Chemical Engineering Journal Advances 10 (2022) 100257
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A theoretical and experimental study of liquid-liquid equilibrium to refine
raw glycerol obtained as a byproduct on the biodiesel production
J.Mendieta López a, F.J.Pérez Flores b, E.Castillo Rosales c, E.Ortiz Muñoz d,
S. Hernández-Anzaldo a, H.Vázquez Lima a, *, Y.Reyes Ortega a, **
a
Benemérita Universidad Autónoma de Puebla, Centro de Química, Instituto de Ciencias, Edif. IC09, C. U., Col. Jardines de San Manuel, Puebla, Pue. 72570, Mexico
Universidad Nacional Autónoma de México, Instituto de Química, Circuito Exterior, C. U., Coyoacán, Ciudad de México, D. F. 04510, Mexico
Instituto de Biotecnología de la Universidad Nacional Autónoma de México, Av. Universidad 2001, Chamilpa, 62210 Cuernavaca, Mor., Mexico
d
Benemérita Universidad Autónoma de Puebla, Facultad de Ingeniería Química, Edif. FIQ 9, C. U., Col. Jardines de San Manuel, Puebla, Pue. 72570, Mexico
b
c
A R T I C L E I N F O
A B S T R A C T
Keywords:
Raw glycerol purification
Liquid-liquid equilibrium
Biodiesel production
Castor oil
Getting high purity glycerol at a low cost from biodiesel (methylricinoleate) production is of great economic
interest. Therefore, exist several strategies for raw glycerol purification. Some involve liquid-liquid extraction
steps using ether, toluene, n-butanol, cyclohexanol, aniline, or solvent mixtures to remove organic impurities
from glycerol. However, the phase’s equilibrium data is not available for the convenient process design in some
cases. This work purified raw glycerol obtained from the alkaline methanolysis of castor oil by neutralization,
filtration, distillation, wash with acetone, adsorption with activated charcoal, and drying with sodium sulfate.
Furthermore, liquid-liquid equilibrium (LLE) of the ternary system glycerol-acetone-biodiesel was monitored by
1
H NMR spectroscopy at 281.15, 290.15, and 299.15 K and correlated by the NRTL model. Finally, we evaluated
the COSMO-RS implicit solvation model predictive methodology due to the lack of LLE data for glycerol puri­
fication systems in the literature. The experimental results indicate that the process produces glycerol at 96.42%
purity wt., and the LLE evaluated consists of two pairs of partially miscible liquids, glycerol-biodiesel, and
glycerol-acetone. Therefore, the glycerol purification with acetone proposed here allows less process dangerous
conditions, a less toxic product for food applications, eliminates 100% of organic impurities with low volumetric
ratios, and helps to precipitate the persistent ash content. The theoretical results indicate COSMO-RS model
overestimated the solubility glycerol-acetone, predicting only the pair of partially miscible liquids glycerolbiodiesel, this limiting the accuracy of COSMO-RS to predict LLE data for glycerol purification systems with
acetone.
1. Introduction
Biodiesel is an old answer to the current trend to move away from
fossil fuels. During its production, glycerol formation as byproduct
yields ~ 10% wt. Several methods accomplish this goal. Among them
are the acid, basic and enzymatic catalysis [1]. Glycerol is a biode­
gradable, colorless, hygroscopic, nontoxic, odorless, transparent, and
viscous liquid with relevant applications in pharmaceutical, food, cos­
metics, explosives, toiletries, polymers, surfactants, lubricants, and
many other industries [2–4]. There are several routes for glycerol pro­
duction: oil saponification, oil feedstock transesterifications and hy­
droxylation of propylene, among others [5–7]. Biodiesel’s glycerol
production would be interesting in economic terms. However, although
glycerol has more than 1000 uses, these applications require a highly
purified product [8,9]. The glycerol marketed today is manufactured to
meet the stringent requirements (99.7% by weight) of the United States
Pharmacopeia (USP) [10–12]. However, the glycerol obtained from
biodiesel plants may contain alcohol, catalyst, salts, soaps, water, free
fatty acids, mono, di, or triglycerides, and residual biodiesel. So due to
the high cost of the purification, the industry has preferred not to treat
the glycerol produced, which results in a worldwide surplus of low-value
glycerol and contamination.
Several glycerol purification processes exist, but the general pro­
cedure filters the liquor, neutralizes the catalyst, precipitates the salts,
* Corresponding author.
