20th European Symposium on Computer Aided Process Engineering – ESCAPE20
S. Pierucci and G. Buzzi Ferraris (Editors)
© 2010 Elsevier B.V. All rights reserved.
Predicting critical properties, density and viscosity
of fatty acids, triacylglycerols and methyl esters by
group contribution methods
Mauricio Sales-Cruz,a Gloria Aca-Aca,b Oscar Sánchez-Daza,c Teresa LópezArenas a
a
Departamento de Procesos y Tecnología, Universidad Autónoma MetropolitanaCuajimalapa, Artificios 40, 01120 Mexico D.F., Mexico, E-mail:
asales@correo.cua.uam.mx, mtlopez@correo.cua.uam.mx
b
Colegio de Ingeniería de Alimentos, Facultad de Ingeniería Química, Benemérita
Universidad Autónoma de Puebla, Ciudad Universitaria, 72570 Puebla Pue., Mexico,
E-mail: gloryaca@yahoo.com.mx
c
Colegio de Ingeniería Química, Facultad de Ingeniería Química, Benemérita
Universidad Autónoma de Puebla, Ciudad Universitaria, 72570 Puebla Pue., Mexico,
E-mail: oosdaza@yahoo.com
Abstract
The knowledge of critical properties, densities and viscosities (in function of
temperature) of the main fatty compounds involved in the biodiesel production are
essential for process engineering. Even though several studies have reported properties
for some compounds (mainly for fatty acids), there are still a necessity of expanding the
databank gathered from literature. In contrast to traditional methods based on
temperature-dependence correlations, in this work, methodologies for property
prediction based on group contribution methods are presented.
Keywords: Group contribution, thermodynamic property estimation, oil compounds,
biodiesel compounds.
1. Introduction
Biodiesel fuels derived from vegetable oils or animal fats, which are used as substitutes
for conventional petroleum fuel in diesel engines, have recently received increased
attention. This interest is based on a number of properties of biodiesel including its
biodegradability and the fact that it is produced from a renewable resource. While the
high density and viscosity of vegetable oils and animal fats tends to cause problems
when used directly in diesel engines, if oils and fats are transesterified using short-chain
alcohols, the resulting methyl esters (biodiesel) have viscosities that are closer to
petroleum-based diesel fuel. So that the knowledge of their physical properties as a
function of temperature and reliable predictive models is of great practical interest for
process engineering, considering the demand of computational tools for process design,
evaluation, simulation, optimization, control, etc.
Recently much work has been done on measuring and estimating density and viscosity
of fatty compounds, vegetable oils and biodiesel fuels as a function of temperature. In
most cases, polynomial correlations or specific equations (like Rackett equation for
density and Vogel equation for viscosity) were generated by adjusting each set of
experimental data to a specific compound. More generalized models were developed for
M. Sales-cruz et al.
fatty acids, triacylglycerols, fatty esters and their mixtures. But few of them used the
widely concept of group contribution, e.g. for viscosity of fatty acids (Yinghua et al.,
2002; Ceriani et al., 2007), for melting points and fusion enthalpies of triglycerides
(Zeberg-Mikkelsen and Stenby, 1999), and for vapor pressure of fatty acids (Ceriani and
Mirelles, 2004).
In particular, the Rackett method as modified by Spencer and Danner (1972) was
recommended for density prediction of pure hydrocarbons, organic liquids and
mixtures. However, this method requires the critical temperature and pressure of the
liquid, and also an experimentally regressed parameter (ZRA), which is reported for fatty
acids (Halvorsen et al., 1993) but is unknown for triacylglycerols and methyl esters.
The objective of this work is the prediction of critical properties, density and viscosity
of the main compounds involved in vegetable oils, animal fats and biodiesel fuels
(namely, fatty acids, triacylglycerols and methyl esters), by means of predictive
methods based on group contribution. Three contribution-group methods were tested for
critical property prediction, which are available in commercial simulators (like Aspen
Plus and ICAS). Rackett method was employed for density prediction, based on the
previous critical property estimation. Ceriani et al. (2007) method was applied for
viscosity prediction. All properties are evaluated as a function of temperature, and the
results are in very good agreement with experimental data obtained in this work and
other studies reported. The main contribution of this work is the generation of a pure
component databank for several fatty acids (FA), triacylglycerols (TAG) and fatty acid
methyl esters (FAME), together with a group contribution methodology that can be
applied to other no reported compounds. In addition, the pure component data can be
used to ascertain mixture property values and to estimate oil and biodiesel properties.
