allen1999

Fuel 78 (1999) 1319–1326
www.elsevier.com/locate/fuel
Predicting the viscosity of biodiesel fuels from their fatty acid ester
composition
C.A.W. Allen a, K.C. Watts a,*, R.G. Ackman b, M.J. Pegg c
a
Department of Biological Engineering, DalTech, Dalhousie University, P.O. Box 1000, Halifax, Nova Scotia, Canada, B3J 2X4
b
Department of Food Science, DalTech, Dalhousie University, P.O. Box 1000, Halifax, Nova Scotia, Canada, B3J 2X4
c
Department of Chemical Engineering, DalTech, Dalhousie University, P.O. Box 1000, Halifax, Nova Scotia, Canada, B3J 2X4
Received 25 June 1998; received in revised form 17 December 1998
Abstract
Viscosity is one of the most significant properties to affect the utilization of biodiesel fuels. This paper presents a method, which has been
verified experimentally, for predicting the viscosities of biodiesel fuels from the knowledge of their fatty acid composition. The applicability
of a logarithmic mixture equation was verified using controlled mixtures of standard fatty acid esters and natural biodiesels. Several binary,
ternary and quaternary mixtures of fatty acid ethyl ester (FAEE) gas chromatography (GC) standards were formulated. Their viscosities were
predicted from their component values and were within ^ 3.7% of their measured values. The fatty acid compositions of six typical oils were
simulated by mixing fatty acid methyl ester (FAME) standards in appropriate amounts. Viscosities of these mixtures were also predicted
within ^ 2.1% of their measured values. Five biodiesel types were produced from natural oils and the logarithmic equation was applied to
predict their viscosities. An average prediction error of ^ 3% was obtained for these samples. The viscosities of fifteen biodiesel types were
then predicted based on their fatty acid composition as published in the literature and were found to vary as much as 100% This is most likely
a principal contributing factor to the variation in performance of some biodiesel fuel types. The viscosity of biodiesel fuels reduce
considerably with increase in unsaturation. Contamination with small amounts of glycerides significantly affects the viscosity of biodiesel
fuels. q 1999 Elsevier Science Ltd. All rights reserved.
Keywords: Biodiesel; Properties; Viscosity
1. Introduction
Biodiesel fuels are generally classified as fatty acid
methyl esters (FAMEs) which are derived from the alkalicatalysed transesterification of fats and oils with methanol,
although other alcohols can be used. The applicability of
this fuel type as a replacement or subsidy for petroleum
based diesel fuels has been investigated by many authors.
Graboski and McCormick [1] provided a recent extensive
review of the utilisation of biodiesel fuels in compression
ignition engines. The general conclusion from the literature
is that, in terms of power, wear, efficiency and emissions,
biodiesel fuels are a viable alternative. There are, however,
some variations in the results reported by some authors. One
of the contributing factors to the variation in the reported
results can be the viscosity of the fuel. This is because the
atomization process, which is the initial stage of combustion
* Corresponding author. Tel: 1 1-902-494-3269; fax: 1 1-902-4232423.
E-mail address: [email protected] (K.C. Watts)
in a diesel engine, is significantly affected by the fuel’s
viscosity.
There exist in the literature several models for predicting
the viscosity of fatty acids. Reid et al. [2] presented several
group contribution methods for computing the viscosity of
individual components but most of these models gave wide
ranging errors and thus were considered unreliable. Fisher
[3] described a method based on limiting properties to
predict several properties of n-fatty acids whereby their
variation was attributed to the increments in the methylene
group of the homologous series. This method worked fairly
well for properties like heat capacity, heat of vaporization,
boiling point, molal volume and density, but unfortunately
the limiting property for viscosity was approximately zero,
rendering this method inaccurate for viscosity predictions.
Noureddini et al [4], Swern [5] and Markley [6] presented
empirical models and data for predicting the viscosity of
individual fatty acids and vegetable oils. The above methods
were applicable to individual fatty acid components but not
to acyl esters or mixtures. This paper presents a method for
predicting the viscosity of mixtures of fatty acid esters of
0016-2361/99/$ - see front matter q 1999 Elsevier Science Ltd. All rights reserved.