** Corresponding author.
E-mail addresses: vazquez.limahugo@correo.buap.mx (H.Vázquez Lima), yasmi.reyes@correo.buap.mx (Y.Reyes Ortega).
https://doi.org/10.1016/j.ceja.2022.100257
Available online 3 February 2022
2666-8211/© 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/).
J.Mendieta López et al.
Chemical Engineering Journal Advances 10 (2022) 100257
and vacuum distillation. In this way, it produces raw glycerol (80–88 wt
%) and technical grade glycerol (98 wt%) [10–12]. If higher purity is
required, the ionic exchange technique is an option. It allows the
adsorption of ionic impurities and their discoloration. This final stage in
the purification process allows purity higher than 99.5%. [2]. However,
the viscosity of the solution must be low enough for the pressure drop­
ped. It is evident that the more diluted the solution, the greater the
purification costs due to the evaporation of water excess. The solution
must have a low salt concentration to avoid exchange columns of large
diameters. The solution’s turbidity must be minimum, as suspended
solids hinder and retard the exchange process and color removal. The
solution must be free of fats or oils to use this refinement method
because non-ionized impurities like esters, sugars, or polyglycerols are
not removed and tend to foul the exchanger beds [10–12]. Therefore,
other methods to purify glycerol by chemical and physical treatment
exist. Those methods rely on repeated cycles of acidification, neutrali­
zation, and phases separation. In these processes, some solvent like
ether, toluene, n-butanol, water, cyclohexanol, or aniline washes the
glycerol-rich phase to extract the organic traces [13–19]. However, the
phases’ equilibrium data of the extraction is not always available for a
convenient solvent selection, process modeling, or design. It is relevant
to mention that phases equilibrium data for glycerol purification sys­
tems by washing are scarce in the literature. Therefore, it is necessary to
develop reliable predictive methods of calculus [9]. Several studies
documented the description of LLE via simulation [20–25]. This work
purified raw glycerol obtained from castor oil by alkaline methanolysis
[26–28] by neutralization, filtration, evaporation, wash with acetone,
adsorption with activated charcoal, and drying with sodium sulfate. LLE
of the ternary system glycerol-acetone-biodiesel was monitored by 1H
NMR at 281.15, 290.15, and 299.15 K, under atmospheric pressure, and
correlated to the NRTL model using the Aspen Properties estimation
package available in Aspen Plus 7.0(R) Chemical Process Simulator
[29–31]. Finally, we used the experimental results to validate the
COSMOtherm’s COSMO-RS implicit solvation model, using DFT
BP86/TZVP calculations with Gaussian 09 [32–36].
2. Experimental methodology
2.1. Materials are resumed in Table 1
Table 1.
2.2. Biodiesel and raw glycerol purification
Biodiesel purification follows the procedure described in a previous
study [28]. First, the raw glycerol was neutralized and filtered; the
methanol and water traces were removed using a rotary evaporator
Buchi R-3 operating under vacuum for 1 hr at 368.15 K. Table 1 sum­
marizes the information of the reagents used. We selected the best sol­
vent to wash the glycerol from previous studies [37]. Comparing
hexane, benzene, ethyl acetate, 2-butanone, i-propanol, THF, methylene
chloride, and acetone showed the latter’s advantages over the others.
Then, raw glycerol was washed with 200% vol of acetone and placed in a
separatory funnel due to salt precipitation from the neutralized mixture.
We repeated the process five times until precipitation no longer
occurred. Next, the glycerol-rich phase was removed and placed on the
rotary evaporator to remove the residual acetone. Then, the dry glycerol
was treated with 20% and 60% by weight of activated charcoal. The
adsorption was carried out in a kitasato flask and a 5 mm glass tube of
internal diameter. The samples obtained were stored in an oven at
100 ◦ C with 20% by weight of sodium sulfate and finally filtered. Before
and after treatment, the samples were characterized by 1H NMR (Bruker
Avance III 500, 500 MHz spectrometer), UV–Vis spectra (Beckman DU
Series 7000 (Beckman Coulter Inc., Brea, CA, USA) equipment in
methanolic solutions at 298 K in the 200–800 nm range), and MS (JEOL
JMS AX505HA) and compared with commercial glycerol. For the
UV–Vis measurements, we used diluted glycerol in ethanol as blank. It
was necessary to increase the initial glycerol concentration from 0.03
g/ml to 0.3 g/ml to obtain a more significant difference in the absor­
bance obtained in the visible region as a function of its discoloration. For
1
H NMR, glycerol was dissolved in water-d at 534 mM ca.
