ARTICLE pubs.acs.org/IECR
Improved Method for Determining the Atmospheric Distillation Curve of Biodiesel Fuels from Reduced Pressure Magín Lapuerta,*,† Laureano Canoira,‡ and Jesus Raez† †
Escuela Tecnica Superior de Ingenieros Industriales, Universidad de Castilla-La Mancha, Avenida Camilo Jose Cela s/n, 13071 Ciudad Real, Spain ‡ Department of Chemical Engineering & Fuels, ETS Ingenieros de Minas, Universidad Politecnica de Madrid, Ríos Rosas 21, 28003 Madrid, Spain ABSTRACT: Vacuum distillation is widely accepted as a useful technique for obtaining the distillation curves of fuels that boil beyond their decomposition temperatures at atmospheric pressure. After their measurement, the obtained curves must be converted to atmospheric-equivalent-temperature curves following the standard method proposed in ASTM D1160. However, this method was originally developed for petroleum-derived hydrocarbons, but not for oxygenated fuels. A specific method to convert reducedpressure distillation curves of biodiesel fuels to their atmospheric distillation curves is proposed, based on their projection toward a focal point specifically selected for the methyl esters usually composing biodiesel fuels. This projection was made using a generalized Antoine-type equation with Antoine coefficients estimated from a two-parameter correlation as a function of the number of carbon atoms of the original fatty acid and the number of double bonds. The method (named here the Calingaert-like method) is based on the observation that saturation Antonie-type curved lines for pure hydrocarbons converge to a focal point when plotted in the form of log p versus 1/T and was found to be more accurate than ASTM D1160 method. Another tested method (named here the Coxlike method), based on the convergence of straight lines to a different focal point, was shown to provide intermediate results. Therefore, the Calingaert-like method is proposed as an improved alternative to the ASTM D1160 method for the distillation of biodiesel fuels at reduced pressure.
1. INTRODUCTION Although global demand for biofuels has risen sharply over the past decade, the diesel biofuels industry is still immature, as a consequence of new technology breakthroughs, economic breakdowns, and environmental concerns that are continuously arising. One of the main discussions regarding biofuels regards the compatibility between novel diesel engine technologies and new biofuel formulations or properties. Among the properties that are frequently close to the limit of acceptability, volatility deserves special attention because of its implications for engine emissions: volatilities that are too low can favor hydrocarbon and particulate emissions due to insufficient mixing, whereas volatilities that are too high can also lead to hydrocarbon and carbon monoxide emissions due to overmixing and flame extinction.1 In addition, the distillation curve provides useful information for estimating other fuel properties that are difficult to measure, such as the molecular weight or the autoignition behavior (through the cetane index2), and establishing the distillation conditions and the theoretical plate fractionation information needed for the design of industrial distillation columns. Distillation columns are becoming increasingly common in the biodiesel industry with the aims of improving cold-flow properties, eliminating impurities, and separating different fractions, thus enabling a wider product diversification.3 Volatility is not a specification for European biodiesel fuels, as no direct limits are included in standard EN-14214,4 but it is limited in the American biodiesel standard ASTM D6751,5 as well as in both the European and U.S. diesel fuel standards EN5906 and ASTM D975,7 respectively. These limits are shown in r 2011 American Chemical Society
Figure 1 (in the case of standard ASTM D975, only diesel grade 2-D is shown). The test method used for the determination of the distillation curves of diesel fuels must follow standards EN-34058 (in Europe) and ASTM D869 (in the United States), both requiring atmospheric pressure. The test method established for determining the distillation curve of biodiesel in the United States is ASTM D1160,10 even though this standard was designed for petroleum products. Thermal cracking of fatty acid methyl esters can occur from 350 °C upward.11 Because biodiesel fuels usually present higher amounts of compounds with high distillation temperatures than diesel fuels,12 to prevent thermal cracking in the distilled sample, this method requires using a reduced pressure between 1.3 and 67 mbar. After the completion of distillation, a conversion algorithm is proposed in the standard to calculate the equivalent atmospheric temperature values. The purpose of this work is to propose a specific method to convert reduced-pressure distillation curves of biodiesel fuels to their atmospheric distillation curves, based on a projection toward a focal point specifically selected for the methyl esters usually composing biodiesel fuels, through a generalized Antoine-type equation. This method is potentially more accurate than the ASTM D1160 method, because the latter was
Received: November 30, 2010 Accepted: April 20, 2011 Revised: April 4, 2011 Published: April 20, 2011 7041
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Figure 2. Diagram for the determination of the atmospheric equivalent temperature.
