Solid–Liquid Equilibria in the Binary Systems of Saturated Fatty Acids

Article pubs.acs.org/jced

Solid−Liquid Equilibria in the Binary Systems of Saturated Fatty Acids or Triglycerides (C12 to C18) + Hexadecane Kazuko Yui,† Yasuhiro Itsukaichi,† Takuro Kobayashi,† Tomoya Tsuji,‡ Keisuke Fukui,§ Kouji Maeda,§ and Hidetoshi Kuramochi*,†,¶ †

Center for Material Cycles and Waste Management Research, National Institute for Environmental Studies, 16-2 Onogawa, Tsukuba, Ibaraki 305-8506, Japan ‡ Shizen iKohza, Malaysia-Japan International Institute of Technology, Universiti Teknologi Malaysia, Off Jalan Sultan Yahya Petra, Kuala Lumpur, 54100, Malaysia § Department of Chemical Engineering, University of Hyogo, 2167 Shosha, Himeji, Hyogo 671-2201, Japan ¶ Department of Physical and Environmental Sciences, University of Toronto Scarborough, 1265 Military Trail, Toronto, Ontario M1C 1A4, Canada S Supporting Information *

ABSTRACT: Solid−liquid equilibria (SLE) for the binary systems of C12−C18 saturated fatty acids or their triglycerides + hexadecane (systems of dodecanoic acid (lauric acid), tetradecanoic acid (myristic acid), hexadecanoic acid (palmitic acic), octadecanoic acid (stearic acid), 1,2,3-propanetriyl tridodecanoate (trilaurin), 1,2,3-propanetriyl tritetradecanoate (trimyristin), 1,2,3-propanetriyl trihexadecanoate (tripalmitin), or 1,2,3-propanetriyltrioctadecanoate (tristearin), + hexadecane) were measured in the hexadecane fractions of 0 to 1 and temperatures from (273.2 to 353.2) K, using differential scanning calorimetry. These systems were selected as model systems for blending oily content extracted from restaurant trap grease with fossil fuel oils. The obtained liquidus curves were discussed in terms of the effects of carbon chain length, chemical form, and variation in the liquid component. In addition, the experimental liquidus curves were compared with predictions based on ideal solution approximation and on the LLE-UNIFAC and Dortmund-UNIFAC models. The triglyceride and hexadecane binary systems were close to the ideal solution, while the fatty acid−hexadecane binary systems were not. The Dortmund-UNIFAC model successfully predicted all liquidus curves of the nonideal, fatty acid−hexadecane systems.

1. INTRODUCTION Recently, waste biomass has received increasing attention as an energy source in both industrial and public sectors. Utilization of waste biomass as an alternative to fossil fuels is a key means of addressing issues related to global warming and diminishing fossil fuel reserves. In our previous work, 1 we have demonstrated that an oily slurry composed of fatty acids (FAs) and triglycerides (TGs) was successfully recovered from restaurant trap grease, which is a mixture of waste oils and fats floating in grease interceptor at a restaurant, using a simple heat-driven extraction method. The gross calorific value of the recovered oily content was 40.2 MJ·kg−1, near to that of fossil fuel oil, such as 45.6 MJ·kg−1 for diesel and fuel oil.2 The oily content from trap grease has yet to be recycled into any fuel in Japan; however, it should be used as an alternative to fossil fuels. In our other previous work,3 we also demonstrated that such oily content could be converted into second-generation biodiesel fuel through high-pressure, high-temperature hydrotreating. However, this technology has not been commercial© 2016 American Chemical Society

ized due to the relatively large volume of hydrogen required for the treatment and the additional purifications required to meet our domestic fuel standards. Therefore, we considered direct fuel utilization of the oily content, without expensive treatments. Unfortunately, the oily content from trap grease is often solidified at ambient temperature because of the presence of a high proportion of saturated FAs (SFAs) and TGs (STGs) with high melting points of over 60 °C, and for commercial use, such solidified compounds may present difficulties during the production, transportation, and/or direct utilization. As a solution to such difficulties, we considered blending the solidified oily content with a fossil fuel oil; that is, dissolving it into the fuel oil at ambient temperature. To determine the proper blending ratio for maintaining the mixture in the liquid state around ambient temperatures, data Received: April 29, 2016 Accepted: December 7, 2016 Published: December 22, 2016 35

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Table 1. Physical Properties and Purities of Chemicals Used in This Study

a

chemical name (alias, abbreviation)

formula

supplier

puritya

Mw/g·mol−1b

octadecanoic acid (stearic acid, SA) hexadecanoic acid (parmitic acid, PA) tetradecanoic acid (myristic acid, MA) dodecanoic acid (lauriic acid, LA) 1,2,3-propanetriyl trioctadecanoate (tristearin, TS) 1,2,3-propanetriyl trihexadecanoate (tripalmitin, TP) 1,2,3-propanetriyl tritetradecanoate (trimyristin, TM) 1,2,3-propanetriyl tridodecanoate (trilaurin, TL) hexadecane (n-hexadecane, HD)