2.3. Experimental phase equilibrium determination by 1H–NMR
Purified biodiesel, glycerol and acetone, were used to prepare the
mixtures described in Table 2 and were shaken for 15 min at 1200 rpm,
then allowed to remain at rest for 24 h in plastic syringes until phase
separation was complete. Mixture 1 corresponds to the equivalent
weight of each component, mixtures 2, 3, and 4 correspond to an excess
2:1 of one component in each case. Mixtures 5, 6, and 7 correspond to
experiments in the absence of one component. In this way, we system­
atically produced a range of compositions to generate relevant data for
LLE. All mixtures presented separation in two phases except mixture 5,
which stayed as monophasic. According to the transesterification reac­
tion temperatures reported, these vary between 283.15 - 340.15 K and
623.15 K using methanol under supercritical conditions [38–40]. In
addition, we carried out a previous study using 301.15 K as maximum
temperature, obtaining good results in kinetic determinations at 299.15
K [41]. We have previously verified that the 1H NMR method is faster
and simpler than chromatographic methods, and so we used it in this
Table 1
Chemical used and their characteristics.
Chemical
Provider
Purity
%
Grade
Further
purification
Methanol
Chemical
Guilps (MEX)
Chemical
Guilps (MEX)
Chemical
Guilps (MEX)
Aromas Flavor
and Colours
(MEX)
Sigma-Aldrich
(USA)
99.9
Industrial
Yes [28]
99.9
Industrial
No
99.9
Industrial
Yes
88.0
Standard
No
Standard
No
Sigma-Aldrich
(USA)
Sigma-Aldrich
(USA)
Sigma-Aldrich
(USA)
Alpha Reagents
(USA)
Fermont (MEX)
99.5
No
99.9
Spectrophotometric
Spectroscopic
99.8
Spectroscopic
No
99.0
Technical
No
98.9
Reagent
No
Meyer (USA)
Not
viable
Reagent
No
Ethanol
Acetone
Castor oil
Activate
Charcoalpowder
Glycerol
Water-d
Chloroform-d
Sodium sulfate
Sodium
hydroxide
Hydrochloric
acid
Table 2
The molar fractions feed composition of biodiesel, acetone and glycerol
mixtures.
No
2
Mixture
Biodiesel
Acetone
Glycerol
1
2
3
4
5
6
7
0.0368
0.0231
0.0709
0.0268
0.0586
0.0000
0.0899
0.5918
0.7429
0.5700
0.4307
0.9414
0.6137
0.0000
0.3722
0.2339
0.3590
0.5425
0.0000
0.3864
0.9101
J.Mendieta López et al.
Chemical Engineering Journal Advances 10 (2022) 100257
work [28]. Afterward, samples of 0.03 g were taken from each phase for
analysis by 1H NMR, ester phase in chloroform-d, and glycerol phase in
water-d as solvents. We recorded spectra of each mixture in Table 2 at
281.15, 290.15, and 299.15 K (three replicates for each temperature).
The average measurements were used to calculate the mole fraction of
the components in each phase as follows: For the ester-phase composi­
tion (light phase), Fig. 1 presents the areas of integration in the spectrum
(S1, S2, S3, and S4) and shows the "i" types of protons (Pi) present in each
compound. For the mixture ester-acetone-glycerol, due to the signals
overlapEqn 1, 2, 3 and 4:
S1 = P6
(1)
S2 = P4 + P11 + P13 + P12
(2)
S3 = P5 + P14
(3)
S4 = P8 + P2 + P3
(4)
P 5 = P6
3
P11 = P6
2
P4 =
2.39
P11
9
(9)
(10)
(11)
Solving the Eqs. (1) to 3, 5, 7, and 8 – 11; MB, MA, and MG can be
rewritten for the light phase as Eqn 12, 13 and 14:
According to the components’ molecular structures, we established
relationships Eqn 5, 6, 7, 8, 9, 10 and 11 for a mixture without mono, di,
or triglycerides. MB, MA, and MG are biodiesel, acetone, and glycerol
moles. Eq. (11) corresponds to a correction due to the content of rici­
noleic acid in the castor oil [28]:
MBL =
S1
2
(12)
MAL =
S3 − S1
6
(13)
MGL =
6S2 − 11.39S1
30
(14)
Fig. 2 presents the areas of integration in the spectrum for the
glycerol phase composition (heavy phase) and shows the Pi present in
the mixture. In this case, it was necessary to choose S2 to S4 as inte­
gration areas for the quantification due to the poor definition of S1,
masked by the water-d pollutants used as a solvent.