Figure 1. Distillation limits for diesel fuels according to European and ASTM standards.
developed not for oxygenated fuels but for petroleum-derived hydrocarbons.
2. METHODS FOR THE DETERMINATION OF THE ATMOSPHERIC DISTILLATION CURVE The ClausiusClapeyron equation relates temperature T and saturation pressure psat to the enthalpy of vaporization Δhvap of any substance (where R is the gas constant) Δhvap d ln psat ¼ 1 R d T
log p ¼ A
B B ¼ A T ð°CÞ þ 230:15 T ðKÞ 43
ð3Þ
This means that an Antoine coefficient, namely, C = 273.15 43 = 230.15 K, can be considered as a mean value for the usual petroleum-derived hydrocarbons. Using this equation, the conversion from measured distillation temperatures to atmospheric temperatures would be (now the pT coordinates of the focal point are different from the previous case) AET ðKÞ ¼
ð1Þ
Cox13 observed that straight log psat versus 1/T lines (with T in K) could be plotted in the range from 0 to 371 °C for a large number of paraffinic hydrocarbons, this meaning that in this range the enthalpy of vaporization varies slightly. Cox also observed that all of these straight lines converged into a common point, which is called the focal point. Using the equation of this straight line, the conversion from measured distillation temperatures to atmospheric equivalent temperatures (AETs) can be made by 1 1 log p log pfoc T Tfoc 1 1 ¼ log patm log pfoc f AET Tfoc 1 AET ¼ 1 1 1 T Tfoc þ log p log pfoc Tfoc log patm log pfoc
130 to 371 °C and to propose that the converging lines were not strictly straight but responded to the following Antoine-type equation
1 þ 43 1 1 1 T 43 Tfoc 43 þ log p log pfoc Tfoc 43 log patm log pfoc
ð4Þ
Based on these observations, Maxwell and Bonnell17 developed an improved method that was later adopted by ASTM committee D02 to define the conversion of distillation temperature of petroleum-derived fuels at reduce pressure (in the range above-mentioned) to the atmospheric equivalent temperature (AET) 748:1R AET ðKÞ ¼ 1 þ 0:3861R 0:00051606 T
ð5Þ
with R¼
5:143222 0:972546 for p g 0:266 kPa 2579:329 95:76log p
R¼
5:897249 0:987672 for p < 0:266 kPa 2962:909 43:00log p
ð2Þ
Cox’s finding was later extended to other organic compounds such as alcohols and acids by Davis.14 More precise data compiled by Wilson and Bahlke15 permitted Calingaert and Davis16 to extend the converging region to the range from
ð6Þ
where T and p are the temperature measured at the reduced pressure. The obtained equivalent temperature is finally corrected as a function of the Watson coefficient,18 which accounts for the paraffinic character of the petroleum-derived fuel. If the Watson coefficient is equal to 12 (corresponding to a purely 7042
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Figure 3. Antoine coefficients for saturated and monounsaturated methyl esters provided by Yaws19.
