Fuel 308 (2022) 122030
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Fuel
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Full Length Article
Theoretical determination of distillation curves of gasoline, ethanol and
ethyl tert-butyl ether ternary blends from the experimental distillation
curve of gasoline
Luis Miguel Rodríguez-Antón *, Mathieu Legrand , Fernando Gutiérrez-Martín ,
Álvaro Serrano-Corroto
Department of Mechanical, Chemical and Industrial Design Engineering, ETSIDI, Universidad Politécnica de Madrid, Ronda de Valencia, 3, 28012 Madrid, Spain
A R T I C L E I N F O
A B S T R A C T
Keywords:
Gasoline
Ethanol
ETBE
Distillation curve prediction
Azeotropic performance
It is now environmentally desirable and legally mandatory to add renewable fuels such as ethanol or ethyl tertbutyl ether to gasoline. However, biofuels affect, among other properties, the distillation curve of gasoline, which
is subject to strict regulations. This work presents a simple mathematical model capable of accurately predicting
the influence that the addition of these oxygenates has on the distillation curve. In order to address this issue, it is
essential to find a simple mathematical correlation between the boiling temperatures of the hydrocarbons present
in gasoline and the properties (boiling temperature and volume or molar concentration of ethanol) of the cor­
responding azeotropic mixtures formed with ethanol. Power functions have been assumed to model the tem­
perature composition diagrams of the vapour-liquid equilibrium. Experimental data previously published by
these and other authors have been used to fit and validate the model. The results provided by the mathematical
model can be of great interest to understand the process of fuel evaporation in spark-ignition engines or the
adjustment of distillation cuts in refineries, in order to comply with the regulations, in terms of the distillation
curve, after adding ethanol or ethyl tert-butyl ether.
1. Introduction
It is widely accepted that the change experienced by the climate and
the global warming in recent decades is largely conditioned by anthro­
pogenic CO2 emissions and other greenhouse gases [1,2]. Proof of this is
that the average temperature is increasing year after year [3].
Between 1990 and 2018 in the European Union (EU) and in North
America greenhouse gas emissions (GHGe) corresponding to the trans­
port sector have grown by 25%, accounting respectively in 2018, for
24.0% and 29.8% of the total GHGe [4].
To reduce this problem, the EU and the USA, like other developed
areas, have established GHGe reduction plans based on the mandatory
use of biofuels in the transport sector [5–8]. In order to mainstream the
use of renewable energy in the transport sector, the EU and the USA have
set some obligations in the transport sector for the next years EU:14% by
2030 [7] and USA: 136.3⋅106 m3 by 2022 [9]. Transport sector emis­
sions are expected to increase by 1.5 times between 2010 and 2050
under business-as-usual conditions [10]. There are two basic options for
reducing GHGe: fuel-use reduction and fuel substitution [11]. According
to some mobility model results, biofuels’ share of total transportationfuel consumption by 2050 is predicted to be 25% [12,13]. In 2019,
ethanol was the most common biofuel (115⋅106 m3), accounting for 71%
of all biofuels [14]. Bioethanol can be used in spark-ignition (SI) engines
in different ways: in its pure (hydrated) state or blended (dehydrated)
with gasoline [15]. It can also be used after conversion to ethyl tert-butyl
ether (ETBE) [16]. The lower polarity and oxygen content of ETBE
compared to ethanol provides it several advantages for its distribution,
storage and use in engines: higher energy density, lower corrosiveness,
almost zero RVP excess in blends with gasoline, stoichiometric fuel/air
ratio closer to gasoline, no azeotropic performance, lower water affinity
and solubility, etc. [17].
Since the use of oxygenated fuels may affect the performance and
exhaust (as well as evaporative) emissions of SI engines [18–22], stan­
dards governing certain fuel properties must be observed (octane
number, vapour pressure -RVP-, distillation curve, vapour lock index,
oxygen content, oxygenates, driveability index, etc.) [23–26]. Proper
* Corresponding author.
E-mail addresses: lm.rodriguez@upm.es (L.M. Rodríguez-Antón), mathieu.legrand@upm.es (M. Legrand), fernando.gutierrez@upm.es (F. Gutiérrez-Martín),
alvaro.serrano.corroto@alumnos.upm.es (Á. Serrano-Corroto).
https://doi.org/10.1016/j.fuel.2021.122030
Received 27 June 2021; Received in revised form 26 August 2021; Accepted 15 September 2021
Available online 27 September 2021
0016-2361/© 2021 Elsevier Ltd. All rights reserved.
L.M. Rodríguez-Antón et al.
