the ethanol vapor pressure at the reaction temperature. The reaction medium was purged with argon several times and kept at this atmosphere during the experiments to avoid oxidation of double bounds in fatty acids. All the screened kinetic conditions are resumed in SM3. The samples were withdrawn at different times (0, 20, 40, 60, 90, 120, 150, 210 min) and after 24 h to check the attainment of equilibrium. Altogether 25 kinetic experiments, including blank ones, were conducted and a total of 200 experimental points were generated. The samples were analyzed by GC. The SM4 presents all the conditions and experiments combinations carried out with the operational variables. Fatty acids and corresponding esters were directly analyzed, without derivatization, in a gas phase chromatograph Shimadzu, model GC-2010 equipped with a flame ionization detector (FID) and a capillary fused silica column, Agilent DB-FFAP (PEG – polyethylene glycol), with 60 m and 0.25 lm of liquid film. Samples were prepared with 200 lL of the internal standard (methyl heptadecanoate) diluted in heptane and 1 mL of pyridine. The injections were performed with 1 lL of the samples at splitting rate of 1/30 using helium as a gas carrier, and the flux was kept constant (2.5 mL/min). The injector and detector temperatures were set at 270 and 250 °C, respectively. The column heating ramp was set with the initial temperature of 180 °C for 2 min, followed by heating with 1 °C/min until 202 °C, keeping constant for 2 min and followed by another ramp of 2 °C/min up to 250 °C, the total analysis time was 51 min. The catalyst recovered after the reactions as well the fresh commercial ZnS and synthetic ZnL were dissolved with the objective to identify the carboxylic acid composition in the recovered catalyst. Approximately, 0.5 g of the catalysts was put inside a round-bottom flask along with a 1 mol/L hydrochloric acid solution (37%). The system was kept under magnetic stirring for 4 h with a reflux

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A

Concentration [mol/L]

0.14

Ac. MR3 Ac. MR8 Ac. MR12 EE. MR3 EE. MR8 EE. MR12

0.12 0.1 0.08 0.06 0.04 0.02 0 0

50

100

150

200

250

Time [min] 0.16

3. Experimental results

B

Ac. MR3 Ac. MR8 Ac. MR12 EE. MR3 EE. MR8 EE. MR12

Concentration [mol/L]

0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0

50

100

150

200

250

Time [min] 0.16

Ac. MR3

C

Ac. MR8 Ac. MR12 EE. MR3 EE. MR8 EE. MR12

Concentration [mol/L]

0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0

50

100

150

with acetone to guarantee the complete removal of the oleic phase sticked in the filter and from the obtained solution the solvent was removed by rota-evaporation under reduced pressure. The contact angle measurements for fresh catalyst surface settled in silicium plates were taken by a tensiometer (DataPhysics OCA 15 plus tensiometer, Filderstadt, Germany) using the sessile drop method in the presence of 3 standards liquids: ultrafiltered water (MilliQ system), diiodomethane (>99.5%) (Sigma–Aldrich) and ethanol (Sigma–Aldrich). The experiments were performed at 25 °C using a Hamilton syringe of 500 lL (Bonaduz, Switzerland) and the contact angle computations were performed by the software SCA 20 DataPhysics (San Jose, CA, EUA). The zinc laurate tablets were molded with approximately 0.10 g of ZnL and pressed employing a set of cylindrical orifice plate and a stainless steel cylinder, under a pressure of 8 bars for 2 min.

200

250

Time [min] Fig. 3. Ethanolysis of oleic acid with 5 wt.% ZnL at different molar ratios and temperature (A) 135 °C, (B) 150 °C and (C) 165 °C (in the legend, Ac. is oleic acid, EE. is ethyl oleate).

condenser continuously flushed with nitrogen. The visual inspection of the mixture, characterized by fading of the white solid color and formation of a supernatant oleic phase, indicated the end of the process. After cooling the mixture, a supernatant white solid appeared and was removed by filtration, washing several times until neutrality. The recovered material was carefully dissolved

