Flash Point of Fatty Acid Methyl Ester Binary Mixtures | Journal of

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Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Flash Point of Fatty Acid Methyl Ester Binary Mixtures Rafael Macedo Dias,† Rafael Thomaz Aquino,‡ Maria Alvina Krähenbühl,† and Mariana Conceiçaõ Costa*,† †

Department of Process and Products Design (DDPP)School of Chemical Engineering (FEQ), University of Campinas (UNICAMP), 13083-852 Campinas, São Paulo, Brazil ‡ School of Applied Sciences (FCA), University of Campinas (UNICAMP), 13484-350 Limeira, São Paulo, Brazil

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S Supporting Information *

ABSTRACT: The flash point (FP) of binary mixtures formed by fatty acid methyl esters (FAMEs), which are the major compounds of methyl biodiesel, is investigated in this study, and the nonideality of the liquid phase was calculated with the ideal model, UNIFAC, UNIFAC-Dortmund (UNIFACDo), and NIST-UNIFAC models. The different models used to calculate the activity coefficient were compared through the FP result that was estimated using Liaw’s approach. The experimental results show that the larger the carbon chain of FAME is, or the richer the solution in the heavier compound is, the higher the FP of the compound and solution is. The results also show that the ideal model is the best one between those tested in this study because the solutions studied here can be considered ideal, and the calculated FP temperature of the binary mixtures presented an average root-mean-square deviation equal to 0.67% using this model. It was observed as an abrupt decrease in the FP value of the mixture with small addictions of the light compound in the region that is rich in the heavier compound, remarkably when the difference in the length of the alkyl carbon chain of these components is large. This behavior is an important factor that must be considered in safety and transportation cases.

1. INTRODUCTION The concerns about environmental consequences of using fossil fuels, associated with the decrease in petroleum supplies, the high energy prices, and the increase in energy imports, have been instigating research studies on fuels.1−3 Biodiesel is a promising renewable alternative fuel to the conventional fossilbased diesel fuel, having several advantages over diesel, such as the absence of aromatic compounds in its composition and almost no sulfur content. Besides, the biodiesel burn yields less carbon monoxide, hydrocarbons, and particulate emissions than the ordinary diesel and shows higher flash point (FP) compared with diesel.4,5 Moreover, biodiesel is biodegradable and nontoxic6 and can be used in diesel engines with little or no modification to the engine or the fuel system,7 improving the lubricity, which results in longer engine component life.8,9 This fuel can be produced by transesterification of vegetable oils and animal fats with an alcohol, such as methanol or ethanol in the presence of a catalyst (generally a strong base), resulting in glycerol and ethyl esters/monoalkyl methyl,10,11 which is called methyl ester, also known as biodiesel.8 All types of fatty acids derived from vegetable oil or animal fats (more than 300 types) can be used as a raw material for biodiesel production,12−15 and the estimation is that the global biodiesel production, which was 29.7 × 106 m3 in 2014, will expand to 39 × 106 in 2024.16,17 In several applications, the accurate determination of the biofuel properties is essential because it © XXXX American Chemical Society

may be used to know how the properties can affect the combustion, safety, and performance of the fuel.18−21 An important property to be determined is the FP. This property is defined as the minimum temperature at which vapor pressure of the hydrocarbon is sufficient to produce the vapor needed for spontaneous fuel ignition with air in the presence of an external source, that is, spark or flame.22 Initially, the FP was used to determine the fire hazard of fuels and oils stored or transported. Along with other tests such as viscosity index, viscosity, and specific gravity, the FP can indicate the quality of the crude oil from which the lubricant or biodiesel was derived and the quality of the refining process. In addition, studies to find a relationship between the structure and FP of organic compounds23−27 and fuel have been performed.28−30 Despite the fact that FP is an important and easily measured property, few information about FP of methyl esters and their binary mixtures are available in the literature. This study aimed to enrich the literature through determination of FP data of pure fatty acid methyl esters (FAMEs) from methyl caprylate to methyl oleate and their binary mixtures, totaling 19 FAME binary mixtures. To complement this study, the ideal and some versions of Received: March 26, 2019 Accepted: July 11, 2019