Fuel 308 (2022) 122030
volatility of gasoline is critical to the operation of SI engines with respect
to both performance and emissions [27]. Volatility may be characterized
by various measurements, one of the most common of which is the
distillation curve [28]. The ASTM D86 (EN: ISO3405) distillation curve
represents the temperature of the fuel vapour versus the volumetric
fraction of the fuel sample distilled [29]. European regulation (UNEEN228) controls the volume evaporated at 70, 100 and 150 ◦ C (E70/
E100/E150) [30]. American regulation (ASTM D4814) controls the
temperatures at which 10%, 50% and 90% of fuel volume are evapo­
rated (T10/T50/T90) [26].
The presence of ethanol or other oxygenates may affect the distilla­
tion curve and, as a result, performance and emissions as well
[17,29,31–34]. That is the reason why many researchers have looked
into empirical changes in these properties when ethanol (EtOH) and/or
ETBE are added to gasoline.
Amine et al. experimentally obtained ASTM-D86 distillation curves
and other volatility properties of binary and ternary blends of gasoline,
ethanol and/or methanol of up to 15% by volume (v/v). They also dis­
cussed the influence of azeotrope formation [35].
Aghahossein et al. [36] and Andersen et al. [37] experimentally
determine volatility properties of gasoline and dual and single-alcohol
blends (of up to 40 and 100% v/v of ethanol, respectively) and anal­
yse their implications on SI engines.
Nita et al. [38] and McCormick et al. [39] experimentally determine
distillation curves and other volatility properties of gasoline and singlealcohol blends (of up to 40 and 30% v/v of ethanol, respectively). They
also analyse the implications of these properties on engine performance
and pollutant emissions.
Cannela et al. provide detailed experimental data on the chemical
and physical properties of a matrix of gasoline test fuels known as the
Fuels for Advanced Combustion Engines (FACE) Gasolines. In addition,
results are reported for blends with ethanol at concentrations of 10%,
15% and 30% v/v with four of these FACE gasolines [40].
This is a small sample of the extensive literature that provides results
of experimental measurements on distillation curves and other blends
properties of fossil gasoline with ethanol and/or ETBE. However, the
prediction of these same properties before the blending process of fossil
gasoline with biofuels is crucial to be able to adjust the composition of
the base gasoline at the refinery in order to avoid non-compliance with
current legislation and tune it to the requirements of SI engines. In this
area, the literature is much less abundant than in the case of experi­
mental measurements.
Mitra et al. [41] and Abdullah et al. [42] develop mathematical
models to predict the influence of ethanol concentration (of up to 25%
and 10% v/v respectively) on distillation behaviour of gasoline-ethanol
fuel blends. They calculate some parameters derived from distillation
curves (maximum temperature drop, area of azeotrope mix, etc.)
correlating them with the ethanol content and different volatility pa­
rameters (RVP, driveability index, vapour lock index, T50 and E70).
Some of the results presented are consistent with those of the present
study.
Adlene et al. [43], Oduola et al. [44] and Landera et al. [45] develop
different models for the prediction of the RVP and other fuel properties
of fossil gasolines [43] and their blends with ethanol [44] or other al­
cohols [45].
Hosseinifar et al. proposed a model that provides a predictive
approach for the estimate of the distillation curve for crude oils and
petroleum fluids using only their physical bulk properties but do not
consider the presence of oxygenates. They obtain percentage deviations
in the averaged distillation temperatures for each sample between
0.75% and 4.11%. [46].
Lanzer et al. developed a thermodynamic model using the Pen­
g–Robinson equation of state with the Fisher–Gmehling mixing rule with
the aim of calculating the distillation curve and other properties of the
Brazilian gasoline (25% EtOH) and, thus, have a new tool for gasoline
formulation and quality control [47].
Burke et al. [48] and Abdollahipoor et al. [49] measured and pre­
dicted, using the UNIFAC theory, the vapour liquid equilibrium of
gasoline-ethanol fuels with insight on the influence of azeotrope in­
teractions on aromatic species enrichment and particulate matter for­
mation in SI engines [48].
Gaspar et al. describe the measurement and prediction of volatility
characteristics, especially Reid vapour pressure, of gasoline blended
with oxygenates such as those that could be derived from biomass. They
point out that oxygenate-gasoline blends typically exhibit non-ideal
behaviour requiring updated measurement and prediction tools to
ensure the resulting fuel meets all safety and performance specifications
[34].
It is well known that the great influence that the addition of bio
oxygenates, especially alcohols, to gasoline has on the volatility of the
blend is due to the formation of azeotropes. However, in spite of the
large number of papers published concerning the experimental deter­
mination and mathematical modelling of the distillation curve, RVP, etc.
of blends of bio oxygenates with gasoline, a model that describes the
distillation process in a simple and accurate way is not easy to find. That
is why the main objective of this work is to obtain a simple mathematical
model to understand the formation of azeotropes, the distillation process
and to accurately obtain the distillation curves of binary or ternary
mixtures of fossil gasoline with ethanol and/or ETBE. Knowledge and
understanding of the evaporation process of blends is essential to be able
to adjust the distillation cuts in refineries in order to comply with the
volatility limits (E70, T10, RVP, etc.) set by regulations, once biofuels
have been added to fossil gasoline. In addition, such a model is also of
great relevance to better understand the evaporation process inside SI
engines [50] as well as the formation of pollutants and engine
performance.