The composition of the commercial ZnS and synthetic ZnL catalysts is displayed in SM1. As can be seen, the synthetized ZnL sample has some minor contaminants (stearic and palmitic acids) while the analysis results of ZnS show that this catalytic matrix is mainly composed by palmitic acid followed by stearic acid. In any case these observations are in agreement with results reported previously by Da Silva [26]. Based on both results the amount of zinc present in the structure was calculated. For the same weight ZnL has 2.2 mmol/g of zinc against 1.5 mmol/g of the commercial catalyst. The results obtained with the contact angle and surface energy measurements [27] reveal (Table 1), the material presents high hydrophobic behavior forming high contact angles with polar solvents. The low angle formed with ethanol is an evidence of affinity with this solvent and the low surface energy values obtained with oleic mix 90% are evidence that this material promotes better interaction between the alcoholic and oleic phase, thus promoting microemulsions formation in the presence of water. The esterification rates of oleic acid with ethanol at 165 °C and the initial molar ratio of 1:8 were compared for both 5% of zinc laurate (ZnL) and the commercial zinc stearate (ZnS). The experimental results are displayed in Fig. 1. The reaction rate with ZnS starts with the same values at the beginning and becomes higher at some points (especially around 100 min), converging to the same values after 200 min. These results were not expected since ZnS has 1.5 times less zinc in the framework compared to synthetic ZnL. The results suggest that not only the availability of the zinc sites plays a role in the esterification but also some inherent surfactant properties can be a possible explanation, similar to the evidences reported by Macierzanka and Szelag [17] and Di Serio et al. [18]. As the temperature is a key factor in esterification reactions [21] and due to relative high temperatures employed in this study, the esterification rates of the blank runs under various conditions (MR8 at all temperatures) were also compared with the reactions catalyzed by ZnL. This comparison is important to understand the real impact of the catalysis on the process and also provides some information about the auto-catalytic behavior of the system. The studies of Pinnarat and Savage [25] showed that blank conversions can be very high (e.g. 50% of conversion at 150 °C and MR ethanol to oleic acid 7:1). As can be observed in Fig. 2, the influence of catalysis is considerable high, especially during the first 100 min of the reaction. At some points (i.e. 50 and 90 min), the conversion gains compared to the blank runs reached 40%. In terms of time the gain to achieve the same conversion can be dozens of hours. The use of ZnS substantially accelerated the reaction rates and the conversion approached of the equilibrium in less than 150 min at 165 °C MR8 and 5 wt.% of ZnS. At this point, it must be emphasized

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449

Fig. 4. Schematic view of the Lewis site in the catalyst structure and the proposed mechanism.

that these results are remarkable when employing ethanol as a reactant, i.e. Aranda et al. [8] reached only 20% of conversion in ethyl esters employing niobium oxide as the catalyst (130 °C and 1 h) and Marchetti and Errazu [14] reached 30% using basic and acidic zeolites. The experimental results to be presented in this section will show only the oleic acid (main compound) conversions, secondary compounds have the same trends (see SM5). Esterification of oleic acid in the presence of ZnL at different temperatures and different MR of the reactants is displayed in Fig. 3, where an increase in the temperature leads to an increase in the reaction rates. The molar ratio (MR) does not play a significant role in this reactive system and very similar conversions can be obtained with the lowest MR. It is worth to highlight that the MR employed in this study is considerably smaller compared to typical MR conditions reported in the literature. Based on the TGA results of Cordeiro et al. [19] and Lisboa et al. [20], it can be suggested that melting of this catalyst in the reaction medium is an important

factor (melting point between 127 and 135 °C). This proposal is in line with the study of Barman and Vasudevan [28]. The experimental error and the reproducibility of the batch experiments as well as the GC analysis procedures were checked. The results are displayed by SM6 and show the bars errors plot recorded in triplicate for instance in the catalytic experiment at 150 °C MR of 12 and 0.7 wt.% of ZnL. The results revealed the accuracy of the catalytic experiments as well as the reproducibility of the chemical analysis. The variability revealed by the bar plots is considerably small even for the sample withdrawn after 24 h of the reaction. The esters analysis is slightly more accurate than for the acids, most probably due to a higher volatility of esters which involves a better reproducibility in GC analysis. The mathematical modeling of the observed reaction kinetics was based on the mechanism presented in Fig. 4. The kinetic process begins with interactions between the Lewis acid site of the catalyst and carboxylic acid generating the first intermediate [I⁄1] which rearranges into another intermediate [I⁄2].