Therefore, solving Eqs. (2) – 4 and 6 – 11; MB, MA, and MG can be
rewritten for the heavy phase as Eqn 15, 16 and 17:
MB =
P6
2
(5)
MB =
P8 + P2 + P3
18
(6)
MBH =
S4
18
(15)
MA =
P14
6
(7)
MAH =
9S3 − S4
54
(16)
MG =
P12 + P13
5
(8)
MGH =
S2 − 11.39S4
5
(17)
Fig. 1. 1H NMR for the light phase of the experiments 1–4, 6 and 7.
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Chemical Engineering Journal Advances 10 (2022) 100257
Fig. 2. 1H NMR for the heavy phase of the experiments 1–4, 6 and 7.
2.4. Theoretical phase’s equilibrium determination by COSMO-RS model
according to the following Eqn 18 [44].
( )
e − kTEi
( )
Pci =
∑N − Ei
i e kT
This methodology involves three steps. First, we generated several
conformers with a conformational search using MMFF implemented in
MOE [42, 43]. Next, we selected the representative conformers and
relaxed them with DFT BP86/TZVP and COSMO-RS implicit solvation
model [32–36]. As a result, the charge distribution on the solute gets
polarized and the adjacent dielectric continuum. From this process, we
obtain screening charges at the surface of the implicit solvent corre­
sponding to the solute charges. These screening charges are then stored
at a file together with the surface area and the cavity volume formed by
the solute. At a second step, the information stored is used to determine
activity coefficients using the COSMOtherm software. Therefore, any
compound mixture can be investigated once the file for a particular
compound is computed. Furthermore, to account for the effect of
different molecular conformations of the solute, this study also includes
the corresponding Boltzmann distribution for methyl ricinoleate
(18)
Where T is the temperature, k is the Boltzmann constant, Ei is the
relative Gibbs free energy of the conformer "i" in the solvent and Pci is the
conformer probability.
Finally, we calculated the activity coefficients of acetone and other
solvents for glycerol washing to clarify the advantages offered by the
washing system reported in this work with respect to others.
Fig. 3. UV–Vis of biodiesel, raw glycerol, and commercial glycerol transitions a) UV region, b) visible region.
4
J.Mendieta López et al.
Chemical Engineering Journal Advances 10 (2022) 100257
3. Results and discussion
protons’ signal at 4.2 ppm reflects the absence of oil (tri, di, or mono­
glycerides) in glycerol [10–12, 28, 45–50]. The ratio between the sig­
nal’s integration and its Pi protons value indicates that for each mole of
glycerol, there are 0.040 mol of methanol (0.12/3) and 0.083 mol of
ester (sum of 0.15, 0.18, and 0.17 between 6). 1H NMR cannot measure
the water content due to the interaction with the water-d used as the
solvent. Table 3 summarizes the composition of the raw glycerol
obtained.
3.1. Raw glycerol characterization
As stated in the introduction, most glycerol applications require a
high-purity compound. Hence, the characterization of raw glycerol is
relevant to assessing if the high-purity glycerol’s goal is achieved. The
raw glycerol obtained after the reaction is a viscous dark orange liquid.
Fig. 3 compares the UV–Vis spectra for the biodiesel, raw glycerol, and
commercial glycerol. Fig. 3a shows raw glycerol exhibits transitions n →
σ*, n1 → σ*, n2 → σ*, n1 → π*andn2 → π* due to residual water,
methanol, FFA (Free Fatty Acids) and FAME (Fatty Acid Methyl Ester),
respectively, in the sample. As a result, there is higher absorbance for the
raw glycerol in the visible region (Fig. 3b) than commercial glycerol due
to its color. Due to the slight difference among the signals absorbance of
commercial glycerol and raw glycerol at low concentrations (0.03 g/ml)
in the visible region, it was necessary to raise the concentration of the
sample used for measurement to 0.3 g/ml for colorimetry purposes. For
this reason, Fig. 3a shows the signals absorbance outside of Beer-Lam­
bert’s law.