Figure 4. Antoine coefficients for saturated methyl esters provided by Yaws,19 Yuan et al.,21 and NIST.20
paraffinic fuel), no correction is needed. In this case, the conversion of the distillation temperature from reduced pressure
to atmospheric pressure proposed by standard ASTM D116010 (eq 5) is compared in Figure 2 with the projection toward the 7043
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Table 1. Boiling Points of Pure Methyl Esters n
db
1
0
formic
107-31-3
20, 23
305.5
1
2
0
acetic
79-20-9
20, 23
330
1
3
0
propionic
554-12-1
20, 23
353
1
1
acrylic
96-33-3
20, 23
353
1 1
4
5 6
methyl ester
CAS number
ref(s)
T (K)
p (bar)
0
butiric
623-42-7
20, 23
375
1
butenoic
3724-55-8
20, 23
385
1
1
crotonic
623-43-8
20, 23
392
1
0 0
valeric caproic
624-24-8 106-70-7
20, 23 20, 23
400 423
1 1
20
325.2
0.02
1
hexenoic
13894-61-6
23
442
1
2
sorbic
689-89-4
20, 23
453
1
20
343.2
0.027
446
1
7
0
heptanoic
106-73-0
20, 23
8
0
caprylic
111-11-5
20, 23, 27 466.5, 466 1
9
0
nonanoic
1731-84-6
20 20, 23
355.5 486.5 388
0.02 1
1
nonenoic
111-79-5
23
10
0
capric
110-42-9
20, 23, 27 497
1
20
388
0.02
11
1
undecenoic
111-81-9
20, 23
520
1
20
394
0.013
12
0
lauric
0.027
111-82-0
20, 23, 27 535
1
20 20
415 368
0.02 0.001
20
404
0.0053
26, 27
569, 568
1
20
429
0.009 0.004
13
0
tridecanoic
1731-88-0
14
0
myristic
124-10-7
15
0
pentadecanoic
7132-61-1
20, 23
414.5
16
0
palmitic
112-39-0
20, 23
435
0.005
20
458
0.013
26, 27 23
688, 611 454.5
1 0.0013 0.001
1
palmitoleic
1120-25-8
20
454.5
17
0
margaric
1731-92-6
23
425.5
0.000066
18
0
stearic
112-61-8
23, 27
625
1
20
488
0.02
23
454.5
0.0053
20
1
oleic
112-62-9
20, 23
491.5
0.02666
1
elaidic
1937-62-8
27 20
622 487.2
1 0.02
2
linoleic
112-63-0
23
465
0.0053
3
R-linolenic
301-00-8
20, 23
455
0.004
3
γ-linolenic
23
435
0.00066
0
arachidic
1120-28-1
20, 23
488.5
0.013
20
461.2
0.003
21
0
heneicosanoic
6064-90-0
20, 23
480
0.0053
22 24
1 0
erucic lignoceric
1120-34-9 2442-49-1
23 20, 23
446.5 505
0.000266 0.0053
focal point up to atmospheric pressure through straight lines (eq 2; denoted as the Cox method in the figure) and with the same projection through the generalized Antoine-type relation (eq 4; denoted as the CalingaertDavis method in the figure).
The diagram is presented in the form of an abacus, where the user can enter with the measured distillation temperature T at any reduced pressure p below the atmospheric pressure, to graphically obtain the AET. The right side of the diagram is just an extended view of the same abacus focused on the pressure range for which standard ASTM D1160 is declared to be accurate. As observed, in this pressure range, the ASTM method (assumed here as the one providing the best prediction of the atmospheric equivalent temperature for petroleum-derived fuels) improves the predictions with respect to the Cox method but does not substantially improve predictions with respect to the Calingaert Davis method.