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The entire reactions scheme can be written as follows:



A () I1

ðIÞ

I1

þ B ()

I2

0.16

RDS

I2 () I3 I3 () C  þ W C  () Eþ

ðIIÞ

0.12

ðIIIÞ

0.1

ðIVÞ ðVÞ

ð2Þ

K2 ¼

½I1  ) ½I1  ¼ K 1 K 2 C A ½ ½A 

ð3Þ

K4 ¼

½I3  ) ½I3  ¼ K 4 ½I2  ½I2 

ð4Þ

C E  ½ C E  ½  C W ¼ CE  K 4 K 5 ½I2 

CE  CW ¼ ½ K4K5K6

0

400

600

800

1000 1200 1400 1600 1800

Time [min] 8

x 10

-3

B

7 6

Ci [mol/L]

5 4 3 2

0

ð5Þ

ð6Þ

200

400

600

800

1000 1200 1400 1600 1800

Time [min] Fig. 5. Esterification of fatty acids with ethanol at 150 °C, molar ratio 3 and 0.7 wt.% ZnL. (A) oleic acid; (B) secondary compounds: (⁄) linoleic acid; (+) stearic acid; (s) ethyl linoleate; (h) ethyl stearate.

  CE  CW 1 c0 ¼ 1 þ K 1 C A þ K 1 K 2 C A þ ð1 þ K 4 Þ þ C E  ½ K6 K4K5K6

ð7Þ

c0 ¼ ð1 þ aC A þ bC E  C W þ cC E Þ  ½

ð13Þ

where

a ¼ K1 þ K1K2 1 1 þ K4K5K6 K5K6

ð15Þ



1 K6

ð16Þ

ð8Þ

ð9Þ ð10Þ

ð14Þ



Taking into account the following relationship, 00

0

k ¼ k c0 1 1 ¼ Kc K1K2K3K4K5K6

ð12Þ

After lumping some parameters,

where

k ¼ kþ3 K 1 K 2

200

0

where [⁄] is the concentration of accessible acid sites on the surface of metallic clusters. The expressions for I1 and I2, Eqs. (3) and (8) respectively, are inserted in the rate equation (RDS) which becomes

  CE  CW 0  ½ r ¼ k CA  CB  Kc

0

1

which gives:

½I2 

0.06

0

ð1Þ

½A  K1 ¼ ) ½A  ¼ K 1 C A  ½ C A  ½

K6 ¼

0.08

0.02

where A = fatty acid; B = ethanol; E = ethyl ester; W = water and [I⁄i ] are the intermediates. A complete rate equation for the catalytic process can be derived by applying the quasi-steady state hypothesis to the reaction intermediates, but here a simplified approach will be used. The nucleophilic attack, step (III) is generally recognized to be the slowest step in esterification processes. Therefore step (III) is presumed to be rate determining, while the other steps are rapid, and the quasi-equilibrium hypothesis can be applied to them. Considering the step (III) as rate determining step (RDS), one can write:

C  CW K5 ¼ E  ½I3 

Oleic Acid Ethyl Oleate model model

0.04

ðVIÞ

A þ B () E þ W

r ¼ kþ3 ½I1   C B  k3 ½I2 

A

0.14

Ci [mol/L]