C17H35COOH C15H31COOH C13H27COOH C11H27COOH C3H5(C18H35O2)3 C3H5(C16H31O2)3 C3H5(C14H27O2)3 C3H5(C12H23O2)3 C16H34

Sigma Aldrich Sigma Sigma Sigma Sigma Sigma Tokyo Chemical Industry SIAL

>0.985 >0.985 >0.99 >0.99 >0.99 >0.99 >0.99 >0.98 >0.985

284.5 256.4 228.4 200.3 891.5 807.3 723.2 639.0 226.4

Purities were provided by suppliers as determined from GC. bMolar masses were cited from the NIST Standard Reference Data.

2. MATERIALS AND METHODS 2.1. Chemicals. All chemicals except for trilaurin were purchased from Sigma-Aldrich, and their mass purities were certified as being greater than 0.985. Trilaurin was purchased from Tokyo Chemical Industry Co. Ltd., with purities of greater than 0.98. Details for the chemicals are listed in Table 1. 2.2. DSC Measurement. The experimental procedure was similar to that of our previous study.17 A fatty acid or triglyceride and hexadecane were weighed using an analytical balance (Mettler-Toledo Co., AB265-S), mixed in a glass vial (2 mL), and sealed. Each mixture was heated to 353 K in a water bath to dissolve the solid component completely, and then 10 mg of the solution was poured into an aluminum pan with the lid and rapidly sealed. The amount of the sample in the pan was weighed. The aluminum pan was put into a DSC apparatus (Netzsch, DSC200 F3Maia) at room temperature. The sample was initially refrigerated to 263 K; the low temperature was maintained for 10 min, and then the furnace was heated to 353 K at a heating rate of 1.00 or 3.00 K·min−1, and the DSC signal was recorded from 273 to 353 K. During the measurement of the DSC signal, nitrogen gas was flowing at 20 mL·min−1 in the sample chamber of the DSC apparatus. The DSC curves for the binary systems showed mainly two endothermic peaks, corresponding to the solidus (Te) and liquidus (Tl) temperatures, respectively. The onset point of the first peak was determined as Te, and the peak top temperature of the last peak was determined as Tl.18 The mole fractions of the samples were determined from the mass fractions calculated from the measured weights. The uncertainty of the weight values provided by the analytical balance was 0.05 mg, and the uncertainties of the mole fractions were calculated to be 0.002. The temperature and heat flow were calibrated using the melting properties of adamantane (−64.5 °C, −22.000 J·g−1),19 In (156.6 °C, −28.6 J·g−1),20 Sn (231.9 °C, −60.5 J·g−1),20 Bi (271.4 °C, −53.1 J·g−1),21 Zn (419.5 °C, −107.5 J·g−1),20 and CsCl (476.0 °C, −17.2 J·g−1)22 by the supplier of the DSC apparatus, and the thermal properties of each material in the parentheses were the values quoted from the references19−22 provided by the supplier.

on the solid−liquid equilibria (SLE) for the SFAs and STGs and alkanes in fossil fuel are important; and in particular, the liquidus curve, which expresses the relationship between the composition and temperature for the complete liquefaction of a given mixture, is essential for achieving homogeneous blending. While the SLE for the systems of components of biofuels such as fatty acids, triglycerides, and esters have been broadly studied, studies on the SLE for systems including SFAs or STGs and alkanes are not so much.4−16 SLE data for SFA + alkane systems are available for lauric acid + hexane (C6H14),11 octadecane (C8H18),13 n-eicosane (C20H42),12 palmitic acid + hexane,9 heptane (C7H16),9 n-octacosane (C28H58),12 and stearic acid + hexane,6−8 heptane,5,8 decane (C10H22),4,6 dodecane (C12H26),10 n-tetracosane (C24H50).12 The SLE data of STG + alkane system are reported for tristearin + n-hexane.14 The SLE data of STAs or STGs and components of fuel oil such as hexadecane (C16H34) have not yet been reported. In the preceding SLE studies, predictive or correlative equations such as the UNIFAC equations have been commonly applied to the measured SLE data. In our previous work, we also reported that two UNIFAC models14,15 were useful in predicting phase equilibria for biodiesel and its related compounds;16 however, we cannot suggest which model is useful for representing the SLE for the SFA or STG + fuel oil component systems because of the aforementioned lack of SLE data. Discussions on the usefulness of each model are important not only for the determination of proper blending ratios of oily contents and fuel oils but also for the process design in the extraction and purification of the oily content from trap grease. The objective of this study is to determine the solid−liquid phase equilibria for eight binary mixtures of SFAs (lauric acid, myristic acid, palmitic acid, and stearic acid) and STGs (trilaurin, trimyristin, triplamitin, and tristearin) + hexadecane. These systems were selected as model systems for blending the oily content upgraded from trap grease with low-sulfur fuel oil. Hexadecane is a major component of low-sulfur fuel oil in Japan. Differential scanning calorimetry (DSC) was employed for the SLE determination. In the present study, we discuss the effect of differences in carbon chain length and chemical form among solid components, and of differences in the liquid component between hexadecane and unsaturated FAs or TGs. In addition, the liquidus curves of the individual systems are estimated using the ideal solution, LLE-UNIFAC, and Dortmund-UNIFAC models, and the estimation performance of the respective models is evaluated by comparing the estimated results with the experimental liquidus curves.