PII: S0016-236 1(99)00059-9
1320
C.A.W. Allen et al. / Fuel 78 (1999) 1319–1326
which biodiesel is comprised. The importance of this work
is that if it is possible to predict the viscosity of any given
vegetable oil source from its components (and hence its
atomization), there may be no need for expensive testing
programmes to determine the functioning of the oil in an
engine.
2. Mixture model
The Grunberg–Nissan [7] equation has been reported by
Monnery et al. [8] and Irving [9] to be the most suitable
equation for computing the viscosity of liquid mixtures.
This equation was developed primarily for binary mixtures
and works best with non-associated liquids. However, good
results were obtained by Irving [9] for some associated
fluids with errors less than 5–10%. This equation has also
been extended beyond the binary mixture level with some
success ([9]). The Grunberg–Nissan equation is
ln mm ˆ
n
X
xi ln mi 1
i
XnX
xi xj Gij
1†
i±j
where mm is the mean viscosity of mixture (Pa s), m the
viscosity of pure ith component (Pa s), xi and xj the mole
fractions of the ith and jth components, Gij the interaction
parameter (Pa s) n the number of components.
Biodiesel fuels are non-associated liquids that are
comprised of mixtures of fatty acid esters whose chemical
structures are similar (aliphatic chains). Due to this similarity, the components in a mixture should not interact with
each other and thus should behave in a similar manner as an
individual component. It was therefore assumed that the
interaction parameter in Eq. (1) would be small and thus
could be neglected. Also, the mass fraction was used in
preference to the mole fraction in Eq. (1) to conform with
the mass unit that is implicit in the units for viscosity used in
this study. With these two modifications, Eq. (2) was used to
predict the viscosity of biodiesel fuels based on their fatty
acid composition.
ln mm ˆ
n
X
yi ln mi
2†
iˆ1
where yi is the mass fraction.
3. Materials and methods
3.1. Sample preparation
Both FAME and ethyl ester (EE) standards were acquired
from Sigma Aldrich Chemical Supplies company. EEs were
used for binary, ternary and quaternary mixtures since it was
more economical to use these standards. The following
samples were prepared for different tests, as described later:
• Twenty EE samples were produced by mixing, on a mass
basis, varying proportions of 8:0, 10:0, 12:0 and 18:1
FAMEs.
• MEs were mixed on a mass basis in appropriate proportions to simulate canola, coconut, palm, peanut, rapeseed
and soybean oil MEs.
• Biodiesel fuels from natural canola, coconut, palm,
peanut and soya oils were produced in a batch transesterification unit described by Allen and Watts [10]. These
ME fuels were also heated to 1008C under nitrogen and
then filtered through a “Reeve Angel” grade 202 coarse
paper filter to remove any sediments in the oil that were
carried over from the oil extraction process. At 1008C, all
of the oil’s fatty acids were fluid with low viscosity,
making it easier for them to pass through the coarse filter.
The purity of the biodiesel fuels produced by the transesterification process was verified using a thin-layer chromatography (TLC) on Chromarods-SIII (silica gel) with flame
ionization of the components (TLC-FID) by scanning in an
Iatroscan Mark III ([11]). The fatty acid composition of the
biodiesel fuels was measured on a Perkin–Elmer Gas Chromatograph, model 8420 as described by Ackman [12].
3.2. Viscosity measurement
A Paar model AMV 200 micro viscometer operating on a
rolling-ball principle was used to measure the viscosity of
all samples at the test temperature. Only one replicate for
each sample was required as the instrument provided consistently repeatable results.
3.3. Error analysis
The maximum allowable error for the predicted results
was derived through a sensitivity analysis of a generalized
atomization model taken from the literature. This model,
which was developed by Msipa et al. [13], computes an
atomization characteristic Ka which gives an overall view
of the atomization quality. It includes the surface tension,
viscosity and density of the fuel. Eqs. (3)–(5) summarise
this model and further details can be found in Ref. [13].