The mass spectrum for raw glycerol (Fig. 4) shows a mass/charge (m/
z) ratio equal to 93, corresponding to the glycerol molecular ion. The m/
z ratios 15, 31, 43, 61, and 75 correspond to its preferential fragmen­
tation patterns due to the electron ionization (IE). The m/z relationships
higher than 93 indicate the presence of contaminant ions produced from
hydrocarbons heavier than glycerol like residual esters, glycerides, or
soaps. The m/z relationship 28 belongs to nitrogen in background
equipment. The m/z relationship 18 belongs to water, mainly coming
from the neutralization of the reaction catalyst. Glycerol fragmentation
generates secondary contributions and absorption of the surrounding
medium due to the glycerol’s hygroscopicity. Therefore, the intensity of
18 and 61 m/z ratios allows an estimation of the water content in the
sample. These m/z correspond to the base peaks of the fragmentation
patterns of the water and glycerol, respectively. Thus, for every 100
glycerol molecules, there are 58 of water.
Fig. 5 shows the 1H NMR spectrum of raw glycerol obtained. The
signals between 3.3 and 3.7 ppm correspond to glycerol. Signals in the
chemical shift interval of 1.8 – 2.2 ppm and 3.2 ppm indicate the pres­
ence of biodiesel residual and methanol traces. The lack of glycerol
3.2. Purified glycerol characterization
Fig. 6 shows the UV–Vis spectra for the best-purified sample of raw
glycerol and commercial glycerol. It is notable that although a discol­
oration even higher than that of commercial glycerol has been achieved
(Fig. 6b), the absorbance of the transition n→σ* is at a very high value
(Fig. 6a). We assigned this transition to water traces in equilibrium with
ash residue not entirely removed yet. On the other hand, Fig. 6b shows
the color removal as a function of the percentage by weight of activated
charcoal, the procedure, and the physical system used. Methanol may
function as a pigment eluent when added to lower the sample’s viscosity
and decrease the bleaching efficiency, even when using large amounts of
activated charcoal. On the other hand, discoloration in a column system
increases the theoretical adsorption stages with respect to using a vac­
uum flask.
Fig. 7 shows the mass spectrum of purified glycerol. There is no m/z
ratio over 93, indicating the total removal of ester traces. The m/z ratio
of 18 in the spectra indicates the water is not entirely removed. Water is
tough to remove from the sample because its vapor pressure is very low
as the mixture composition approaches pure glycerol [51]. According to
water and glycerol base peaks intensities, for every 100 glycerol mole­
cules, there are still 14 of water.
Fig. 8 shows the 1H NMR spectrum for the purified glycerol. Signals
located at 2.05 and 3.2 ppm belong to impurities in water-d (4.7 ppm)
used to prepare the samples. Both MS and 1H NMR studies indicated the
purified glycerol contains no ester traces because the acetone can
remove 100% of residual biodiesel. From the spectra analysis, the
composition of the purified glycerol was 97.33% wt of glycerol and
2.66% wt of water. The ash content could not be detectable by 1H NMR
or MS. According to the maximum solubility of sodium chloride in water
Fig. 4. EM of crude glycerol.
5
J.Mendieta López et al.
Chemical Engineering Journal Advances 10 (2022) 100257
Fig. 5. 1H NMR spectrum of raw glycerol.
used in the phases equilibrium study ensures that the behavior of the
phases strictly reflects the acetone-glycerol-biodiesel system. It is
necessary to clarify that before washing it with acetone, removing the
highest possible content of methanol and water from the sample is
required. These compounds function as surfactants that modify the
phase balance and the extraction of the polluting ester from the sample.
Table 3
Resume of the raw glycerol composition.
Components
Moles
%wt
Glycerol
FAME
Water
Methanol
Sodium chloride
1.00
0.08
0.58
0.04
0.16
66.69
17.91
7.56
0.93
6.91
3.3. Experimental liquid-liquid equilibrium
Table 4 summarizes the experimental data obtained for the LLE at
281.15, 290.15, and 299.15 K for the seven mixtures. We selected the
lower temperature because it is the minimum temperature in which all
components are liquid, the highest temperature as the room tempera­
ture, and the temperature of 290.15 K as a medium point between those
two values. The mean standard deviation presented is 3.15 by weight to
ensure good reproducibility in experimentation.
Fig. 9 shows the ternary diagram for the experimental data obtained
at 299.15 K, a type II diagram showing two pairs of partially miscible
liquids acetone-glycerol and biodiesel-glycerol. It contains five tie lines
whose trends indicate biodiesel-acetone’s high solubility and the low
solubility of glycerol-acetone. This characteristic makes acetone a
(0.36 g/cc) for every 97.33 gs of glycerol and 2.66 gs of water, the
sample could not contain more than 0.95 gs of sodium chloride.