3. RESULTS AND DISCUSSION 3.1. Accuracy. Prior to the SLE determination, the melting properties of pure SFAs and STGs were examined to confirm our experimental accuracy. In most DSC measurements for the pure components, we measured the DSC signals of powdery samples purchased from the suppliers with 10 mg of amount of load and heating rate of 3.00 K·min−1. Typically, the DSC curves of the pure components had an endothermic peak: the 36

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Table 2. Melting Temperature (Tm) and Heat of Fusion (ΔfusHm) for Pure Fatty Acids and Triglycerides at Pressure p = 0.1 MPaa abbreviation name

Tm/K

SA

343.1 338.3−344.1 342.4 340.95 342.44* 344.04* 343.75* 335.9 332.7−336 334.7 332.05 335.35* 336.34* 336.36* 336.3* 327.6 326.2−327 326.5 325.45 326.62* 328.13* 317.4 316.6-216.9 316.2 315.75 316.056 316.44* 318.29* 346.6 345.7 346.0 345.8* 345.6 345.8* 340.7 338.9−340.5 338.6* 338.8* 331.1 330.2 330.5* 321.9 319.5 319.44* 319.39* 319.67*

PA

MA

LA

TS

TP

TM

TL

ΔfusHm/kJ·mol−1

RD% 0.3−1.4 0.2 0.6 0.2 −0.3 −0.2 0.0−1.0 0.4 1.1 0.2 −0.1 −0.1 −0.1 0.2−0.4 0.3

63.31 57.8−68.45 63.2 56.58 61.10 63.07 55.84 51.37−54.94 53.0 48.62 53.3 53.02 53.97 44.87 45−45.75 45.0 40.3

RD% −7.5−9.5 0.2 10.6 3.5 0.4 1.6−2.7 5.3 12.9 4.5 5.0 3.3 −1.9 ∼ −0.3 −0.3 10.2

0.3

0.1−0.2 0.4 0.5 0.4 0.3 −0.3 0.3 0.2 0.2 0.3 0.2 0.0−0.5 0.6 0.6 0.3 0.2 0.7 0.8 0.8 0.7

43.8 37.61 36.1−36.65 36.1 35.3 35.2

ref

2.4 2.6−4.2 4.0 6.1 6.4

35.6 195.3 203.26 195.8

5.3 −4.1 −0.3

193.5

0.9

181.1 162.6−179.37

1.0−11.4

153.74 152.2

1.0

127.18 123.51

2.9

116.45 118.03

8.4 7.2

this 25 24 26 28 32 33 this 25 24 26 29 32 33 34 this 25 24 26 29 32 this 25 24 26 28 29 32 this 25 27 29 30 31 this 25 29 31 this 25 29 this 25 29 32 33

study

study

study

study

study

study

study

study

a

The melting temperatures of this study are the mean values from three measurements. The expanded uncertainties with 95% confidence level (k = 4.303)38 for Tm, U(Tm) is 0.6 K. U(ΔHfus) values for SA, PA, MA, LA, TS, TP, TM, and TL are 1.2 kJ·mol−1, 1.0 kJ·mol−1, 0.7 kJ·mol−1, 0.5 kJ·mol−1, 7.8 kJ·mol−1, 4.1 kJ·mol−1, 5.5 kJ·mol−1, and 1.0 kJ·mol−1, respectively. Standard uncertainty for pressure, u(p), is 5 kPa. RD% refers to the relative deviation (measured − literature mean value)/ literature mean value expressed in %. The values of melting temperature marked with an asterisk (∗) are the values cited from the literature which were obtained from the peak top temperatures in the heating run of the DSC study.