2. Property prediction approach for pure components
2.1. Critical property prediction
Many group-contribution methods have been widely used for the prediction of
physicochemical properties of pure organic compounds, where a compound or a mixture
of compounds is considered as a solution of groups and its properties are the sum of the
contribution of each group. One of the first widely used group-contribution methods
was the UNIFAC method (Fredenslund et al. 1977) where the value of each property
was obtained as the sum of contributions of simple first-order groups. The methods of
Joback and Reid (1983) and of Horvath (1992) are also methods of this kind. More
recently, a new class of group-contribution methods has been proposed, which defines
second order groups to provide more structural information, to distinguish isomers, and
to afford more accurate predictions (Mavrovouniotis, 1990; Constantinou and Gani,
1994). Second-order groups have a strong physicochemical meaning and can improve
the accuracy of property predictions. Moreover, Marrero and Gani (2001) introduced a
higher level of approximation by defining third-order groups to provide more structural
information about systems of fused aromatic and nonaromatic rings.
In particular, three group contribution methods were selected to estimate the critical
properties: Joback-Reid (JR), Constantinou-Gani (CG) and Marrero-Gani (MG), which
are available in commercial simulators (such as Aspen Plus and ICAS). To choose the
most accurate method, the values of the estimated properties were compared with
experimental values reported in literature.
Predicting critical properties, density and viscosity of fatty acids, triacylglycerols and
methyl esters by group contribution methods
2.2. Density prediction
There are a number of methods for predicting the liquid density of compounds and their
mixtures. The most important and accurate among them is the modified Rackett method
(Spencer and Danner, 1972). According this technique, the pure compound (saturated)
liquid density (ρ) is evaluated as follows:
RT ⎡⎢⎣1+(1−Tr ) 7 ⎤⎥⎦
,
Vs = c Z RA
Pc
2
Vs =
M
(1)
ρ
Where Vs, R, M, Vc, Tc and Pc are the molar volume of saturated liquids, the gas ideal
constant, the molecular weight, and the (estimated) critical volume, temperature and
pressure, respectively. ZRA is the Rackett parameter, a correlating parameter unique to
each compound determined experimentally. Values of ZRA for FA were reported in
Halvorsen et al. (1993), which were calculated by solving the modified Rackett equation
(1) directly for ZRA with a reference density at a given temperature. However, there are
no values reported for TAG and FAME. In this work, values of parameter ZRA for all
compounds were estimated by a least-squares fitting of available experimental values
(from this research and other reported studies) of density as a function of temperature.
2.3. Viscosity prediction
The viscosity prediction is based on the group contribution model, proposed by Ceriani
et al. (2007), for fatty compounds (such as FA, FAME and TAG):
B
B
⎛
⎞ ⎡
⎛
⎞⎤
lnηi = ∑ N k ⎜ A1k + 1k − C1k ln T − D1k T ⎟ + ⎢ M i ∑ N k ⎜ A2 k + 2 k − C2 k ln T − D2 k T ⎟ ⎥ + Q
T
T
⎝
⎠
⎝
⎠⎦
k
k
⎣
Q = ξ1q + ξ2 ,
q =α +
β
T
− γ ln T − δ T ,
ξ1 = f 0 + N c f1 ,
(2)
ξ2 = s0 + N cs s1
where ηi is the dynamic viscosity of molecule i (mPa·s), T is the absolute temperature
(K), Nk is the number of groups k in the molecule i, M is the component molecular
weight that multiplies the perturbation term; Ajk, Bjk, Cjk, Djk, (j = 1, 2), α, β, γ, δ , f0, f1,
s0 and s1 are regressed parameters; Q is a correction term due to the effect of functional
groups on the dynamic viscosity; ξ1 is function of the total number of carbon atoms Nc
in the molecule; and ξ2 describes the differences between the vapor pressure of isomer
esters at the same temperature and is related to the number of carbons of the substitute
fraction (Ncs). All adjusted parameters for equations (2) are reported in Ceriani et al.
(2007) and are available for the following functional groups: CH3, CH2, COOH, CH=,
OH, COO and CH2-CH-CH2.