3. ANTOINE COEFFICIENTS AND BOILING TEMPERATURES OF METHYL ESTERS Although much isolated data on the Antoine coefficients of methyl esters of fatty acids can be found in the literature, few references have been found providing data for a large set of methyl esters. The largest database is provided by Yaws,19 and the Antoine coefficients A, B, and C are shown in Figure 3 for saturated (from C1:0 to C26:0) and monounsaturated (between C3:1 and C18:1) methyl esters as a function of the acid carbon number, whereas no data are given for di- or polyunsaturated methyl esters. NIST20 provides data for 10 saturated methyl esters (between C2:0 and C18:0) and two monounsaturated methyl esters (C3:1 and C18:1). Yuan et al.21 provide data for nine saturated methyl esters (between C8:0 and C24:0), three monounsaturated ones (C18:1, C20:1, and C22:1) and for C18:2 and C18:3, but these data were obtained by adjusting the Antoine equation to the saturation curves obtained with the contribution-group method proposed by Ceriani and Meirelles,22 which is applicable only in the temperature range from 100 to 210 °C and leads to a significant underestimation of boiling points above this range. A comparison between Antoine coefficients for saturated methyl esters obtained from these databases is shown in Figure 4. The following conclusions can be derived from this comparison: (1) A high dispersion can be found between different sources for the same esters, possibly because many different combinations of coefficients AC can reach experimental fittings very close to the optimal one. (2) When coefficients AC of esters with the same degree of unsaturation are plotted as a function of their carbon number, large deviations from a supposed baseline can also be found for the three coefficients. The same explanation given above can be used to explain this point. (3) Coefficient C depends strongly on the range of pressure or temperature used, because it simulates the curvature of the log p1/T curves. Although small or even nil values for this coefficient might be be useful for simulating saturation curves in a short range, it must be more accurately determined if a large range is to be predicted. More literature review was done to collect individual values of boiling points (mostly at 1 bar) in order to propose an optimized correlation to predict the Antoine coefficients. The collected values are presented in Table 1. An optimization process was followed to obtain a generalized set of equations to determine the Antoine coefficients of any methyl ester as a function of the number of carbon atoms of the original fatty acid and the number of double bonds. The obtained equations (eq 7-9) were initially based on the equations simulating the base lines of the Antoine coefficients provided by Yaws 7044
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Figure 5. Antoine coefficients for methyl esters obtained from eqs 79.
(see Figure 3), but they were then corrected to minimize the sum of the square differences the experimental data shown in Table 1. A ¼ 8:816 þ ð0:088 þ 0:0122 dbÞn
ð7Þ
B ¼ 1168:15 þ ð97:399 þ 6:172 dbÞn
ð8Þ
C ¼ 263:09 þ ð3:860 þ 0:3007 dbÞn
ð9Þ
where n is the number of carbon atoms of the acid chain and db is the number of double bonds. The Antoine coefficients resulting from these equations are shown in Figure 5. It must be pointed out that the reliability and accuracy of the Antoine coefficients obtained for saturated methyl esters should be much higher than for unsaturated ones, because the quantity of data available for the latter is scarce.
4. NEW METHOD FOR THE DETERMINATION OF THE ATMOSPHERIC DISTILLATION CURVES OF BIODIESEL FUELS A method based on the generalized Antoine equations for fatty acid methyl esters is potentially more accurate than the ASTM D1160 method, because the latter was developed not for oxygenated fuels but rather for paraffinic hydrocarbons or, if the Watson correction is considered, for a wide spectrum of petroleum-derived hydrocarbons. The method proposed here is of the type of the Calingaert Davis method, and it is based on correcting eq 4 to provide a better approximation to the mean Antoine equation simulating the saturation curves of the methyl esters typically composing biodiesel fuels. A mean Antoine coefficient, Cmean, was selected by weighting the specific C coefficients obtained
Table 2. Parameters Proposed for the Two Methods Tested and Compared with the ASTM D1160 Standard specific Cox-like method
specific Calingaert-like method
Tfoc (K)
1176.5
1515.15
pfoc (Pa) Cmean (K)
2.35808 108 273.15
0.28614 108 202.17
from eq 9 and shown in Figure 5 (third panel) for all methyl esters composing the oils whose typical compositions are listed in refs 24 and 25. The weighting factor for each methyl ester was proportional to the sum of its concentrations within all of the listed oils. All listed oils were weighted with the same value except those that are currently considered as the preferred oil feedstocks for biodiesel production, namely, rapeseed, soybean, palm, cooking oil, and animal fat, which were valued double. The new focal point was determined as the intersection of the Antoine curves for these methyl esters when substituting their specific C coefficient by the mentioned Cmean. Once the coordinates of the focal point are known (see Table 2, left column), the proposed equation is AET ¼
1 Cmean 1 1 1 T þ Cmean Tfoc þ Cmean þ log p log pfoc Tfoc þ Cmean log patm log pfoc ð10Þ
The whole process is summarized in Figure 6. This method (referred to here as the “specific Calingaert-like method”) is compared to the “specific Cox-like method”, following eq 2 7045
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Table 3. Methyl Ester Profile of Biodiesel from Animal Fat n
Figure 6. Scheme of the process followed for designing the proposed method for the determination of the atmospheric distillation temperatures of methyl esters.