triglycerides observed here corresponded to the melting temperatures of the β-phase. Similarly, fatty acids are also known as polymorphic compounds,24 and in the present DSC measurements the fatty acids mostly had a single peak corresponding to the fusion of the C form, though in stearic acid and lauric acid, a small peak which possibly corresponds to the phase change of the B to C or E to C form were also found,

melting point (Tm) was determined from the onset point of the peak, and the heat of fusion was determined from the integrated value of the peak area. The baseline was corrected as a straight line connecting the baseline parts of each DSC curve before and after the peak. In earlier research on the polymorphism of triglycerides, α, β, and β′ phases were found around room temperature.23 The onset temperatures of the 37

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Table 3. Solid−Liquid Equilibrium Data for the Binary Systems of Stearic Acid or Tristearin (1) + Hexadecane (2) at Pressure p = 0.1 MPaa stearic acid/hexadecane w(1)/−

x(1)/−

Tl/K

1.000 0.900 0.800 0.699 0.600 0.501 0.400 0.350 0.302 0.250 0.205 0.151 0.102 0.0511 0.000

1.00 0.88 0.76 0.65 0.54 0.44 0.35 0.30 0.26 0.21 0.17 0.12 0.08 0.04 0.00

343.1 343.3 340.7 338.3 336.0 333.8 331.3 330.0 328.6 326.9 325.4 322.9 319.6 314.0 291.3

tristearin/hexadecane Te/K

w(1)/−

x(1)/−

Tl/K

Te/K

290.9 291.0 291.0 291.1 291.1 291.1 291.1 291.2 291.1 291.2 291.2 291.1 291.1

1.000 0.898 0.798 0.700 0.601 0.501 0.399 0.350 0.301 0.250 0.200 0.150 0.100 0.0507 0.000

1.00 0.69 0.50 0.372 0.28 0.20 0.14 0.12 0.10 0.08 0.06 0.04 0.03 0.01 0.00

346.6 346.3 344.0 342.1 340.2 338.3 336.3 335.3 334.4 333.3 332.0 330.4 328.4 324.7 291.3

287.3 288.4 289.1 289.5 290.1 290.7 291.1 291.1 291.2 291.3 291.2 291.3 291.4

a The rate of temperature increase in the DSC measurements for this table is 3.00 K·min−1. The standard uncertainty of mole fraction u(x) = 0.002 and u(p) = 5 kPa. The solidus and liquidus temperatures (Te and Tl) are the average values from three measurements. The combined standard uncertainties, uc(Te) and uc(Tl) are estimated to be 0.3 and 1.3 K, respectively.38

Table 4. Solid−Liquid Equilibrium Data for the Binary Systems of Palmitic Acid or Tripalmitin (1) + Hexacdecane (2) at Pressure p = 0.1 MPaa palmitic acid/hexadecane w(1)/−

x(1)/−

Tl/K

1.000 0.898 0.799 0.700 0.600 0.499 0.398 0.349 0.300 0.250 0.200 0.150 0.100 0.000

1.00 0.89 0.78 0.67 0.57 0.47 0.37 0.32 0.27 0.23 0.18 0.13 0.09 0.00

335.9 336.1 333.6 331.4 329. 326.8 324.3 323.1 321.4 319.7 317.9 315.1 311.9 291.3

tripalmitin/hexadecane Te/K

w(1)/−

x(1)/−

Tl/K

Te/K

291.2 291.6 291.4 291.5 291.4 291.6 291.3 291.2 291.3 291.1 291.1 291.2

1.000 0.900 0.797 0.699 0.598 0.500 0.400 0.351 0.300 0.249 0.200 0.150 0.100 0.000

1.00 0.71 0.53 0.40 0.30 0.22 0.16 0.13 0.11 0.09 0.07 0.05 0.03 0.00

340.7 339.6 337.2 335.3 333.7 331.6 329.8 328.8 327.7 326.9 325.4 323.5 321.5 291.3

288.1 289.1 289.6 290.7 290.6 291.0 291.0 291.0 291.1 291.2 291.2 291.3

a The rate of temperature increase in the DSC measurements for this table is 3.00 K·min−1. The standard uncertainties are u(x) = 0.002 and u(p) = 5 kPa. The solidus and liquidus temperatures (Te and Tl) are the average values from three measurements. The combined uncertainties, uc(Te) and uc(Tl) are estimated to be 0.2 and 1.3 K, respectively.38

loading, for our UNIFAC prediction described in the later section. Table 2 lists the melting points (Tm) and enthalpies of fusion (ΔfusH) determined in this study with a sample amount of 10 mg, and reported in the literature.25−34 The measured and literature values for Tm and ΔfusH are within 1.4% and 12.9% of each other, respectively. Our ΔfusH values tend to be larger than the reported values and the reason for that is not clear: the deviations in the ΔfusH are probably due to the existence of impurities or due to the differences in the crystallinity of the samples because we measured the DSC curves of the samples without preheating them above the melting temperatures before the heating run, while some literature measured the same values for once molten and cooled samples. The scatter among the literature values was also large. The Tm can be

respectively. These smaller peaks disappeared by recrystallizing the samples at 1−3 K below the melting temperatures, and there was no large difference of the mean values of the onset temperatures and the heats of fusion between the original and recrystallized samples. We also ran the measurements for pure palmitic acid (PA) powdery samples with different sample amounts (1, 2, 5, or 10 mg) to evaluate the effect of the amount. The DSC thermograms are indicated in the Supporting Information as Figure S1. The onset temperature and the heat of fusion calculated from the peak area were almost constant against the change in the sample amount, and the measured melting points and heats of fusion are also both consistent with the literature values. We thus employed the values determined from the onset temperature of the melting peak for the original powdery samples with a 10 mg amount of 38