A

DOI: 10.1021/acs.jced.9b00267 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

yP = xiγiPisat i

UNIFAC models were applied to predict the FP of FAME binary mixtures, and the models were compared with experimental data.

where γi is the activity coefficient of component i, xi is the liquid phase composition, and Psat i is the vapor pressure for a pure substance. Substituting eqs 3 and 2 in eq 1, as proposed by Liaw et al.,36 results in eq 4, allows the determination of FPs for flammable liquid mixtures

2. MODELING OF FP TO ESTER MIXTURES Different methods found in the research literature to calculate the FP are constructed combining Le Chatelier’s rule and the vapor pressure-based models.31−36 Based upon Raoult’s law, Affens and McLaren34 have developed a model to predict the FP of hydrocarbons, which was able to estimate the vapor pressure and composition in the vapor phase above the liquid phase valid only for ideal mixtures. White et al.31 successfully predicted the FP of aviation fuels simplifying the Affens and McLaren34 model: the mole fraction in the liquid phase may be approximately determined by the volume fraction of the fuel. According to the authors, this assumption enhances the Affens and McLaren’s method because this approach can be used to fuel mixtures instead of just pure fuels. Some authors have considered the liquid phase as nonideal. Lee and Ha35 have developed a model to binary aqueous mixtures combining the Clausius−Clapeyron and the vapor− liquid equilibrium equation. The vapor pressure was calculated by Antoine equation, while van Laar37 or Wilson38 models were used to calculate the activity coefficient. Usually, an average absolute deviation (AAD) less than 3.5 °C is stated. Hanley32 calculated the FP of mixtures based upon meticulous liquid−vapor equilibrium calculations, combining information about heat of combustion and lower flammable limits (LFL), and the activity coefficient of the liquid phase was calculated applying Margules’ model.37 Hanley’s model has been used to predict FP of multicomponent mixtures which presents an inert component and one (or more) flammable chemicals. Gmehling and Rasmussen33 considered the nonideality of vapor−liquid equilibrium and Le Chatelier’s equation to estimate the nonideal mixture FP. The authors used the UNIFAC activity coefficient model39 to calculate the deviations of ideality, and the prediction efficiency was considerably improved than considering the ideal model. Finally, the most used FP prediction model nowadays is Liaw’s model.36 This model is based on Le Chatelier’s rule40 for the LFL of binary or multicomponent solutions. The LFL is considered constant and independent of temperature, and the vapor-air phase is considered ideal. The flammability limits of mixtures containing air plus a substance vapor can be expressed as follows 1=

∑ i

1=

ln Pisat =

Pisat ,FP

(4)

∑ NkijjjA1k +

y − C1k ln T − D1k T zzz {

T k ÉÑ ÄÅ ÅÅ B 2k i yÑÑÑÑ ÅÅ j z + ÅÅMi∑ Nk jjA 2k + 1.5 − C2k ln T − D2k T zzÑÑ ÅÅ T k {ÑÑÑÖ ÅÇ k k

B1k

1.5

+Q

(5)

where Nk is the number of groups k present in the molecule structure, Mi is the component molecular weight, A1k, B1k, C1k, D1k, A2k, B2k, C2k, and D2k are parameters obtained through regression of the experimental data realized by Ceriani and Meirelles,41 T is the temperature, and Q is a correction term (eq 6) Q = ζ1q + ζ1

(6)

where ζ1 and ζ2 are parameters associated to each class of compounds, and q is a function of temperature q = 3.4443 −

499.3 − 0.6136 ln T + 0.00517T T1.5

(7)

The ζ1 and ζ2 parameters which depend on the total number of carbon atoms in the molecule (NC) and the number of carbons of the substitute fraction (NCS) can be calculated as follows ζ1 = f0 + NCf1

(8)

ζ2 = s0 + NCSs1

(9)

where f 0, f1, s0, and s1 are optimized constants by Ceriani and Meirelles41 to different classes of compounds. The activity coefficient must be calculated (eq 3) when the liquid phase is not ideal. This calculation can be performed by nonpredictive models such as the NRTL,42 Wilson,38 or UNIQUAC43 or by using predictive models based on the group contribution approach, such as the original UNIFAC39,44 or modified UNIFAC models,45,46 such as UNIFAC-Do and NIST-UNIFAC. In this study, nonpredictive models were not used due to the lack of parameters in the literature for such systems. Just for comparative purposes, the ideal approach was also considered (γi = 1). The deviations were calculated between the experimental data and those resulted from the models considered.