3. Results and Discussion
3.1. Validation approach
The critical properties, density and viscosity were estimated for several compounds of
each family, involved in the production of biodiesel. The names of FA are: caprylic
acid, C8:0; capric acid, C10:0; lauric acid, C12:0; myristic acid, C14:0; palmitic acid,
C16:0; stearic acid, C18:0; oleic acid, C18:1; linoleic acid, C18:2; linolenic acid, C18:3;
and ricinoleic acid C18:1(OH). The names of TAG are: tricaprylin, CCC; tricaprin,
CaCaCa; trilaurin, LLL; trimyristin, MMM; tripalmitin, PPP; triestearin, SSS; triolein,
M. Sales-cruz et al.
OOO; trilinolein, LiLiLi; trilinolenin, LnLnLn; and triricinolein, RRR. The names of
FAME are the methyl esters of the aforementioned FA.
For the validation of predicted values for all properties, experimental data available
from this work and other reported studies were used to evaluate the average relative
deviation (ARD) according to the relationship:
ARD ( % ) =
∑D
i
N
× 100,
Di =
exp− calc
exp
( N : number of points )
(3)
3.2. Prediction of critical properties
The critical properties were predicted for all compounds according three groupcontribution methods: JR (first-order groups), CG (second-order groups), and MG
(third-order groups). The predictions were done through two simulators: ICAS (2009),
developed by the Computer Aided Process Engineering Center, Department of
Chemical Engineering, Technical University of Denmark; and Aspen Plus (2009),
developed by Aspen Technology, Cambridge Massachussets. The former includes the
three methods, while the latter only includes methods of CG and JR. Then the ARD was
evaluated, first individually for each compound, then a mean value for all compounds of
each family (see in Table 1). It is important to mention that experimental data was
available for all compounds of FA family, unfortunately no experimental values were
available for TAG family, and few data were found for FAME family (only for C10:0
andc12:00). However we consider that results for FA and available FAME are enough
to validate the method. So that, according the results, the most accurate method is CG
(with similar results in both simulators, ICAS and Aspen Plus). Predictions for critical
properties with CG method are shown in Table 2, 3 and 4 for FA, TAG and FAME,
respectively.
Table 1. ARD (%) of each property for each compound family (1ICAS, 2Aspen Plus)
Parameter
Tc
Pc
Vc
MG1
6.83
10.97
3.64
CG1
1.21
4.12
3.82
FA
JR1
4.99
5.71
4.10
TAG
CG2
1.27
5.74
4.01
JR2
3.91
6.42
4.60
-
MG1
0.77
0.00
3.49
CG1
6.93
2.71
3.22
FAME
JR1
1.45
2.41
3.95
CG2
6.93
2.71
3.22
JR2
0.39
2.39
4.09
Table 2. Estimated properties for FA: CG method (Tc in K, Pc in bar, Vc in cm3/mol)
C8:0
C10:0
C12:0
C14:0
C16:0
C18:0
C18:1
C18:2
C18:3 C18:1(OH)
Tc 695.00 720.40 742.68 762.51 780.38 796.65 795.17 793.68 792.18
Pc 27.67 22.79 19.14 16.36 14.18 12.44 12.16 11.90 11.64
Vc 507.1 618.6 730.2 841.7 953.2 1064.7 1054.2 1043.7 1033.2
Zc 0.24
0.23
0.22
0.22
0.21
0.20
0.19
0.19
0.18
811.21
12.79
1061.2
0.20
Table 3. Estimated properties for TAG: CG method (Tc in K, Pc in bar, Vc in cm3/mol)
CaCaCa
Tc
Pc
Vc
Zc
793.40
7.43
1609.7
0.18
CCC
LLL
MMM
PPP
SSS
OOO
LiLiLi LnLnLn
835.60 869.80 898.56 923.37 945.19 943.23 941.25
5.91
4.89
4.18
3.67
3.28
3.22
3.17
1944.2 2278.8 2613.4 2947.9 3282.5 3251.0 3219.6
0.17
0.15
0.15
0.14
0.14
0.13
0.13
939.25
3.11
3188.1
0.13
RRR
964.18
3.36
3271.9
0.14
Predicting critical properties, density and viscosity of fatty acids, triacylglycerols and
methyl esters by group contribution methods
Table 4. Estimated properties for FAME: CG method (Tc in K, Pc in bar, Vc in cm3/mol)
C9:0
C11:0
C13:0
C15:0
C17:0
C19:0
C19:1
C19:2
C19:3 C19:1(OH)