"
#1=3
rf Wef
Ka ˆ
3†
rg Ref
where Ka is the atomization characteristic, Wef the Weber
number for fuel, Ref the Reynolds number for fuel, r the
densities for fuel [r f] and gas atmosphere [r g] (kg/m 3).
The Reynolds and Weber numbers are given by
Ref ˆ
V 0 d0
vf
4†
Wef ˆ
rf V02 d0
sf
5†
where s f is the surface tension of the fuel (N/m), vf the
C.A.W. Allen et al. / Fuel 78 (1999) 1319–1326
1321
Table 1
Mean value of properties used for sensitivity analysis
was converted to an effective shear rate per unit rolling
distance and is given in Eq. (8).
Property
Mean value
g_ L ˆ
Surface tension of fuel
Viscosity of fuel
Density of fuel
Nozzle diameter
0.0292 N/m
4.18 mPa s
871.4 kg/m 3
0.4 mm
3.4. Rheological properties
To ensure a correct comparison of the viscosities of
different biodiesel types, a check was made to determine
whether these fuels were significantly non-Newtonian at
the test temperature of 408C. All of the biodiesel ME fuels
produced were subjected to controlled, variable shear stress
viscosity measurements on the rolling-ball viscometer and
the effective shear rate was determined as a function of the
rolling time. The effective shear rate and the effective shear
stress for a rolling-ball viscometer [15] are given in Eqs. (6)
and (7).
Mean Velocity of Ball
4dV
ˆ
2
Mean Gap area based†
D 2 d2 †
tE ˆ d Dr†gsin u†
8†
where g_ L is the equivalent shear rate per unit length (1/
(m s)) and t the rolling time of ball (s).
kinematic viscosity of the fuel (m 2/s) and V0 the velocity of
the fuel jet (m/s).
Using the conventional 95% confidence, it was decided to
vary the viscosity to a maximum of ^ 5% from its mean
value to determine if there was any significant change in the
atomization characteristic. The mean value of all properties,
taken from Allen et al. [14], are given in Table 1.
g_ E ˆ
4d
D2 2 d2 †t
6†
7†
where g_ E is the equivalent shear rate (1/s), t E the equivalent
shear stress (Pa), D the capillary diameter (m), d the ball
diameter (m), V the velocity of the rolling ball (m/s), Dr the
difference in density between ball and fluid (kg/m 3), u the
angle of inclination of capillary (8) and g the acceleration
due to gravity (9.81 m/s 2).
The viscometer measured the rolling time of the ball over
a fixed distance. This distance was not known for the instrument used in these tests, therefore, the effective shear rate
4. Results and discussion
4.1. Allowable error
Fig. 1 shows a graphical representation of the results of
the sensitivity analysis. A ^ 5% variation in the viscosity
resulted in a 3% variation in Ka from its maximum value.
This 3% variation in Ka over the entire ^ 5% (10% variation from maximum viscosity) range of viscosities used can
be considered negligible. Therefore, the maximum allowable error for a prediction equation to estimate the viscosities of the ester mixtures was set at 5%.
4.2. Rheological properties of experimentally produced
biodiesel fuels
For every biodiesel fuel type that was produced, a plot of
the equivalent shear stress versus the equivalent shear rate
per unit length was made (Fig. 2) and linear regression lines
were then fitted to these points. For each fuel type, all the
data points fell on their regression line which passed
through a point very close to the origin (Fig. 2). This very
small shear stress (yield stress) at zero flow indicates a slight
“Bingham-plastic” behaviour which is more pronounced for
peanut, palm and coconut oils. However, this effect is small
and these fuels can, therefore, be considered to behave in a
Newtonian manner at 408C which means that the higher
saturates present in some of the oils did not significantly
affect the nature of the fuel’s viscosity. Also, during the
utilization of these vegetable oil ME fuels in engines, the
shear stresses encountered are much higher than the yield
stresses observed. Therefore, these fuels may be considered
to behave in a Newtonian manner in actual engine operations.