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Table 5. Solid−Liquid Equilibrium Data for the Binary Systems of Myristic Acid or Trimyristin (1) + Hexacdecane (2) at Pressure p = 0.1 MPaa myristic acid/hexadecane w(1)/−

x(1)/−

Tl/K

1.00 0.900 0.800 0.699 0.602 0.501 0.401 0.351 0.300 0.250 0.200 0.150 0.101

1.00 0.90 080 0.70 0.60 0.50 0.40 0.35 0.30 0.25 0.20 0.15 0.10

327.6 327.7 325.1 322.7 320. 318.3 315.7 314.2 312.8 310.7 308.9 306.3 302.4

0.000

0.00

291.3

trimyristin/hexadecane Te/K 290.4 290.5 290.6 290.7 290.8 290.8 290.8 290.8 290.8 290.9 290.8 290.8

w(1)/−

x(1)/−

Tl/K

Te/K

1.000 0.900 0.800 0.700 0.598 0.501 0.400 0.350 0.302 0.250 0.201 0.150 0.102 0.0515 0.000

1.00 0.74 0.56 0.42 0.32 0.24 0.17 0.14 0.12 0.09 0.07 0.05 0.03 0.02 0.00

331.1 330.8 328.7 326.7 325.0 323.5 321.7 320.8 319.6 318.7 316.9 315.3 313.0 309.3 291.3

289.0 290.6 290.8 291.0 290.8 290.9 291.1 291.1 291.2 291.2 291.3 291.3 291.2

The rate of temperature increase in the DSC measurements for this table is 3.00 K·min−1. The standard uncertainties are u(x) = 0.002 and u(p) = 5 kPa. The solidus and liquidus temperatures (Te and Tl) are the average values from three measurements. The combined uncertainties, uc(Te) and uc(Tl) are estimated to be 0.3 and 1.3 K, respectively.38 a

Table 6. Solid−Liquid Equilibrium Data for the Binary Systems of Lauric Acid or Trilaurin (1) + Hexacdecane (2) at Pressure p = 0.1 MPaa lauric acid/hexadecane w(1)/−

x(1)/−

Tl/K

1.000 0.894 0.799 0.700 0.599 0.500 0.400 0.350 0.300 0.250 0.200

1.00 0.91 0.82 0.73 0.63 0.53 0.43 0.38 0.33 0.27 0.22

317.4 315.9 313.7 311.4 309.1 306.8 304.2 302.9 301.3 299.4 297.1

0.000

0.00

291.3

trilaurin/hexadecane Te/K 290.0 290.2 290.3 290.3 290.4 290.4 290.4 290.4 290.4 290.4

w(1)/−

x(1)/−

Tl/K

Te/K

1.000 0.899 0.800 0.700 0.601 0.500 0.400 0.350 0.300 0.250 0.200 0.150 0.101 0.0503 0.000

1.00 0.76 0.59 0.45 0.35 0.26 0.19 0.16 0.13 0.11 0.08 0.06 0.04 0.02 0.00

321.9 318.5 316.5 314.7 313.0 311.7 310.4 309.5 307.9 307.2 306.0 303.9 301.8 297.3 291.3

290.6 291.0 291.1 291.1 291.2 291.2 291.1 291.1 291.2 291.2 291.2 291.2 291.2

The rate of temperature increase in the DSC measurements for this table is 1.00 K·min−1. The standard uncertainties are u(x) = 0.002 and u(p) = 5 kPa. The solidus and liquidus temperatures (Te and Tl) are the average values from three measurements. The combined uncertainties, uc(Te) and uc(Tl) are estimated to be 0.2 K and 0.6 K, respectively.38 a

measurements are summarized in Tables 3 to 6. The melting temperatures for the end components are also included in the tables as Tl. The standard uncertainties (standard deviations) of Te and Tl calculated from each three runs were smaller than 0.3. The systematic errors due to our measurement conditions were also evaluated by running the measurements for palmitic acid + hexadecane system with different heating rates of 1.00 and 3.00 K·min−1 or by changing the sample amount of 10 mg to 5 mg. The results are indicated in the Supporting Information, Figures S2 and S3. The differences in the solidus temperatures were smaller than 0.3 K and appeared to be random, while the liqudus temperatures of 1.00 K·min−1 heating rate were always lower than that of 3.00 K·min−1; the average difference and the standard deviation were 0.7 and 0.3 K, respectively. Similarly, the liquidus temperatures of 5 mg of sample loading were lower