Therefore, it comprises 96.42% wt of glycerol, 2.63% wt of water, and
0.95% wt of sodium chloride. The objective of the purification process
carried out in the present work was to limit the phases equilibrium
system studied to a biphasic system. If this purification is not achieved,
the system would be a multi-component system with four phases: vapor
phase composed primarily of acetone, two liquid phases, and a solid
phase. As mentioned in the methodology, washing with acetone induces
the precipitation of sodium chloride. The study of a system with these
characteristics is outside this project’s scope. The components purity
Fig. 6. Purified glycerol transitions a) UV region, b) visible region.
6
J.Mendieta López et al.
Chemical Engineering Journal Advances 10 (2022) 100257
Fig. 7. Glycerol purified, MS spectrum.
Fig. 8. Glycerol purified, 1H NMR spectrum.
suitable solvent for biodiesel extraction systems in a wide range of
compositions. The red point corresponds to the homogeneous biodieselacetone mixture. However, there is an 18.93% wt loss of acetone due to
settling time and the high vapor pressure of the acetone.
Figs. 10a and 10b show the ternary diagrams for the experimental
LLE obtained at 281.15 and 290.15 K. These diagrams are of type II, too.
Again, the diagrams confirm that as the temperature decreases, there is a
lower loss of acetone generated during the decantation time.
3.3.1. Data correlation
Eq. (19) define the binary parameters of NRTL model.
τij = aij +
bij
+ eij lnT
T
(19)
The parameter aij for glycerol and acetone is retrieved from the
Aspen Properties package and the values for the parameter eij of the
NRTL model are set to zero. Besides, the physical properties of the
biodiesel were calculated with the estimation models in the same
package. Table 5 shows NRTL parameters obtained from the
7
J.Mendieta López et al.
Chemical Engineering Journal Advances 10 (2022) 100257
Table 4
Summary of LLE obtained for the glycerol-acetone-biodiesel system at 281.15, 290.15, and 299.15 Ka, η (mole fraction).
T, K
P = 67 kPa
Mixture
1
2
3
4
*5
6
7
a
*
Phases
Components
281.15
Low density
nB-A
Biodiesel
Glycerol
Acetone
Biodiesel
Glycerol
Acetone
Biodiesel
Glycerol
Acetone
Biodiesel
Glycerol
Acetone
Biodiesel
Acetone
Glycerol
Acetone
Biodiesel
Glycerol
0.288
0.004
0.706
0.212
0.004
0.784
0.279
0.002
0.719
0.281
0.003
0.712
0.203
0.80
0.034
0.97
1
0.00
290.15
Low density
nB-A
High density
nG
0.00
0.891
0.108
0.377
0.919
0.00
0.001
0.875
0.123
0.00
0.872
0.127
0.314
0.00
0.685
0.165
0.011
0.825
0.429
0.00
0.571
0.318
0.015
0.667
0.239
0.761
0.498
0.79
1
0.00
0.593
0.406
0.002
0.998
High density
nG
0.00
0.901
0.0986
0.00
0.847
0.153
0.00
0.886
0.113
0.00
0.906
0.093
0.736
0.265
0.007
0.993
299.15
Low density
nB-A
High density
nG
0.348
0.010
0.643
0.200
0.009
0.790
0.451
0.00
0.548
0.393
0.006
0.599
0.294
0.706
0.047
0.953
0.998
0.002
0.0007
0.898
0.102
0.000
0.801
0.199
0.00
0.892
0.107
0.00
0.900
0.019
0.00
0.00
0.80
0.02
0.00
0.999
Standard uncertainties: u(T) = 0.1 K, u(η) = 0.0008, u(P) = 0.05 kPa.
Mixture was monophasic.
Fig. 9. Ternary diagram for the experimental LLE glycerol-acetone-biodiesel. Weight percentage values at 299.15 K taken from Table 4.
experimental LLE data regression using the Maximum Likelihood Al­
gorithm available in Aspen Properties. The details of the properties
estimation of the biodiesel and the regression model can be consulted in
the complementary information file of this article.
The Fig. 11 represents the experimental results together with the
correlated results for the used system at 299.15 K. Correlation using the
NRTL model exhibits acceptable agreement with a Root Mean Square
Deviation (RMSD) of 0.1498.
three values of temperature under study. This way confirms the stability
criterion for the mixing Gibbs energy for the conditions depicted in the
experimental study. Although biodiesel - glycerol is the only one pre­
sented, we also obtained the thermodynamic consistency proof for
acetone - glycerol. The details are in the complementary information
file.