4.3. Viscosity of individual ester components
The measured viscosities of individual FAMEs and EEs
had a complex pattern with respect to the saturation of the
fatty acids and their chain length. For saturated fatty acid
esters, the measured data at 408C indicated that the viscosity
increased with carbon number (CN) in a curvilinear trend
rather than a linear one. Good correlation was found
between the measured data and a second-order polynomial
function over the CN range 8:0–18:0. Eqs. (9) and (10) give
the fitted polynomials for saturated MEs and EEs.
Fig. 1. Variation of normalized atomization characteristic (Kai/Kamax) with
5% variation of viscosity for constant surface tension and density: (B) Ka
and (K) % variation.
mME2sat ˆ 1:05E 2 4M 2 2 0:0242M 1 2:15 s ˆ 0:0145
9†
1322
C.A.W. Allen et al. / Fuel 78 (1999) 1319–1326
Fig. 3. Viscosity trend lines for methyl ester and ethyl ester GC standards at
408C: (A) EEs and (W) MEs.
Fig. 2. Rheograms for vegetable oil methyl ester biodiesel fuels at 408C
plotted on a linear scale: (W ) canola; (X) coconut; (K) diesel; ( 1 ) palm;
(A) peanut; (B) soya.
mEE2sat ˆ 1:16E 2 4M 2 2 0:0264M 1 2:28 s ˆ 0:0182
10†
where m is the viscosity (mPa s), M the molecular weight (g/
mol) and s the standard error.
Fig. 3 shows the data points and their trend curves. The
viscosities of the saturated EEs were only slightly higher
than those for MEs, an average of 5.4% higher over the CN
range 8:0–18:0.
The viscosity trend for unsaturated esters at 408C showed
a sharp deviation from the trend of the saturated esters when
18:0 became unsaturated to 18:1. A completely different
curve was observed as the degree of unsaturation progressed
from 18:1 to 18:3 (Fig. 3). As the number of double bonds
increased, there was a non-linear decrease in viscosity, with
a 21% difference between 18:0 and 18:1 (based on 18:0), an
18% difference between 18:1 and 18:2 (based on 18:1), and
a 13% difference between 18:2 and 18:3 (based on 18:2).
Although this phenomenon was not verified at other CN
due to the cost and availability of these individual
components, there is no a priori reason why the same result
would not occur at other CN since their chemical structures
are similar.
The trend for unsaturated C18 esters also correlated well
with second-order polynomial functions given in Eqs. (11)
Table 2
Viscosities of binary, ternary and quaternary mixtures of fatty acid ethyl ester GC standards at 258C
Sample #
Fatty acid ethyl ester
Measured viscosity (mPa s)
Predicted viscosity (mPa s)
5.50
2.88
1.99
1.37
1.67
1.91
2.39
1.51
1.82
1.62
2.32
2.19
2.62
1.94
1.77
1.91
2.12
2.51
3.31
2.62
2.32
2.01
–
–
–
–
1.66
1.98
2.39
1.5
1.81
1.65
2.39
2.19
2.62
1.99
1.81
1.93
2.18
2.57
3.38
2.67
2.35
2.06
Per cent error
Mass fraction
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