A þ  () A



ð17Þ

and Eq. (14), the rate Eq. (9) becomes 00

k ðC A C B  C E C W =K c Þ 1 þ aC A þ bC E C W þ cC E

The total concentration of the catalyst can be replaced by the following equation:



c0 ¼ ½ þ ½I1  þ ½I2  þ ½I3  þ ½I4  þ C A þ C E

If water (W) and ester (E) have week interaction with zinc, the corresponding terms in the denominator of Eq. (18) are negligible, i.e. 1 + a CA >> bCECw + cCE. Eq. (18) is thus simplified to

thus,

ð11Þ

ð18Þ

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0.16

A

0.14

Oleic Acid

0.12

model

A

Ethyl Oleate

0.12

model

0.1 0.08 0.06

0.1 0.08 0.06 0.04

0.04

0.02

0.02

0

0 0

200

400

600

800

1000 1200 1400 1600 1800

0

200

400

600

Time [min] 8

x 10

1000 1200 1400 1600 1800

-3

B

7

6

6

5

5

Ci [mol/L]

Ci [mol/L]

x 10

B

4 3

4 3

2

2

1

1

0

0 0

200

400

600

800

1000 1200 1400 1600 1800

0

Time [min]

00

k ðC A C B  C E C W =K c Þ 1 þ aC A

ð19Þ

In the case of strong deviations from experimental data, Eq. (19) should be modified to include the adsorption of ethanol and water, which leads to 00

k ðC A C B  C E C W =K c Þ 1 þ aC A þ bC B þ cC W

ð20Þ

The amounts of substance coupled to the catalyst are assumed to be negligible compared to the amounts in the liquid bulk; thus the concentrations of the components can be related to the concentration of the carboxylic acid (A), measured by GC.

ð21Þ

a0 ¼ C 0A  C 0B Eq. (21) is valid in the actual case, because neither ester nor water was present at the beginning of the experiment. The mass balance for an arbitrary component (i) in the batch reactor is given by

dni ¼ mi  r  mcat dt

400

600

800

1000 1200 1400 1600 1800

Fig. 7. Esterification of fatty acids with ethanol at 165 °C, MR12 and 0.7 wt.% ZnL. (A) oleic acid; (B) secondary compounds: (⁄) Linoleic acid; (+) stearic acid; (s) ethyl linoleate; (h) ethyl stearate.

where mi is the stoichiometric constant. The amount of substance is related to the concentration and to the liquid volume: ni ¼ C i  V liq: The change of the liquid volume must be included in the model, because the liquid volume is stepwise diminished during the reaction because of sampling: V liq: ¼ V 0;l  sV s , where s denotes the number of samples and Vs is the sample volume. After introducing the stoichiometric relations (21) and the concentration of A (fatty acid) and the rate Eq. (20) (neglecting the effect on water and alcohol on the catalyst) into the mass balance of A, it can be written as

h i 00 2 2 dC A k C A  a0 C A  ðC A0  C A Þ =K c  ¼  qcat dt 1 þ aC A where

C B ¼ C A  ðC 0A  C 0B Þ ) C B ¼ C A  a0 C C ¼ C D ¼ C 0A  C A

200

Time [min]

Fig. 6. Esterification of fatty acids with ethanol at 135 °C, molar ratio of reactants equal to 3 and 0.7% wt. ZnL. (A) oleic acid; (B) secondary compounds: (⁄) linoleic acid; (+) stearic acid; (s) ethyl linoleate; (h) ethyl stearate.



800

Time [min]

-3

7



Oleic Acid Ethyl Oleate

0.14

Ci [mol/L]

Ci [mol/L]

0.16

ð22Þ

ð23Þ

cat mA ¼ 1 and qcat ¼ mV liq: .

Eq. (23) was used for the determination of the parameters (k00 , Kc and a) by non-linear regression. The differential equation models were solved numerically with the backward difference method using lsqnonlin, a Matlab subroutine. The differential equation solver operated under a parameter estimation routine, which minimized the following objective function, the residual sum of squares:



2 X ^ A ðtÞ C A ðtÞ  C i

ð24Þ

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E.J.M. de Paiva et al. / Fuel 153 (2015) 445–454

0.16

0.16

A

0.14

Oleic Acid

A

Oleic Acid Ethyl Oleate model model

0.14

Ethyl Oleate model

0.12

model

0.1

Ci [mol/L]

Ci [mol/L]