(1)

sat Pi,FP

P

xiγiPisat

A predictive model that was specially developed to fatty compounds41 was used to calculate the FAMEs vapor pressure. This model correlates the vapor pressure and the temperature according to eq 5

where yi is the vapor phase composition of a flammable component i, and LFLi can be expressed in relation to the pure component i vapor pressure at its FP, Psat i,FP, as LFLi =

∑ i

yi LFLi

(3)

(2)

where P represents the ambient pressure. The FP of pure substances is determined at atmospheric pressure. Usually, at this pressure, the vapor phase is considered as ideal gas. To liquid mixtures presenting flammable substances in the presence of the noncondensable components of the air, the vapor−liquid equilibrium of component i can be calculated by eq 3

3. EXPERIMENTAL METHODS 3.1. Materials. All FAMEs used in this study were purchased from Sigma-Aldrich (Germany) and used without B



Article

Table 1. FAME Binary Systems Evaluated

Table 2. FP of Pure Esters Measured in This Studya chemical name (CAS number) methyl methyl methyl methyl methyl methyl methyl

caprylate (111-11-5) caprate (110-42-9) laurate (111-82-0) myristate (124-10-7) palmitate (112-39-0) stearate (112-61-8) oleate (112-62-9)

Cx:y

molar mass

purityb/GC (%)

C8:0 C10:0 C12:0 C14:0 C16:0 C18:0 C18:1

158.2380 186.2912 214.3443 242.3975 270.4507 298.5038 296.4879

99 99 98 99 95 96 97

experimental FP/K 346.9 373.0 396.7 418.0 438.6 455.5 444.1

± ± ± ± ± ± ±

0.6 0.6 1.0 0.6 1.0 1.5 0.6

estimated FP/Kc

AD/%

343.1 367.2 390.4 412.6 433.8 454.1 434.2

1.6 2.0 2.0 1.7 1.5 0.3 2.6

a

Cx:yx: number of carbons in the carbon chain from the radical fatty acid, y: number of unsaturations in the fatty acid chain. bAccording to the supplier. cFP estimated using the correlation developed by Carareto et al.23

4. RESULTS AND DISCUSSION 4.1. FP of Pure Substances. Table 2 shows the FP temperature measured in this study and those predicted using Carareto’s correlation23 as well as the absolute deviation (AD) calculated between the experimental FP data and the predicted values as demonstrated in eq 10

further purification because their purity is guaranteed by the supplier. 3.2. Solutions. Binary mixtures were prepared gravimetrically weighting previously known amounts of each component. In the cases in which the binary mixture compounds were liquid at ambient temperature (298 K), the chemicals were just mixed to guarantee the homogeneity of the solution. On the contrary, when one or both compounds were solid, they were heated until they melted and afterward mixed. The FAME binary systems evaluated in this study are shown in Table 1. 3.3. FP Measurements. In this study, a MiniFlash FLPH analyzer (Grabner Instruments, Austria) with ±1.9 K precision was used to measure the FP of pure chemicals and their binary mixtures. Equipment was operated according to the standard test method ASTM D6450, recommended to biofuel at least in triplicate. Once a day, before starting the measurements, the FP of dodecane was determined to verify the equipment calibration. Besides the equipment calibration, the ASTM D6450 recommends a pressure correction when the ambient pressure is different from 101.3 kPa, which is the case of Campinas (Brazil). To do this correction, the ambient pressure was measured with a barometer, and the corrected values are shown in data tables. The FP standard deviation was evaluated based on at least three measurements for each pure FAME or binary mixture and is within the range of (0.6−1.5) and (0.6− 2.9) K, respectively. Because of the standard deviation value, the FP of C16:0 + C18:1 and C18:0 + C18:1 binary mixtures were not measured. 3.4. FP Calculations. The activity coefficient was calculated using UNIFAC, UNIFAC-Do, and NIST-UNIFAC models using the MS Excel Solver, which is Excel’s tool (MS Excel 2013) based on the generalized reduced gradient method. 47,48 The activity coefficient calculations were performed to calculate the FP temperature values, which must obey eq 1. The predictive model developed by Ceriani and Meirelles41 was used to predict the vapor pressure of methyl esters used in this study. The prediction capacity of this model was compared with more than 320 experimental values on vapor pressure of methyl esters.49−53 The AAD and the plots of FAMEs vapor pressure are presented in the Supporting Information (Table S1 and Figures S1−S7).