3.4. Theoretical LLE results
⎛
)2 ⎞1/2
∑ ∑ ∑ ( exp
cal
w
−
w
ijk
ijk
k
j
i
⎜
⎟
RMSD = ⎝
⎠
6N
Table 6 shows the Boltzmann distribution for methyl ricinoleate in
acetone, estimated with DFT. In this study, we found more than 800
conformers for methyl ricinoleate. Because most of them are equivalent,
we considered the most crucial intramolecular interaction: the hydrogen
bond formation between the hydroxyl and the carbonyl groups. This
interaction generates the coiling of the chain, presented in Fig. 13.
Therefore, the length change produced was divided into ten groups, and
The thermodynamic consistency of the regression is tested with the
evaluation of the mixing Gibbs energy of the system using the NRTL
model and the obtained binary parameters [52, 53]. Fig. 12 presents the
dimensionless mixing of Gibbs energy for biodiesel - glycerol and the
8
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Chemical Engineering Journal Advances 10 (2022) 100257
Fig. 10. LLE glycerol-acetone-biodiesel at a) 281.15 and b) 290.15 K.
when all glycerol conformers from the database TZVP and all ester
conformers obtained are employed. The software predicts only a
partially miscible pair of liquids, glycerol-methylricinoleate, and not the
partial solubility glycerol-acetone. Since the results obtained using the
total number of conformers as an only component did not coincide with
the experimental results, the treatment conformer-by-conformer was
carried out. In this way, it is possible to obtain 110 combinations of
ternary systems from the ester and glycerol available conformers, 11
chosen for the ester and 10 corresponding to the COSMOtherm TZVP
database. Concerning the ester conformers, the conformers 9, 2, and 1
approximate the phase diagram to the experimental behavior, with
minimal variations in the ester-glycerol solubility. The best option of
glycerol conformers is conformer 7 of the COSMOtherm TZVP database.
Fig. 14b shows the best result obtained from these combinations.
However, the software continues predicting only a partially miscible
pair of liquids, glycerol-methylricinoleate, overestimating glycerolacetone solubility, so it is not suitable for generating predictive data
for the extraction system of the present study. It should be considered
Table 5
NRTL binary interaction parameters for the experimental LLE.
Components
glycerol(1) acetone(2) biodiesel(3)
Component i
Component j
2
1
− 1.88
1773.45
140.02
0.20
aij
bij
bji
cij
3
2
0.00
− 715.40
620.36
0.30
3
1
0.00
1616.98
1912.11
0.30
the conformers with the lowest energy were selected. After that, we
relaxed them with DFT. Table 6 shows the conformer’s normalized
weight factor (NWF) in acetone and glycerol, obtained from COSMO­
therm software. Glycerol presence generates significant changes in the
conformers abundance due to the changes in polarization of the solvent.
Fig. 14 shows the diagrams of LLE generated by COSMOtherm soft­
ware for ternary systems selected. Fig. 14a shows the result obtained
9
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Chemical Engineering Journal Advances 10 (2022) 100257
Fig. 11. Data correlation for the system glycerol-acetone-biodiesel at 299.15 K, (— experimental, — NRTL model).
Fig. 12. Mixing Gibbs energy for the pair biodiesel - glycerol.
that COSMOtherm software performs iterations with compositions
outside the limits of infinite dilution. At some point, any of the three
components: glycerol, ester, or acetone, can be the solvent. Therefore, it
is expected variations in the populations predicted in Table 6 with
respect to the NWF or the Boltzmann distribution, remembering that the
latter used only acetone as solvent.
makes it suitable for recovery with low energy expenditure and appli­
cation in recirculation in a continuous process. In addition, acetone is
more stable to light and air than ether; therefore, it presents a lower risk
of explosion. Another important characteristic is its relatively low
toxicity, except for water. It is necessary to mention that water as a
solvent for glycerol washing is limited to small areas of immiscibility
and is restricted to the extraction of methanol [17]. Finally, as shown in
Table 7 and supported by the experimental LLE studies presented here,
qualitatively, there is excellent solubility of ester in acetone with less
dangerous implications.
3.4.1. Advantages of the acetone wash system
One of the main advantages of using acetone as a crude glycerol wash
solvent over the solvents is its low boiling point. This characteristic
10
J.Mendieta López et al.