0.12

0.08 0.06

0.1 0.08 0.06

0.04

0.04

0.02

0.02

0 0

200

400

600

800

0

1000 1200 1400 1600 1800

0

200

400

600

8

x 10

1000 1200 1400 1600 1800

-3

B

7

6

x 10

-3

B

5

6 5

4

Ci [mol/L]

Ci [mol/L]

800

Time [min]

Time [min]

4 3 2

3 2 1

1 0

0 0

200

400

600

800

1000 1200 1400 1600 1800 0

Time [min]

400

600

800

1000 1200 1400 1600 1800

Time [min]

Fig. 8. Esterification of fatty acids with ethanol at 165 °C, MR8 and 5 wt.% ZnL. (a) oleic acid; (B) secondary compounds: (⁄) linoleic acid; (+) stearic acid; (s) ethyl linoleate; (h) ethyl stearate.

^ A denote the experimental and the predicted conwhere CA and C ^ A are obtained from the numerical solucentrations. The values of C tion of Eq. (23) during the parameter estimation. The model subroutine employs an algorithm originally proposed by Levenberg [29] and Marquardt [30] in which the minimum search is a hybrid between the gradient method and the Gauss–Newton method. The minimization is started with the gradient method, but is switched to the more rapid Gauss–Newton algorithm as the minimum is approached. The quality of the model fit and the model parameters was checked by calculating the typical statistical quantities, such as the standard deviation of the parameters and the degree of explanation of the model. The degree of explanation was defined as follows:

2 P ^ A ðtÞ C A ðtÞ  C i R2 ¼ 1  P  2  i C A ðtÞ  C A ðtÞ

200

ð25Þ

 A is the average value of the experimentally recorded where C concentrations. In the sequence, the results obtained with the proposed model based on Eq. (23) under different experimental conditions will be presented. In Figs. 5–8(A and B) the lines represent the predictions of the model. The parts (A) represent the main compound (oleic acid) and part (B) the minor compounds (linoleic and stearic acid).

Fig. 9. Esterification of fatty acids with ethanol at 165 °C, MR8 and 5 wt.% ZnS. (A) oleic acid; (B) secondary compounds: (⁄) linoleic acid; (+) stearic acid; (s) ethyl linoleate; (h) ethyl stearate.

As Fig. 5A reveals, the fitting of the model is excellent for the main compounds (oleic acid and ethyl laurate). Moreover, a very good fitting was also obtained for the secondary compounds. The good fitting de facto endorses the simplifications introduced in Eq. (23), assuming that adsorption is dominated by the main carboxylic acid (oleic acid). Water and esters have evidently only week interactions with the zinc sites in agreement with the modeling results. Figs. 6–8 display the model fit at low and high temperatures for different amounts of catalyst and molar ratios between components. It must be highlighted that model is especially accurate in the critical region of the concentrations changes (between 0 and 200 min); all the trends and conversions in this region were successfully fitted by the model, even for secondary compounds and the model was able to predict with acceptable accuracy of the equilibrium conditions after 24 h. An adequate fitting under different conditions of temperature, molar ratios and amount of ZnL was demonstrated (Figs. 6–8). The model was able to predict the conversions not only employing ZnL but also employing ZnS. Fig. 9 shows the results obtained in the presence of ZnS. The accuracy of the model was very high for the main compound (oleic acid). On the other hand, while the model with this catalyst can predict the consumption of the acids, the formation of esters has some deviations possibly to the catalytic matrix composition, and hence, some fatty acid exchange

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E.J.M. de Paiva et al. / Fuel 153 (2015) 445–454 Table 2 Estimated rate and equilibrium parameters as well as the degree of explanation of esterification of oleic mix with ethanol in the ZnL and ZnS presence. k00 mol1 L2 (min g)1

Reactor setup 135 °C 150 °C 165 °C 165 °C 165 °C a b c d e * **

a

MR3/0.7% MR3/0.7%b MR12/0.7%c MR8/5%d MR8/5%e

7.33 1.07 0.52 0.70 0.68

±* 25.30 0.26 0.19 0.21 0.12

K

±

0.24 0.69 1.28 2.55 1.66

0.02 0.06 0.80 1.29 0.37

a (mol L1) 90.08 0.11 0.01 22.15 5.35

R2 (%)