determined with sufficient accuracy by our measurement system. 3.2. Liquidus Curves and Differences among Solid or Liquid Components. The DSC curves for the binary systems of saturated fatty acids (SFAs) or triglycerides (STGs) + nhexadecane (HD) were recorded with a heating rate of 3.00 K· min−1 in most cases, and it was sufficient to determine the SLE data. However, for the lauric acid + hexadecane and trilaurin + hexadecane systems, because of the closeness of the melting point of the pure components, two endothermic peaks overlapped when using 3.00 K·min−1 and we ran the measurements at 1.00 K·min−1 for these systems. The DSC signals showed two endothermic peaks in most cases, corresponding to the solidus (Te) and liquidus (Tl) temperatures, respectively. The average values for Te and Tl from three 39

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than that of 10 mg sample loading; the average difference and the standard deviation were 0.5 and 0.3 K, respectively. The bias of the liquidus temperatures at 3.00 K·min−1 and 10 mg sample amount from the true values is estimated to be 0.7 + 0.5 = +1.2 K with a standard uncertainty of 0.4 K. The liquidus temperatures measured at 1.00 K·min−1 have a bias of +0.5 K with a standard uncertainty of 0.3 K as described above. Hence, the combined standard uncertainties for the bias-corrected Tl values are calculated to be 0.4 K for both 1.00 K·min−1 and 3.00 K·min−1 from the root-sum-of-square manner,38 and the combined uncertainty for the bias-uncorrected Tl values measured at 3.00 K·min−1 and 1.00 K·min−1 tabulated in Tables 3 to 6 are estimated to be 1.3 and 0.6 K, respectively. Figures 1 and 2 show the solid−liquid equilibrium data for SFAs and STGs with hexadecane (HD), respectively. The

Figure 2. Solid−liquid equibria at ambient pressure of binary systems of fatty acid triglycerides (1) + hexadecane(2), and tripalmitin (1) + unsaturated triglycerides (2) or fatty acids (2). White symbols represent solidus line (Te); square, trisearin (TS) + hexadecane (HD); circle, tripalmitin (TP) + HD; diamond, trimyristin (TM) + HD; triangle, trilaurin (TL) + HD. Other symbols represent liquidus line (Tl); gray square, TS + HD; gray circle, TP + HD; gray diamond, TM + HD; gray triangle, TL+ HD; asterisk, TP + oleic acid;17 plus, TP+ linoleic acid;17 hyphen,TP + triolein;17 cross, TP+ trilinolein.17

and solidus peaks. In the literature, the systems of lauric acid + hexane, heptane (C6, C8), palmitic acid + hexane, heptane, stearic acid + alkane (C6, C7, C10, and C12) systems also have similar phase diagrams: there is no eutectic point, with immiscible solid phases, while stearic acid (C18) + n-tetracosane (C24) and palmitic acid (C16) + n-octacosane (C28), and lauric acid (C12) + n-eicosane (C20) systems are eutectic. These phase equilibrium data, including ours, suggest that as the melting points of the two end-components of SFAs and alkanes become closer, the systems are more likely to be eutectic. In Figure 3, the liquidus curves are replotted as a function of the weight fraction of the solid component (w(1)), owing to the greater value of this function in actual use. With fixed carbon numbers, the liquidus curves of the STG + HD systems lie above those of the SFA + HD systems, suggesting that STGs require higher temperatures for homogeneous blending with HD than SFAs. Our previous SLE data on the binary systems of (PA or TP) + (oleic acid, triolein, linoleic acid, or trilinolein)17 are also shown in Figures 1 and 2. All the liquidus curves of the TP− solvent binary systems are observed to coincide, whereas that of the PA + HD system is located above those of the systems combining PA and other liquids, and this difference increases with a decrease in the PA concentration. Since oleic acid and linoleic acid and their triglycerides have an acceptor or donor− acceptor for the hydrogen bond, the difference may be accounted for by the absence of an acceptor for the hydrogen bond in the HD molecule. 3.3. Prediction by Ideal Solution Approximation and Two UNIFAC Models. We investigated several estimation approaches for the liquidus curves for the studied binary systems. Generally, the liquidus curve can be described by the Schröder−van Laar equation:35