Figure 7. Scheme of the specific Cox-like and Calingaert-like methods for the determination of the atmospheric distillation temperatures of methyl esters.
(where the focal point was obtained as the intersection of the straight regression log p1/T lines for each methyl ester), and with the method proposed in the ASTM D1160 standard. The two specific methods are schematically described in Figure 7, and the parameters needed in each case are listed in Table 2. The atmospheric equivalent temperatures defining the atmospheric distillation curve are determined by linear (in the case of the specific Cox-like method) or quasi-linear (specific Calingaert-like method) interpolation between the measured values of log p-1/T at reduced pressure and those at the corresponding focal point.
5. EXPERIMENTAL VALIDATION OF THE PROPOSED METHOD To experimentally validate the proposed method, a biodiesel fuel made from animal fat was used. Animal fat is currently
db
methyl ester
content (% w/w)
8
0
caprilic
0.06
10
0
capric
0.06
12
0
lauric
0.19
14
0
myristic
1.46
16
0
palmitic
22.77
16
1
palmitoleic
17
0
margaric
18 18
0 1
stearic oleic
18
1
elaidic
0.78
18
2
linoleic
24.03
18
2
linoleadic
18
3
R-linolenic
2.16
20
0
arachidic
0.27
20
1
eicosenoic
0.49
22 22
0 1
behenic erucic
0.30 0.02
24
0
lignoceric
0.01
3.26 0.42 10.04 31.67
2.03
Figure 8. Distillation curves of biodiesel from animal fat measured at different pressures.
among the nonimported feedstocks for biodiesel production in Europe. This biodiesel fuel fulfils standard EN-14214 and was supplied by Stock del Valles (Spain). Its methyl ester profile is presented in Table 3. Distillation curves were obtained at different reduced pressures with a distillation system equipped with a 0.5 L heated flask, a digital vacuum meter, a needle valve for vacuum regulation, different Pt100 RTD sensors, and a digital temperature controller. The measured distillation curves of the biodiesel fuel at different pressures [atmospheric pressure (960 mbar) and 50, 10, 5, 2, and 1.5 mbar] are presented in Figure 8, and the distillation curves transformed to atmospheric pressure from reduced pressure are presented in Figures 9 and 10. The distillation curves shown in Figure 9 are composed of the atmospheric equivalent temperatures (AETs) obtained with the method proposed in standard ASTM D1160, whereas those presented in Figure 10 contain the atmospheric equivalent temperatures obtained with the Calingaert-like method 7046
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Figure 9. Atmospheric distillation curves of biodiesel from animal fat transformed from reduced pressure using standard ASTM D1160.
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Figure 12. Comparison between distillation curves measured at atmospheric pressure and transformed from reduced pressure with the distillation curve simulated from boiling points of individual methyl esters.
Figure 11. Errors in T50 (temperature for 50% distilled volume fraction) derived from transformation from reduced pressure by different methods.