18:1
12:0
10:0
8:0
1.00
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
0.25
0.52
0.16
0.16
0.16
–
1.00
–
–
–
0.50
0.50
–
–
0.25
0.75
0.25
0.74
0.34
0.25
0.19
0.50
0.25
0.16
0.51
0.16
0.16
–
–
1.00
–
–
–
1.00
0.48
0.50
0.52
0.50
0.25
0.75
–
–
0.75
0.26
0.33
0.25
0.54
0.25
0.25
0.16
0.16
0.51
0.16
0.75
0.25
0.75
0.25
–
–
0.33
0.51
0.27
0.25
0.25
0.16
0.16
0.16
0.51
–
–
–
–
0.60
2 3.66
0.00
0.66
0.55
2 1.85
2 3.02
0.00
0.00
2 2.58
2 2.26
2 1.05
2 2.83
2 2.39
2 2.11
2 1.91
2 1.29
2 2.49
C.A.W. Allen et al. / Fuel 78 (1999) 1319–1326
1323
Table 3
Viscosities and mass fraction of simulated vegetable oil ME at 408C (using measured viscosities of pure components)
Fatty acid methyl ester
Viscosity (mPa s)
Simulated vegetable oil methyl ester-component mass fraction
Coconut
Palm
Rapeseed
Peanut#1
Soybean
Canola
Peanut#2 a
0.000
0.000
0.000
0.000
0.106
0.010
(0.054) b
0.499
0.334
0.005
0.013
(0.000) b
0.031
(0.000) b
0.002
3.57
3.51
0.06
1.49
0.000
0.000
0.000
0.002
0.102
0.046
0.000
0.000
0.000
0.002
0.037
0.024
0.000
0.000
0.000
0.000
0.104
0.033
0.222
0.546
0.082
0.000
0.600
0.218
0.113
0.000
0.529
0.327
0.005
0.000
0.000
0.000
0.000
0.000
3.26
3.27
20.01
20.24
0.005
3.45
3.45
0
0.11
0.002
3.51
3.50
0.01
0.31
8:0
10:0
12:0
14:0
16:0
0.75
0.99
1.40
1.95
2.69
3.60
4.74
0.078
0.070
0.466
0.182
0.092
0.028
0.001
0.001
0.009
0.013
0.441
0.051
0.000
0.000
0.000
0.000
0.029
0.025
18:1
18:2
18:3
20:0
3.73
3.05
2.65
–
0.068
0.017
0.000
0.000
0.384
0.095
0.004
0.000
0.128
0.116
0.085
0.000
22:0
–
0.000
0.000
0.000
22:1
Measured viscosity (mPa s)
Predicted viscosity (mPa s)
Error (mPa s)
Per cent error
5.91
0.000
2.15
2.19
20.04
22.04
0.000
3.59
3.59
0
20.08
0.617
4.7
4.72
20.03
20.57
a
b
Peanut#2 has no 22:0 and 20:0.
Mass fraction after being combined with 18:0.
and (12) for MEs and EEs, respectively.
mME2unsat2C18 ˆ 0:153 NDB 2 1:15 NDB 1 4:73
2
11†
s ˆ 0:0112
mEE2unsat2C18 ˆ 0:147 NDB2 2 1:09 NDB 1 4:82
12†
s ˆ 0:000
where NDB is the number of double bonds in the C18 chain.
4.4. Measurement and prediction of the viscosity of mixtures
of GC standards
The logarithmic equation (Eq. 2) for predicting the
viscosities of multi-component mixtures was tested by
comparing measured and predicted viscosities of fatty acid
ester standards. Initially, the model was tested using binary,
ternary and quaternary mixtures of 8:0, 10:0, 12:0 and 18:1
EE standards at 258C. The mixing ratios and results are
summarized in Table 2 where it can be seen that the errors
in predicting the viscosities are all less than 3.7%, showing
that the assumption of a negligible interaction parameter,
and that the use of the measured mass fraction of the control
samples provide acceptable results. It was thus decided to
extend the verification procedure to more complex mixtures
of MEs that simulated biodiesel fuels.