Tc 580.31 625.53 661.69 691.81 717.63 740.23 738.21 736.16 734.09
Pc 23.07 19.36 16.52 14.31 12.55 11.12 10.89 10.67 10.46
Vc 561.0 672.5 784.1 895.6 1007.1 1118.6 1108.1 1097.6 1087.2
Zc 0.27
0.23
0.24
0.22
0.21
0.20
0.20
0.19
0.19
759.83
11.41
1115.1
0.20
3.3. Prediction of densities and viscosities
As explained in section 2.2, firstly values of ZRA were fitted as shown in Table 5. It is
worth of mention that the original Rackett equation employs the compressibility factor
Zc instead of ZRA as proposed by Spencer and Danner (1972). However this last method
has been demonstrated to be more accurate (Poling et al., 2001). Nonetheless, values of
Zc and ZRA are similar according Tables 2-4 and 5. Secondly, the densities were
predicted according the modified Rackett equation (Eq. 1). Predictions and experimental
data for some representative compounds are shown in Fig. 1. Results were quite
accurate, with ARD for each compound family: 0.84% for FAME, 1.19% for TAG, and
0.19% for FAME. Thirdly, the viscosities were predicted according the groupcontribution method of Eq. (2). Comparison of predictions and experimental values for
some compounds are shown in Fig. 2. Results were satisfactory, mainly for TAG family
(ARD 3.63%) and FA (ARD 11.91%), but not too accurate for FAME family (ARD
24.39%). This last high value was due to the lack of enough experimental values, but
predictions of FA and TAG may be acceptable within measuring and predicting errors.
FA
ZRA
TAG
ZRA
FAME
ZRA
C8:0
C10:0
C12:0
C14:0
C16:0
C18:0
C18:1
C18:2
C18:3
C18:1(OH)
0.24920
0.24426
0.23983
0.23466
0.22953
0.22467
0.21939
0.22550
0.22840
0.22429
CCC
CaCaCa
LLL
MMM
PPP
SSS
OOO
LiLiLi
LnLnLn
RRR
0.21412
0.20990
0.19336
0.19308
0.18554
0.18332
0.18168
0.17860
0.17432
0.18951
C9:0
C11:0
C13:0
C15:0
C17:0
C19:0
C19:1
C19:2
C19:3
C19:1(OH)
0.25938
0.25124
0.24397
0.23757
0.23154
0.22559
0.22134
0.21606
0.21261
0.22413
ηFA (mPa.s)
0.88
-3
0.86
C10:0
C12:0
C14:0
C18:0
0.84
-3
ρTAG (g cm )
0.82
C10:0
C12:0
C14:0
C18:0
10
100
0.96
LLL
CCC
PPP
SSS
0.94
0.92
0.90
ηTAG (mPa.s)
ρFA (g cm )
Table 5. Values of ZRA
CCC
LiLiLi
PPP
SSS
10
ηFAME (mPa.s)
-3
ρFAME (g cm )
0.88
0.86
0.84
C11:0
C13:0
C15:0
C19:0
0.82
0.80
20
40
60
T (°C)
80
Figure 1. Predictions of density.
100
120
C11:0
C13:0
C15:0
C19:0
10
1
20
40
60
T (°C)
80
Figure 2. Predictions of viscosity.
100
120
M. Sales-cruz et al.
It is worth of mention that although only pure compounds properties have been
predicted, they can be used to predict mixture properties by mixing rules. For instance,
Rackett mixture density (Spencer and Danner, 1973) (Eq. 4a, b) and the modified Kay’s
rule for viscosity (Eq. 4c) can be applied (xi is the mole fraction of each compound):
ρm =
1
Vm
c
⎡1+ (1−T ) 2 7 ⎤
r
⎢
⎦⎥
∑ xi M i , Vm = A ⋅ R ⋅ Z RA⎣ ,m
i =1
c
;
lnηm = ∑ xi lnηi
(4a, b, c)
i =1
4. Summary and Conclusions
The main contribution of this work was the generation of a databank for the most
important FA, TAG and FAME involved in the biodiesel production, together with
group contribution methodologies for critical properties, density and viscosity that can
be applied to other no reported compounds. In most cases, good agreement between
experimental data and predicted values was obtained. Currently, we are working on the
direct application of these results for the estimation of temperature-dependence
properties for mixtures, such as oils and biodiesels, which are useful for several research
areas of process engineering.
5. Acknowledgements
We acknowledge to Prof. Rafiqul Gani for the use of ICAS software. This work has
been supported by CONACyT research grants (Projects 84535 and 91222).
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