Chemical Engineering Journal Advances 10 (2022) 100257
quantitative results should be considered cautiously because we found a
considerable overestimation of the glycerol-acetone solubility. The
modification of the conformer and the insertion of experimental data
can still be explored. This discrepancy will be a follow work.
Table 6
Boltzmann distribution for methyl ricinoleate in acetone and comparison with
COSMOtherm calculus.
Conformer
1
2
3
4
5
6
7
8
9
10
11
Relative
electronic
energy in
solution (kcal)
Fraction in
acetone
(%)
Normalized
weight factor
(acetone)
Normalized
weight factor
(glycerol)
1.0
6.6
11.0
9.8
6.3
2.0
1.4
3.3
3.9
2.2
2.6
50.92
0.00
0.00
0.00
0.01
10.04
28.15
1.12
0.36
6.18
3.22
43.82
1.95
0.05
0.08
0.06
2.71
28.51
3.84
1.34
2.32
15.26
30.54
1.31
0.10
0.10
0.13
2.30
31.07
7.99
1.18
3.27
21.95
4. Conclusions
We have explored the LLE of the ternary system glycerol-acetonebiodiesel and its corresponding use. This system has not been previ­
ously reported in the literature to the best of our knowledge. In this way,
the purification process of raw glycerol obtained in the present work
assures economic benefits. Washing with acetone constitutes a cheaper,
less dangerous technological innovation over other wash systems for the
purification of raw glycerol. In this step, the total biodiesel residues are
removed, a component that constitutes a severe problem for the use of
ion-exchange resins or fractional distillation. Also, the reliability of
1H–NMR as an analytical technique for these types of phase equilib­
rium studies was confirmed with this study. The experimental LLE re­
ported was useful for validating the COSMO-RS implicit solvation model
predictive methodology and confirming the acetone’s selection as the
3.4.2. Limitations of COSMO-RS model for predicting the LLE data
As important as exploiting the advantages of the COSMO-RS model
for predicting the LLE data of glycerol purification systems is to be aware
of its limitations. This study indicates that COSMO-RS cannot correctly
predict the insolubility between glycerol and acetone. The experimental
section presented in this work found that the glycerol-acetone-ester
mixture is a miscible partially liquids two system. This fact is different
from the COSMO-RS model predictions because it suggests a glycerolacetone total solubility. Furthermore, other systems from the literature
were analyzed [54–56], which contain glycerol and acetone inside a
ternary system, and the COSMO-RS model fails to predict the LLE data.
Therefore, after analyzing the predicted results, the LLE data should also
be verified experimentally. Finally, it should be noticed that COSMO-RS
model predictions are in good qualitative agreement with the experi­
mental data, especially in the case of the glycerol_c7 conformer. The
unique feature of this conformer is its lower polarity and the formation
of an intramolecular hydrogen bond. However, polarization is insuffi­
cient to generate insolubility with the acetone molecule (Fig. 15). The
Table 7
Solubility of the ester in different solvents.
Solvents
Solubility (g/mL)a
Hexane
Chloroform
Acetone
Toluene
Diethyl ether
n-butanol
Aniline
Cyclohexanol
Water
409.06
52,379.88
1927.18
1176.15
3493.84
857.07
636.93
824.61
0.00006
All solubilities were calculated at 299.15 K using COSMO­
therm software database information for solvents and our
data for ester.
Fig. 13. Hydrogen bonds formed in methyl ricinoleate. Conformer a) with, conformer b) without.
Fig. 14. Theoretical LLE a) treatment by conformers b) best approximation.
11
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Chemical Engineering Journal Advances 10 (2022) 100257
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COSMO-RS model might predict, at least qualitatively, the experimental
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Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
Acknowledgments
The authors thankfully acknowledge computer resources, technical
advice and support provided by Laboratorio Nacional de Supercómputo
del Sureste de México (LNS), a member of the CONACYT network of
national laboratories, project201701056C, 202004056C, to the Vice­
rrectoría de Investigación y Estudios de Posgrado for the visitor schol­
arship of HVL and resources of PAPIIT-UNAM (grant PAPIIT-IT200220).
Projects: 100049155-VIEP2018–2020, 38945739-VIEP2018–2020, to
Dr. Samuel Hernández Anzaldo and Dra. Yasmi Reyes Ortega for PhD
studies scholarship of José Mendieta López 2018–2021.
Supplementary materials
Supplementary material associated with this article can be found, in
the online version, at doi:10.1016/j.ceja.2022.100257.
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