The ME standards that were mixed on a mass basis to
simulate rapeseed, canola, peanut, soybean, palm and coconut oil ME fuels were used in this phase. Peanut oil has
greater than 4% of 20:0 and 22:0 fatty acids combined
whose viscosities are not measurable at the test temperature
of 408C, since these individual components are solid at this
temperature. For comparison purposes, it was decided to
Table 4
Viscosities of individual fatty acid methyl ester
FAME
Viscosity taken from Swern [5]
Viscosity of GC standard
Per cent difference
8:0
10:0
12:0
14:0
16:0
18:0
18:1
18:2
18:3
22:1
1.01
1.47
1.98
2.81
3.76
4.88
3.87
3.17
2.84
6.27
1.01
1.4
1.95
2.69
3.6
4.74
3.73
3.05
2.65
5.91
0.00
4.76
1.52
4.27
4.26
2.87
3.62
3.79
6.69
5.74
1324
C.A.W. Allen et al. / Fuel 78 (1999) 1319–1326
Table 5
Viscosities of methyl ester biodiesel fuels at 408C (using viscosities of pure components taken from Swern [5] and combined mass fractions)
Fatty acid methyl ester
Viscosity (mPa s)
24:0
–
22:1
22:0
6.27
–
20:1
–
20:0
–
8:3
18:2
18:1
2.84
3.17
3.87
18:0
4.88
16:1
–
16:0
14:0
12:0
10:0
8:0
Measured viscosity (mPa s)
Predicted viscosity (mPa s)
Error (mPa s)
Per cent error
3.76
2.81
1.98
1.47
1.01
a
b
Methyl ester component mass fraction
Coconut
Peanut
Soya
0.000
–
0.000
0.000
–
0.000
–
0.002
(0.000)*
0.000
0.014
0.055
–
0.019
–
0.000
–
0.073
0.171
0.533
0.060
0.075
2.32
2.19
0.13
5.72
0.035
(0.000) a
0.000
0.024
(0.000) a
0.014
(0.000) b
0.013
(0.000) a
0.010
0.301
0.466
(0.485) b
0.027
(0.099)
0.004
(0.000) b
0.105
0.000
0.000
0.000
0.000
3.77
3.71
0.06
1.71
0.000
(0.000) a
0.000
0.000
(0.000) a
0.016
(0.000) b
0.007
(0.000) a
0.096
0.199
0.600
(0.623) b
0.017
(0.023)
0.008
(0.000) b
0.058
0.000
0.000
0.000
0.000
3.67
3.62
0.05
1.25
Palm
Canola
0.000
–
0.000
0.000
–
0.001
(0.000) b
0.003
(0.000) a
0.002
0.080
0.373
(0.377) b
0.040
(0.042)
0.003
(0.000) b
0.481
0.013
0.004
0.000
0.000
3.87
3.76
0.11
2.76
0.000
–
0.000
0.001
(0.000) a
0.021
(0.000) b
0.012
0.112
0.213
0.574
(0.599) b
0.020
(0.033)
0.004 (0.000) b
(0.000) b
0.042
0.000
0.000
0.000
0.000
3.7
3.61
0.09
2.50
Mass fraction after being combined with 18:0.
Mass fraction after being combined with 18:1.
produce two mixtures to simulate peanut oil, one including
the 20:0 and 22:0 components (peanut#1) and the other
without the 20:0 and 22:0 components (peanut#2). In the
peanut#1 sample, the 20:0 and 22:0 were assumed to have
the same viscosity as the 18:0 and so the mass fractions of
the three components were combined for calculation
purposes. All other simulations required less than 1% of
these fatty acids which were thus considered negligible.
Table 3 shows the predicted and measured viscosities along
with the mass fractions of the simulated vegetable oil FAMEs.
The errors in predicting the viscosities of all the simulated oils
were 2% or less, with the highest absolute error being
0.06 mPa s. The peanut#1 oil sample with the mass fractions
of its 20:0 and 22:0 components combined together with 18:0,
had a 1.5% error compared with a 0.3% error for the peanut#2
sample with those two components excluded from the mixture.
Although the error obtained by lumping the three components
together is higher than the sample without 20:0 and 22:0, this
error is well within the acceptable limit previously defined
and is comparable with the errors obtained for the other
simulated oils. As all the errors were within the defined
acceptable limit, it was concluded that, for practical
purposes, the logarithmic equation (Eq. 2) was applicable
for predicting the viscosities of MEs and EEs of multicomponent fatty acid ester mixtures used as biodiesel fuels.