Deviation (%) =

(Tiexp − Timodel) 100% Tiexp

(10)

(i = pure methyl esterC8:0; C10:0; C12:0; C14:0; C16:0; C18:0; C18:1) To our knowledge, only the FP of pure methyl palmitate54 is available in the literature (452.15 K), and this value is not in accordance with our experimental data determined for the same compound. The difference observed, of about 14°, can be attributed to the different experimental methods used to measure the FP (our studyASTM D6450 and research literatureASTM D7467), the equipment error, and the purity of the methyl palmitate too. As will be discussed later, a small amount of short chain FAME, which can be a possible contaminant of FAMEs, can cause a significant decrease in the FP. Also, according to American Society for Testing and MaterialsASTM,55 the FP values are a function of the apparatus design and conditions used, and also of the operational procedure applied. FP can be defined only in terms of a standard test method, and in general, no valid correlation can be assured between results obtained by different test methods or apparatus designs. Therefore, the absence of other experimental data using the same standard test method in the research literature enables a direct comparison between our data and the literature data. The results obtained by Carareto et al.23 show that the FP of FAEEs (fatty acid ethyl esters) is attached to the carbon chain size. The same behavior is observed to FAMEs, whose increase in the carbon chain implies in an increase in the FP, as shown in Table 2 and Figure 1A, confirming the observation by Carareto et al.23 This behavior can be explained by comparing the volatility of the compounds: the higher the carbon chain of the fatty compound, the lower is its volatility, which is associated with lower vapor pressure. However, this fact is not true for unsaturated compounds (Table 2), as can be seen by C


Journal of Chemical & Engineering Data RMSD/% =

Article

ij (Tiexp − Timodel)2 yz zz 100 zz N k {

∑ jjjj i

(12)

(i = pure methyl esterC8:0; C10:0; C12:0; C14:0; C16:0; C18:0; C18:1); N = number of experimental data. 4.2. FAME Binary Mixture FP. The FP of binary mixtures formed by FAMEs (methyl caprylate, methyl caprate, methyl laurate, methyl myristate, methyl palmitate, methyl stearate, and methyl oleate) determined at ambient pressure (P) is shown in Tables 3−7. The experimental FP temperature measured for methyl caprylate plus another FAMEs are shown in Figure 2 along with the results obtained using the ideal assumption for the same mixtures. The FP plots of the other systems are shown in the Supporting Information. The rmsd between FP experimental data and the ideal model results were calculated using eq 12 and are shown in Table 8. As previously explained, due to the small difference between the FP of pure C16:0 and C18:1 (5.5 K), this system was not evaluated. Figure 2 shows a steep decrease in the FP value with small addition of the light component into the binary mixture in the region that is poor in such components. This behavior is accentuated, for example, for the binary mixture formed by methyl caprylate + methyl stearate, which has a difference equal to 108.6 K between the FP of their pure components (346.9 and 455.5 K, respectively). For this mixture with an addition of 20% of methyl caprylate, the binary mixture FP decreases more than 70°. This decrease in the FP temperature is less significant in binary mixtures formed by FAMEs with a difference of 4 or less than 4 carbon atoms between their carbon chains. For example, the binary mixture formed by methyl caprylate and methyl laurate shows a decrease of only 22° with the addition of 20% of the lighter component (methyl caprylate). This result is an indication of the risk involved in the production and transportation of such compounds, being important to consider the difference in the length of the alkyl carbon chain of the compounds present in the mixture. For all mixtures, a decrease in the FP value was observed when the lighter compound is added to the solution, and this trend was not linear. Some authors have reported the predicted FP for ideal solutions.31,34,56−58 According to these authors, when the ideal behavior is observed, the mixture FP always present an intermediate value between the most and least flammable compound. As observed in Figure 2 and in Tables 3−7, this is true to the data reported in this study. Indeed, we can also observe a good agreement between the experimental data and those calculated using the ideal approach that was confirmed