± **

338.82 2.08 3.26 10.29 2.87

99.99 99.99 99.97 99.98 99.98

Fig. 6. Fig. 5. Fig. 7. Fig. 8. Fig. 9 (ZnS). Confidence intervals (95%). The wide value for confidence intervals presented here is a consequence of the melting point transitions of zinc salts.

should occur with the medium thus minor compounds (linoleic acid 4.3% and stearic acid 2.3%) are more sensitive to exchange rate. This will be discussed in the subsequent session. The estimated rate and equilibrium constants along with the combined parameters as well as the degrees of explanation for the eq. 23 using a commercial oleic mixture are presented in Table 2, which reveals that the degree of explanation is very high. SM7 shows the Arrhenius plot for the second-order forward rate constant recorded at three temperatures. The apparent activation energy estimated from the slope of the Arrhenius plot is about 80 kJ/mol. There is scarce activation energy data concerning ethanolysis of long chain carboxylic acid in the literature, thus, the value presented is slightly high compared to our previous work [21] on the esterification of lauric acid with ethanol; in which activation energy of 68 kJ/mol was reported. Besides, this value is endorsed by the value of 68 kJ/mol reported by Zhang et al. [24]. The average of the thermodynamic equilibrium constant found with all the experiments was about K = 1.4. The spent catalyst used in some experiments was recovered, washed several times with acetone and analyzed by GC as explained in the experimental section. SM8 presents the composition of the ZnL and ZnS after 24 h of the reaction. The results showed that 86% of ZnS matrix was displaced by other fatty acids, mainly by oleic acid (41.4%) followed by stearic acid (24.9%) at 150 °C, MR3 and 5 wt.% of ZnL. The experiments carried out with the synthesized ZnL revealed a displacement of 84% of the catalyst original matrix (SM8), mainly by oleic acid. It is worth to remind that according to SM1 there was no oleic acid in the ZnL catalyst at the beginning. As can be observed, the catalyst promotes the exchange of the fatty acids initially present in their structure by the most available fatty acid in the medium preferably followed by stearic acid. As a consequence, peaks related to ethyl laurate were recorded with the GC analysis thus lauric acid initially present in the matrix was esterified and the evolution of this process was rapid following the same rate of other fatty acids.

4. Conclusions The experimental work showed that the esterification of fatty acids with ethanol, considered by many authors as less reactive compared to methanol, can be successfully carried out over zinc laurate and a commercial zinc stearate catalyst. A comparison between the activities of both catalysts showed that practically equal high fatty acid conversions, around 92%, were achieved in less than 120 min (i.e. 165 °C, MR8 and 5 wt.% of ZnS). The molar ratio of the reactants did not play a significant role. The rate equation based on the advanced reaction mechanism particularly on the adsorption of the fatty acids was proposed for the esterification of commercial oleic mixture of 90% of oleic acid with ethanol. The

mechanism explained the experimentally recorded reaction kinetics in an adequate way. The most important advantage with this catalyst is the ability to be recovered as a powdered heterogeneous catalyst at the end of the reaction with no diffusion limitations in the particles. The surfactant behavior of this catalyst was demonstrated by the surface energy measurements pointing out its affinity by non-polar molecules and a high hydrophobic behavior, these results help to explain the high conversions. The exchange of fatty acids in the catalyst matrix occurs with the most abundant acid in the reaction medium. Once the catalyst can be recovered at the end by a simple filtration and precipitation procedure it can be reused without any further treatment which is very desirable in a potential industrial process. Acknowledgments This work is part of the activities of the Interdisciplinary PostGraduation Program in Engineering and Chemical Materials (PIPE, 2011-2015) at the Federal University of Paraná, granted by CAPES Scholarships Agency/ Brazil. Financial support was also provided by CNPq and FINEP/Brazil. Part of this project was conducted at Åbo Akademi University Process Chemistry Centre (PCC). The authors wish to thank Prof. Maria Rita Sierakowski for the use of the tensiometer.

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