Figure 1. Solid−liquid equilibria at ambient pressure of binary systems of fatty acids (1) + hexadecane (2), and palmitic acid (1) + unsaturated triglycerides (2) or fatty acids (2). White symbols represent solidus line (Te); square, stearic acid (SA) + hexadecane (HD); circle, palmitic acid (PA) + HD; diamond, myristic acid (MA) + HD; triangle, lauric acid (LA) + HD. Other symbols represent liquidus line (Tl); solid square, SA + HD; solid circle, PA + HD; solid diamond, MA+ HD; solid triangle, LA+ HD; asterisk, PA + oleic acid;17 plus, PA+ linoleic acid;17 hyphen, PA + triolein;17 cross, PA+ trilinolein.17

liquidus curves of the components with a larger carbon number + HD systems are located above those of smaller carbon number + HD in Figures 1 and 2. Therefore, SFAs and STGs with longer carbon chains are more difficult to blend homogeneously with HD at low temperatures. The SLE data also indicates that the eutectic points for our measured systems are positioned at the end of the HD side where the mole fraction of the SFA or STG is small. In the C16−C18 SFA + HD (C16) systems and C14−C18 STGs + HD systems, the eutectic points are positioned at the edge of the HD side, where the fatty acid fractions are almost zero and thus the solidus temperature of the binary systems are almost the same as the melting temperature of pure HD, accordingly. In myristic acid (C14) + HD and lauric acid (C12) + HD systems, the SLE data show the eutectic features more clearly and the solidus temperatures are slightly lower than the melting point of pure HD, although it was difficult to determine the eutectic point of both systems due to the overlapping of the liquidus 40

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represent phase equilibria for biodiesel production systems and fatty acid and triglyceride or fatty acid and alkane systems. The liquidus curves predicted using the ideal solution approximation are shown in Figure 4, and the absolute mean

Figure 3. Liquidus curves for the binary systems: fatty acids (1) + hexadecane (2), and fatty acid triglycerides (1) + hexadecane (2). Symbols: solid square, stearic acid (SA) + hexadecane (HD); solid circle, palmitic acid (PA) + HD; solid diamond, myrisitic acid (MA)+ HD; solid triangle, lauric acid (LA) + HD; gray square, tristeartin (TS) + HD; gray circle, tripalmitine (TP) + HD; gray diamond, trimyristin (TM) + HD; gray triangle, trilaurin (TL)+ HD.

ln x(1)γ(1) =

ΔfusH ⎛ 1 1⎞ − ⎟ ⎜ R ⎝ Tm Tl ⎠

(1)

where Tm and ΔfusH are the melting temperature and the heat of fusion of pure component 1 (such as SFAs or STGs), respectively; Tl is the liquidus temperature at a given composition; and x(1) and γ(1) are the mole fraction and activity coefficient of component 1 in the liquid phase, respectively. First, the ideal solution approximation, which means γ(1) is equal to unity, was used. This is often employed as a preliminary method for estimating the phase equilibrium of unknown systems. In addition, the LLE-UNIFAC model14 and the Dortmund-UNIFAC model15 were used to determine γ(1). The former incorporates a revision of the group interaction parameter table in the original UNIFAC model36 for estimating liquid−liquid equilibria, while the latter includes a modification of the combinatorial term and accounts for the temperature dependence of group interactions. The group assignments of individual compounds in the present study are listed in Table 7. On the basis of our previous studies16,17 and other earlier work,12 we hypothesized that both models were appropriate to

Figure 4. Estimates of the liquidus curves for the present systems, using ideal solution approximation: (a) the fatty acid (1) + hexadecane (2) systems: stearic acid (SA) + hexadecane (HD), palmitic acid (PA) + HD, myristic acid (MA) + HD, and lauric acid (LA) + HD systems. (b) the fatty acid triglyceride (1) + hexadecane (2) systems; tristearin (TS) + HD, tripalmitin (TP) + HD, trimyristin (TM) + HD, and trilaurin (TL) + HD systems. Symbols: solid square, SA; solid circle, PA; solid diamond, MA; solid triangle, LA; gray square, TS; gray circle, TP; gray diamond, TM; gray triangle, TL. Dotted line, ideal solution; dashed line, LLE-UNIFAC;14 solid line, Dortmund-UNIFAC.15

Table 7. UNIFAC Groups for Triglycerides and Fatty Acids compounds stearic acid palmitic acid myristic acid lauric acid tristearin tripalmitin trimyristin trilaurin hexadecane

deviations of the predicted and experimental liquidus temperatures are listed in Table 8. For the STG + HD systems, the predicted values agree well with the experimental values; average absolute deviations are consistently below 1 K. Such systems are considered to be close to the ideal solution, and thus there is only a slight difference in molecular interaction between the STGs and HD. On the other hand, the ideal solution approximation is not valid for representing the liquidus curve of the SFA + HD systems; average absolute deviations are consistently larger than 4 K. The deviations increased with lower mole fractions of SFA. The estimated curves lying below