Figure 1. (A) FP of pure FAMEs and comparison with Carareto’s model.23 (◇) Experimental data (saturated carbon chains), () Carareto’s model (B) FP values predicted using the empirical model fitted by Carareto et al.23 vs experimental values of FAME. (◇) FP experimental vs FP predicted, () x = y.

comparing the FP of methyl stearate (C18:0) with that of methyl oleate (C18:1). Carareto et al.23 also fitted an empirical model (eq 11) to estimate the FP temperature of pure FAEEs because the number of carbon atoms in the fatty acid residue chain (nC) and the number of double bonds (nCC) are known TFP,i /K = 251.2 + 13.97nC − 0.1198nC 2 − 19.9nCC, (11)

where TFP,i is the FP temperature of FAEE. The FP experimental data measured in this study were compared with the values calculated using eq 11, and are higher than the values estimated by Carareto’s correlation, as shown in Figure 1B. As mentioned before, the Carareto’s correlation was proposed to FAEEs using only FAEEs experimental data; this fact can justify the difference observed because in this study, the data were determined only to FAMEs that have one less carbon atom in the carbon chain when compared with FAEEs. The FP temperature deviations between the experimental data measured for pure FAMEs and the value calculated using Carareto’s approach were in the range of (0.3−2.0) % for saturated FAMEs, and a maximum deviation value equal to 2.2% was obtained for the methyl oleate, which has a double bond, suggesting that the presence of the double bond in the chain induces greater deviations when compared with the presence of only the saturated chain. Therefore, the FP prediction of unsaturated compounds should be analyzed carefully. Nevertheless, Carareto’s approach was able to predict the FP temperature of FAMEs within a good accuracy because the root-mean-square deviation (rmsd) was equal to 0.7% (eq 12)

Table 3. Binary Mixture FP of Methyl Caprylate (1) + FAMEs (2) for Different Compositionstbl3fna methyl caprate

methyl laurate

methyl myristate

methyl palmitate

methyl stearate

methyl oleate

x1

TFP/K

P/Pa

TFP/K

P/Pa

TFP/K

P/Pa

TFP/K

P/Pa

TFP/K

P/Pa

TFP/K

P/Pa

0.00 0.10 0.20 0.40 0.60 0.80 1.00

374.7 370.6 365.6 360.6 354.6 351.3 348.6

95 300 95 010 95 250 95 100 95 140 95 070 94 850

398.4 384.6 376.3 364.6 357.6a 351.9 348.6

94 690 95 300 95 100 95 050 94 950 95 050 94 850

419.7 393.5 380.1 366.7 357.7 352.7 348.6

95 110 94 660 94 330 95 040 93 950 94 930 94 850

440.3 396.9 382.6 366.9 358.3 352.6 348.6

94 950 94 700 93 870 93 600 94 650 94 500 94 850

455.5 401.3 385.5 367.5 357.3 352.0 348.6

95 000 94 000 95 000 94 750 94 800 95 050 94 850

445.8 400.4 383.1 367.8 358.5 353.5 348.6

95 150 94 560 94 320 94 720 95 020 94 430 94 850

a

Composition: x1 = 0.59; u(x1) = 0.0014; u(P)/Pa = 300 Pa; u(TFP)/K = (0.6−2.9) K D