Table 6
Biodiesel fuel purity and composition obtained by TLD-FID analysis
(FFA ˆ free fatty acids)
Oil type
Component type
Composition (%)
Soya
ME
TG&FFA*
Others
Total
ME
TG
Others
Total
ME
TG&FFA*
Others
Total
ME
TG&FFA*
Others
Total
ME
TG&FFA*
Others
Total
99.76
0.00
0.24
100.00
98.21
0.00
1.79
100.00
99.81
0.00
0.19
100.00
95.01
0.00
4.99
100.00
100.00
0.00
0.00
100.00
Palm
Peanut
Coconut
Canola
1325
0.0
0.0
0.0
0.0
8.3
0.0
0.1
0.0
0.0
0.0
0.0
0.0
0.0
5.5
0.0
0.0
0.0
0.0
0.0
6.0
0.0
0.1
0.0
0.0
0.0
0.0
0.0
0.1
3.0
0.1
0.0
0.0
0.0
0.0
46.7
0.0
0.9
0.0
0.0
0.0
0.0
0.0
0.1
3.6
0.1
0.0
0.0
0.1
0.0
18.3
0.0
1.3
0.1
0.1
0.1
0.0
0.8
3.3
11.6
1.4
10.4
2.7
3.9
11.0
9.2
9.9
43.9
6.6
6.0
10.3
3.0
22.9
25.2
33.4
25.5
8.9
2.8
3.1
3.6
2.9
3.1
4.9
3.3
5.9
4.7
4.4
3.1
19.2
11.4
15.8
47.1
21.9
60.2
75.3
6.9
29.1
39.0
14.4
16.0
22.5
88.2
18.5
48.9
27.8
47.1
32.9
13.1
21.1
9.5
1.7
56.8
9.5
75.5
71.4
54.1
4.3
54.2
2.7
3.1
8.9
0.5
8.6
11.1
0.6
0.0
1.1
0.3
0.1
0.6
8.3
0.1
0.5
0.5
0.6
1.1
0.2
50.9
0.5
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
4.5. Measurement and prediction of the viscosity of five
biodiesel types
Peanut
Rapeseed
Canola
Olive
Coconut
Corn
Palm
Safflower
Sunflower
Soybean
Sunola
Cottonseed
Beef Tallow
Butterfat
Lard
Lauric 12:0
Capric 10:0
Caprylic 8:0
Fatty acid composition
Oil type
Table 7
Fatty acid composition of 15 fats and oils (From Ref. [15])
Myristic 14:0
Palmitic 16:0
Stearic 18:0
Oleic 18:1
Linoleic 18:2
Linolenic 18:3
Erucic 22:1
C.A.W. Allen et al. / Fuel 78 (1999) 1319–1326
As Eq. (2) was demonstrated to predict viscosities well,
knowing the fatty acid ester composition, it was possible to
estimate the viscosity of five biodiesel fuels prepared in the
laboratory. The FAME composition of the fuels were determined by GC analysis and determined to be the same as in
Ackman. When the viscosities of the component FAME as
determined above were used to predict the viscosity of the
biodiesel fuels, the error on viscosity (compared to the
measured values) were low by 7.1, 8.1, 7.0, 6.0 and 6.3%
for canola, coconut, palm, peanut and soya oil, respectively.