UNIFAC group assignment 1 1 1 1 1 1 1 1 2

× × × × × × × × ×

CH3, 16 × CH2, 1 × COOH CH3, 14 × CH2, 1 × COOH CH3, 12 × CH2, 1 × COOH CH3, 10 × CH2, 1 × COOH CH, 3 × CH3, 47 × CH2, 3 × CH, 3 × CH3, 41 × CH2, 3 × CH, 3 × CH3, 35 × CH2, 3 × CH, 3 × CH3, 29 × CH2, 3 × CH3,14 × CH2

CH2COO CH2COO CH2COO CH2COO

41

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combination with A-type Fuel Oil (AFO, low-sulfur fuel oil grade in Japan), and further investigate systems of the oily content upgraded from trap greases and AFO. The STG + hexadecane systems are well described by assuming ideal solution behavior, while the SFA + hexadecane systems are not, showing positive deviations from the ideal solution. Therefore, the activity coefficient must be estimated in order to obtain good representation of the experimental liquidus curve. Activity coefficient predicted by the DortmundUNIFAC model described the liquidus curves for the SFA + hexadecane systems well, while the LLE-UNIFAC model was not valid at lower mole fractions of SFAs and STGs.

Table 8. Mean Deviation between Three Predictions and Experimental Dataa mean deviation/K

stearic acid/hexadecane palmitic acid/hexadecane myristic acid/hexadecane lauric acid/hexadecane tristearin/hexadecane tripalmitin/hexadecane trimyristin/hexadecane trilaurin/hexadecane

ideal solution

LLEUNIFAC

DortmundUNIFAC

5.9 5.4 6.6 4.3 0.8 1.1 0.8 0.9

4.8 4.4 5.3 3.0 2.9 2.9 5.0 5.9

0.8 0.6 0.6 1.2 1.2 1.3 2.7 3.4

■

Mean deviation =1/(N)∑|Tl, expt − Tl, calc| (= average absolute deviation, AAD). a

ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.6b00355. DSC curves for pure palmitic acid measured with different sample amounts, DSC curves for palmitic acid−hexadecane binary system (50 wt %−50 wt %), and the liquidus and solidus curves for the palmitic acid− hexadecane binary system obtained from the DSC measurements with different sample amount and sample heating rate (PDF)

the experimental lines indicate that the activity coefficient of SFA is higher than unity at lower mole fraction. These types of positive deviation from the ideal solution were observed in earlier studies on SLE for binary mixtures involving chemicals capable of forming hydrogen bonds, such as fatty acids and alkanols, and nonpolar hydrocarbons.12,13,37 Figure 4 also shows the estimated results of the two UNIFAC models. The absolute mean deviations in Tl between the measured and calculated values are again summarized in Table 8. The Dortmund-UNIFAC model correctly represented the experimental liquidus curves for the binary systems involving SFAs, with average absolute deviations smaller than 1.2 K. However, the liquidus curve predicted by the DortmundUNIFAC model for binary systems involving STGs deviated more from observations than the one obtained using the ideal solution assumption. On the other hand, the LLE-UNIFAC model performed poorly in predicting the liquidus curves for all systems at low mole fractions of SFAs and STGs; it underestimated γ(1) in the case of the SFA + HD systems, and overestimated it in the case of the STG + HD systems. Although the LLE-UNIFAC model can predict the activity coefficient of fatty acids or triglycerides in some mixtures involving them,17 it should be carefully used when either are present with hydrocarbons.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Hidetoshi Kuramochi: 0000-0003-2992-8358 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We would like to thank Professor Frank Wania (University of Toronto Scarborough) for helpful comments during the preparation of this manuscript. We are also grateful to Ms. Megumi Ito for the experimental assistance. This work was supported by JSPS KAKENHI Grant No. 24360377.

■

4. CONCLUSION We have measured the solid−liquid equilibria for binary mixtures of saturated fatty acids (SFAs) or triglycerides (STGs) + hexadecane, using DSC. The liquidus curve in particular, which expresses limitations on maintaining the homogeneity of the mixture, is important for blending SFAs or STGs and hexadecane. The liquidus curves of SFAs and STGs with longer carbon chains were typically higher than those with shorter chains. SFAs do not require higher temperature to blend homogeneously with hexadecane, in comparison with STGs. The minimum value of the liquidus curves measured in the present work was 297.1 K for the LA + HD system, in which the weight fraction of LA was 20 wt %. This indicates that it is difficult to maintain homogeneity in the blended mixture at ambient temperature. In actual applications, however, both the oily component of the trap grease and the fuel oils are composed of more components and the freezing temperature of the blended oils may be different from the temperature observed for the pure binary systems studied here. To address this issue in the future, we are preparing to report the liquidus curves for the binary systems of the same SFAs and STGs in

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