Article

Table 4. FP of the Binary Mixture of Methyl Caprate (1) + FAMEs (2) for Different Compositions methyl laurate

methyl myristate

methyl palmitate

methyl stearate

methyl oleate

x1

TFP/K

P/Pa

TFP/K

P/Pa

TFP/K

P/Pa

TFP/K

P/Pa

TFP/K

P/Pa

0.00 0.10 0.20 0.40 0.60 0.80 1.00

398.4 393.7 390.7 385.4 380.7 377.4 374.7

94 690 93 950 94 100 94 050 94 850 95 030 95 300

419.7 407.9 400.3 389.9 383.6 377.6 374.7

95 110 93 540 93 330 94 040 94 140 93 990 95 300

440.3 418.0 405.0a 391.4b 384.0 379.3 374.7

94 950 95 040 94 760 94 550 94 650 95 100 95 300

455.5 426.9 408.6 393.7 384.1 378.1 374.4

95 000 95 100 94 600 94 000 93 740 94 530 95 300

445.8 418.2 407.8 392.8 385.4 379.1 374.7

95 150 94 560 93 450 94 600 94 600 94 550 95 300

a

Composition: x1 = 0.21. bComposition: x1 = 0.41; u(x1) = 0.0016; u(P)/Pa = 300 Pa; u(TFP)/K = (0.6−1.1) K.

Table 5. FP of the Binary Mixture of Methyl Laurate (1) + FAMEs (2) for Different Compositionsa methyl myristate

methyl palmitate

methyl stearate

methyl oleate

x1

TFP/K

P/Pa

TFP/K

P/Pa

TFP/K

P/Pa

TFP/K

P/Pa

0.00 0.10 0.20 0.40 0.60 0.80 1.00

419.7 415.9 412.3 407.6 403.3 400.6 398.4

95 110 93 700 93 760 93 690 93 840 93 950 94 690

440.3 431.7 422.9 413.9 406.6 402.3 398.4

94 950 95 000 95 010 94 870 94 680 94 880 94 690

455.5 438.4 427.3 415.5 407.1 402.8 398.4

95 000 95 000 95 120 95 150 95 240 95 020 94 690

445.8 434.2 425.2 415.2 406.9 401.9 398.4

95 150 94 600 94 230 94 100 94 000 94 320 94 690

a

u(x1) = 0.0027; u(P)/Pa = 300 Pa; u(TFP)/K = (0.6−2.1) K.

Table 6. FP of the Binary Mixture of Methyl Myristate (1) + FAMEs (2) for Different Compositions methyl palmitate

methyl stearate

methyl oleate

x1

TFP/K

P/Pa

TFP/K

P/Pa

TFP/K

P/Pa

0.00 0.10 0.20 0.40 0.60 0.80 1.00

440.3 437.3 434.9 429.6 425.9 422.3 419.7

94 950 93 780 93 910 94 590 94 220 93 890 95 110

455.5 447.4 442.4a 435.0 429.4 423.4 419.7

95 000 94 500 94 500 94 560 94 200 94 100 95 110

445.8 442.5 436.8b 432.8 426.2 423.2 419.7

95 150 94 800 94 560 94 780 94 650 94 320 95 110

a

Composition: x1 = 0.19. bComposition: x1 = 0.23; u(x1) = 0.0029; u(P)/Pa = 300 Pa; u(TFP)/K = (0.6−1.0) K.