This caused the authors to question the composition of the
standards especially because there were some inexplicable
anomalies in the surface tension of some of the standards
compared to literature values, as reported by Allen [16]
which included a sharp drop for 16:0 EE from an otherwise
smooth trend of saturated esters, and very erratic surface
tension data for the unsaturated esters. Thus another source
of viscosity for the component ME was sought. Since Swern
[5] has a complete listing of viscosities for 8:0 to 18:0, 18:1
to 18:3 and 22:1 at 408C, it was decided to compare viscosities developed by Swern with the viscosities measured in
this study. A comparison of these two sets of data showed
that the values measured in this study were 1.6–6.7% lower
than that reported by Swern [5] (Table 4). No anomalous
trends were noted in his data, and thus more confidence was
obtained in the absolute value of his viscosities. The biodiesel fuels produced contained minor quantities of some
FAMEs whose viscosities were not available. To approximate for these components, their mass fractions were
combined together with a component that had a comparable
CN and saturation. For example, the mass fractions of
higher saturates 20:0, 22:0 and 24:0, which occurred in
minor quantities, were combined together with 18:0, and
the mass fractions of the unsaturates 16:1 and 20:1 were
combined together with 18:1.
The viscosities predicted using the component viscosities
taken from Swern [5], and with some of the mass fractions
combined together were all within 2.8% of the measured
viscosities, except for coconut oil which had a 5.7% error
(Table 5).
The results of the TLC-FID analysis, given in Table 6,
showed that all of the oils contained 98% or more MEs
except for coconut oil which contained approximately
95% MEs with the remaining 5% being one or a combination of mono-, di-glycerides, sterols or polar lipids. Since
mono- and di-glycerides were not available to the researchers, small amounts of triglycerides (TG) were systematically
added to ME to give an indication of the effect of glycerides
on viscosity. Canola oil, which was readily available, was
used in these tests. TG in the form of canola oil in mass
fractions of 1, 2, 4 and 6% were respectively added to canola
oil ME. It was found that 1% TG in the ME resulted in a
1.5% increase in viscosity; 2% gave a 3.8% increase; 4%
1326
C.A.W. Allen et al. / Fuel 78 (1999) 1319–1326
Table 8
Predicted viscosities for 15 biodiesel fuel types (408C)
Oil type
Acknowledgements
This project was supported by the Natural Science and
Engineering Research Council, Ottawa, grant to K.C. Watts.
Viscosity (mPa s)
Predicted Lower prediction limit Upper prediction limit
Peanut
Rapeseed
Canola
Olive
Coconut
Corn
Palm
Safflower
Sunflower
Soybean
Sunola
Cottonseed
Beef Tallow
Butterfat
Lard
3.69
4.72
3.61
3.81
2.25
3.46
3.74
3.35
3.39
3.41
3.87
3.46
3.94
3.31
3.74
3.58
4.59
3.51
3.70
2.19
3.36
3.64
3.25
3.29
3.32
3.76
3.36
3.83
3.22
3.63
3.79
4.85
3.72
3.92
2.32
3.56
3.85
3.44
3.48
3.51
3.98
3.56
4.05
3.41
3.84
gave a 7.8% increase; and 6% resulted in an 11.8% increase
in the viscosity of the mixture. Assuming that mono- and diglycerides may have similar effects, these results serve to
explain why the measured viscosity of coconut oil was 5.8%
higher than its predicted viscosity compared with an average
2.1% error for the other oils. This also indicates a possible
source of variation between different worker’s results.
4.6. Predicted viscosities of 15 biodiesel types
The results obtained above showed that the errors
obtained for predicting the viscosities of mixtures of MEs
were within the maximum allowable error previously
defined. It was thus decided to use Eq. (2) to predict the
viscosities of the MEs of typical oils.
The fatty acid composition of 15 fat and oils are given by
Ackman [17]. To predict the viscosity of the MEs of these
oils using Eq. (2), some minor quantities of their fatty acids
had to be combined together in the manner previously
described. Table 7 gives a listing of the oils/fats and the
fatty acid composition used in the analyses.
The predicted viscosities of the MEs of the 15 oils are
summarized in Table 8 along with the upper and lower
prediction limits, based on the average error of the model.
It can be seen that most of the oils had similar viscosities
ranging from 3.31 to 3.94 mPa s. However, rapeseed oil ME
had the highest predicted viscosity (4.72 mPa s) while coconut oil ME had the lowest (2.25 mPa s). This 100% difference in viscosity range is significant in the utilization of
biodiesel fuels.
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