point. Such overestimation is much lower when the specific Coxlike method is used, and it is even lower when the specific Calingaert-like method is used. As the curves are quite plane and parallel throughout a wide range of distilled volume fractions, comparisons were focused on T50 (the temperature for 50% distilled volume fraction), as this temperature is representative of the entire curves, except for the initial boiling point (as discussed below) and the final boiling point (where no comparison is possible because this point was not reached at atmospheric pressure). The comparison is expressed in the form of errors (differences in K) with respect to the measured atmospheric distillation curve, and it is shown in Figure 11. It can be observed that the specific Calingaert-like method slightly improves the transformation from reduced to atmospheric pressure with respect to the Cox-like method (around 1 K on average), but it improves the transformation significantly with respect to the ASTM D1160 method (almost 12 K on average). Finally, the distillation curve transformed from reduced pressure (2 mbar was taken as an example) and the measured atmospheric curve were compared to the simulated distillation curve obtained from the boiling points of the individual methyl esters. As can be seen in Figure 12, the curve transformed from reduced pressure fits the simulated curve better in the lowtemperature range than the measured curve. This can be explained because the interaction between different components is lower at reduced pressure than at atmospheric pressure. Apart from the well-known benefits in the high-temperature range, such as avoiding thermal cracking and enabling more complete distillation, this is an additional benefit of distillation at reduced pressure. Considering this, together with the large amount of information derived from the distillation curve, a method specifically optimized for biodiesel fuels for determining the equivalent atmospheric distillation temperature appears to be essential. The method proposed here could be adopted by standardization committees in the case that volatility requirements are included among the biodiesel specifications.
specifically proposed here for biodiesel fuels. Although not shown here, the distillation curves made up of temperatures obtained following the Cox-like method were also obtained and compared with the above-mentioned curves. As can be observed in the figures, the ASTM D1160 method, not specifically developed for biodiesel, overestimates the distillation temperatures, except in the case of the initial boiling
6. CONCLUSIONS Distillation at reduced pressure has been demonstrated to be an improved alternative with respect to atmospheric distillation in the case of low-volatility fuels such as biodiesel fuels, because it prevents thermal cracking and it allows for more complete and precise distillation curves in both the low-temperature range
Figure 10. Atmospheric distillation curves of biodiesel from animal fat transformed from reduced pressure using the specific Calingaert-like method.
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Industrial & Engineering Chemistry Research (initial distilled fractions) and the high-temperature range (final distilled fractions). The methods currently adopted by standards for the transformation of measured distillation temperatures to equivalent atmospheric temperatures were developed for petroleum-derived fuels. However, biodiesel fuels are composed of a uniform type of molecules (commonly methyl esters) whose vaporliquid saturation curves have specific characteristics. After proposing a two-parameter equation for the calculation of the Antoine coefficients describing such saturation curves, we proposed two specific methods for transforming distillation temperatures from reduced pressure to atmospheric pressure. The former method (named here the Cox-like method) is based on the initial observation13 that saturation straight regression lines for pure hydrocarbons converge to a focal point when plotted on a log p versus 1/T diagram. The latter (named here the Calingaert-like method) is based on the further observation16 that such convergence is more precise and generic when the saturation lines are fitted not to straight lines but to Antonie-type curved lines. Although both methods, specifically adjusted for biodiesel fuels, were found to provide improved results with respect to the nonspecific method adopted in standard ASTM D1160 for transforming distillation curves from reduced to atmospheric pressure, it is the Calingaert-type method that provides the best results. Therefore, this method is proposed as an improved alternative to the ASTM D1160 method for the distillation of biodiesel fuels at reduced pressure.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Tel.: þ(34) 926295431. Fax: þ(34) 926295361.
’ ACKNOWLEDGMENT The authors acknowledge the Spanish Ministry of Science and Technology for financial support (MECINBIO Research Project, Ref ENE2007-67529-C02-01) and the company Stock del Valles for supplying the biodiesel fuel. ’ NOMENCLATURE A = Antoine coefficient (for p expressed in Pa) AET = atmospheric equivalent temperature (K) B = Antoine coefficient C = Antoine coefficient (for T expressed in °C) db = number of double bonds in the original fatty acid Δhvap = enthalpy of vaporization (kJ/kg) n = number of carbon atoms in the original fatty acid p = pressure (Pa, kPa, or bar) R = gas constant [kJ/(kg K)] T = temperature (K) Subscripts
atm = atmspheric foc = focal point i = index for the literature data mean = mean sat = saturation
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dx.doi.org/10.1021/ie102402k |Ind. Eng. Chem. Res. 2011, 50, 7041–7048