Table 7. FP of the Binary Mixture of Methyl Palmitate (1) + Methyl Stearate (2) for Different Compositionsa Figure 2. FP of binary mixtures containing C8 (1) + FAMEs (2) and the ideal model. Experimental data: (■) C8 + C10, (◇) C8 + C12, (▲) C8 + C14, (○) C8 + C16, (□) C8 + C18:0, and (◆) C8 + C18:1. Ideal models: () C8 + C10, (− · −) C8 + C12, (---) C8 + C14, (····) C8 + C16, (− − −) C8 + C18:0, and (−··−) C8 + C18:1.

methyl stearate x1

TFP/K

P/Pa

0.00 0.10 0.18 0.37 0.57 0.78 1.00

455.5 454.4 449.9 448.3 446.3 443.3 440.3

95 000 94 300 94 500 94 550 94 360 94 400 95 110

different UNIFAC models to the system containing C8 + C10: the activity coefficient value close to unity is indicative of ideal solution behavior, as demonstrated in Figure 3. Because of the exposed, the ideality is responsible for the trends of the FP curvatures observed in the investigated systems.56,58 To evaluate the capacity of predicting FP temperature of binary mixtures formed by FAMEs, the UNIFAC, UNIFACDo, and NIST-UNIFAC models were used and compared with the experimental data through rmsd (Table 8). Based on the close value of rmsd for these models (0.85, 0.84 and 0.92, respectively), they were considered fairly comparable, with the advantage that the parameters of the traditional UNIFAC are temperature independent that is simpler to use than the modified UNIFAC models. Although the UNIFACs model

a

u(x1) = 0.0019; u(P)/Pa = 300 Pa; u(TFP)/K = (0.6−2.1) K.

by rmsd (Table 8). The average of rmsd for all systems studied was 0.67%, a value with no significant deviation from the ideality, confirming that the binary FAME mixtures can be considered an ideal mixture because the molecules present in the system are similar and the bonds between them are weak enough to be considered negligible. The ideal behavior was also confirmed by calculating the activity coefficient with the E



Article

Table 8. rmsd (K) between Experimental Data and Models system

ideal

UNIFAC

UNIFAC-Do

NIST-UNIFAC

fitted NRTL

C8 + C10 C8 + C12 C8 + C14 C8 + C16 C8 + C18:0 C8 + C18:1 C10 + C12 C10 + C14 C10 + C16 C10 + C18:0 C10 + C18:1 C12 + C14 C12 + C16 C12 + C18:0 C12 + C18:1 C14 + C16 C14 + C18:0 C14 + C18:1 C16 + C18:0 average

0.55 0.45 0.35 0.33 1.01 1.04 0.46 0.66 0.52 1.57 0.44 0.84 0.57 0.91 0.56 0.24 0.74 0.59 0.93 0.67

0.56 0.51 0.51 0.70 0.75 1.06 0.47 0.73 0.71 1.29 1.47 0.85 0.59 1.10 1.31 0.23 0.76 1.65 0.93 0.85

0.57 0.57 0.66 0.95 0.89 0.96 0.48 0.76 0.79 1.25 0.97 0.86 0.60 1.13 1.04 0.23 0.76 1.51 0.93 0.84

0.57 0.56 0.63 0.93 0.89 0.83 0.48 0.76 0.79 1.51 1.49 0.86 0.60 1.15 1.62 0.23 0.76 1.87 0.93 0.92

0.50 0.31 0.31 0.31 0.78 1.01 0.21 0.38 0.30 1.45 0.27 0.27 0.55 0.30 0.41 0.22 0.23 0.54 0.83 0.46

Figure 3. Activity Coefficient of the Binary Mixture Containing C8 (1) + C10 (2) Calculated Using Ideal Approach and UNIFAC Models: () Ideal, (---) UNIFAC, (····) UNIFAC-Do, (−·−) NISTUNIFAC.

Figure 4. FP of binary mixtures containing C10 (1) + FAMEs (2) and the UNIFAC-Do model. Experimental data: (■) C10 + C12, (◇) C10 + C14, (▲) C10 + C16, (◆) C10 + C18:0, (○) C10 + C18:1. UNIFAC-Do models: () C10 + C12, (−·−) C10 + C14, (---) C10 + C16, (−··−) C10 + C18:0, (····) C10 + C18:1.

show good results, the rmsd calculated considering the ideal model was smaller except for C8 + C18:0 and C10 + C18:0 systems, which was expected because the binary systems are formed only for similar species (esters) and the UNIFAC models are a predictive model whose parameters were fitted based on another system and thermodynamic equilibrium data. Moreover, the difference of 10 and 8 carbon atoms between the carbon chain of the methyl caprylate + methyl stearate and methyl caprate + methyl stearate systems (Figures 2 and 4, respectively) confirms that the difference between the size of molecules implies in a deviation of the ideal behavior because the rmsd of the ideal model is larger than those calculated using the UNIFAC models. The plots of all the systems studied with the FP data calculated using all UNIFAC models are shown in the Supporting Information. The results point out that the larger deviations are observed in mixtures in which C18:0 and C18:1 are present, to both ideal and UNIFAC models. This result leads us to believe that the ideal assumption is not the most suitable approach to these cases, and also that better parameters need to be provided to

improve the FP temperature calculation of mixtures formed with an unsaturated compound or with a compound of large carbon chain length. Indeed, a slight negative deviation from ideality can be demonstrated in Figure 5 when UNIFAC, UNIFAC-Do, and NIST-UNIFAC models were applied to calculate the activity coefficient, which corroborates our observations. Despite that biodiesel is a multicomponent mixture and its composition varies according to the source from which they were produced,59 it is known that it is formed mainly by larger methyl esters, remarkably methyl palmitate, methyl stearate, methyl oleate, and linoleate.20,30,59,60 However, smaller methyl esters such as methyl caprylate, methyl caprate, methyl laurate, and methyl myristate can also be found in its composition,22,28,59 and, as demonstrated in this study, small fraction addition of lighter components may affect significantly the FP of the mixtures formed by methyl esters. Therefore, special F



Article

Mariana Conceiçaõ Costa: 0000-0003-1710-7202 Funding

This study was financed in part by the Coordenaçaõ de ́ Aperfeiçoamento de Pessoal de Nivel SuperiorBrasil (CAPES)Finance Code 001. The authors also would like to thank national funding agencies FAPESP [2012/05027-1, 2014/21252-0], CNPq [310272/2017-3, 140723/2016-1], and FAEPEX/UNICAMP for the financial support. The authors thank Espaço da EscritaPró-Reitora de Pesquisa UNICAMPfor the language services provided. Notes

The authors declare no competing financial interest.

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Figure 5. Activity coefficient of the binary mixture containing C10 (1) + C18:0 (2) calculated using the ideal approach and UNIFAC models: () ideal, (---) UNIFAC, (····) UNIFAC-Do, and (−·−) NIST-UNIFAC.

attention should be taken to evaluate the FP considering this behavior.

5. CONCLUSIONS The results of this study show the FP of FAMEs increases with the carbon chain length and decreases with the presence of unsaturation in the carbon chain. The comparison between ideal assumption, UNIFAC, UNIFAC-Do, and NIST-UNIFAC models show that the ideal model, despite of its simplicity, can describe the binary systems formed by FAMEs appropriately because the solutions studied in this work can be considered ideal solutions, not being necessary for the use of the UNIFAC model or of its modifications. The rmsd calculated between the ideal model and experimental FP was equal to 0.67%, whereas the rmsd was equal to 0.85, 0.84, and 0.92% for UNIFAC, UNIFAC-Do, and NIST-UNIFAC models, respectively. Also, the FP value steeply decreases with small addition of the light component into the mixture in the region that is poor in such components, when large differences in the length of the alkyl carbon chain of the compounds present in the mixture are observed. Therefore, it is an important behavior that must be considered in the production and transportation of methyl esters.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.9b00267. Experimental data and ideal assumption, UNIFAC, UNIFAC-Do, and NIST-UNIFAC models plots to the systems studied: C8 + C10; C8 + C12; C8 + C14; C8 + C16; C8 + C18:0; C8 + C18:1; C10 + C12; C10 + C14; C10 + C16; C10 + C18:0; C10 + C18:1; C12 + C14; C12 + C16; C12 + C18:0; C12 + C18:1; C14 + C16; C14 + C18:0; C14 + C18:1; and C16 + C18:0 (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +551935213962. ORCID

Rafael Macedo Dias: 0000-0002-0810-2381 G



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