The experimental determination, as well as the modelling of fossil
gasoline from its composition or bulk properties, of ASTM D86 (EN:
ISO3405) distillation curves is outside the scope of this work. However,
modelling the distillation curve of base gasoline can be an important
complement to obtain the distillation curve of gasoline/ETBE/EtOH
blends without the need for experimentation.
This work details the process followed to predict the distillation
curves of binary and ternary mixtures of gasoline, ethanol and ETBE.
Once the model has been developed, the results obtained are validated
with experimental data by the authors and others found in the literature.
Base gasolines whose distillation curves differed greatly have been used,
subjecting the model to more severe validation. Finally, the results ob­
tained are analysed and evaluated and final conclusions are presented,
emphasizing the simplicity of the model and the high level of accuracy
obtained in a wide range of ethanol and/or ETBE concentrations.
2. Materials and methods
2.1. Materials
The experimental data used for model fitting and validation were
obtained and published by this and other research teams. The wide
variety of base gasolines and oxygenate concentrations (ethanol and/or
ETBE) used will allow for greater applicability of the presented model.
Rodríguez-Antón et al. published results concerning the distillation
curves of blends of ETBE (of up to 30% v/v) and/or ethanol (of up to
100% v/v) with gasoline. The gasoline used as base fuel to prepare the
tested blends (RVP = 60.5 kPa) was a 95-octane gasoline bought at a
REPSOL fuel station (EN 228: volatility class A), the ethanol (EN15376)
was provided by the ACCIONA group and it had a purity grade of 99.9%.
The ETBE (99%) is used by REPSOL for blending in refineries. The tests
were performed in an official laboratory accredited by the UNE-EN ISO/
IEC 17025 standard and following the UNE-EN ISO 3405 standard. This
work resulted in 11 binary gasoline/EtOH blends (2%, 4%, 6%, 8%,
10%, 15%, 15%, 20%, 30%, 45%, 60% and 85% v/v), 9 binary ETBE/
gasoline blends (5%, 10%, 15%, 20%, 25%, 30%, 45%, 60% and 85% v/
2
L.M. Rodríguez-Antón et al.
Fuel 308 (2022) 122030
v) and 51 ternary gasoline/EtOH/ETBE blends ([EtOH]vol, volumetric
content of ethanol, of up to 85% v/v and [ETBE]vol of up to 30%). The
uncertainty of the equipment and the method was ± 0.4% (v/v) for E70,
±0.2% (v/v) for E100, ±0.1% (v/v) for E150, ±1.2 ◦ C for Final Distil­
lation Point (FDP) and ± 0.1% (v/v) for distillation residue [31,32].
Aghahossein et al. present experimental results of distillation curves
for blends of gasoline with ethanol at concentrations of up to 40% v/v.
The base gasoline used was an unleaded test gasoline (UTG-96) from
Phillips 66 (RVP = 52 kPa) and ethanol (200 proof) were obtained from
Fisher Scientific. Error ranges for each parameter (T10, T50 and T90)
are mentioned in the paper and correspond to ± one standard deviation
of duplicate measurements for distillation temperatures. The average
standard error for all data points range between 0.56 and 1.68 ◦ C [36].
Andersen et al. report experimental data of distillation curves for
blends of gasoline with ethanol at concentrations of up to 100% v/v. The
base gasoline used was Haltermann EEE gasoline (Channelview, TX)
with RVP = 60–63 kPa (Standard gasoline used to certify vehicles for
compliance with emissions regulations) and the ethanol (99.5%, 200
proof and water <0.005%) was obtained from Sigma-Aldrich. Error
ranges for each parameter (E5, E10, … E85) and blend are mentioned in
the paper’s supporting information and correspond to ±one standard
deviation of duplicate or triplicate measurements for distillation tem­
peratures. These errors range between 0.1 and 3.0 ◦ C depending on the
parameter [37].
McCormick et al. provide experimental data of distillation curves for
blends of gasoline with ethanol at concentrations of up to 30% v/v [39].
The base gasoline used (RVP = 36.4 kPa) is a reformulated blendstock
for oxygenate blending (RBOB). It is intended for blending with 10%
ethanol to make a Class AA gasoline with T10 < 70 ◦ C, 77 ◦ C < T50 <
121 ◦ C and T90 < 190 ◦ C. Ethanol specifications are not mentioned in
the paper.
Cannela et al. show experimental data on distillation curves for
blends of four types of gasoline (A,B,C,H) with ethanol at concentrations
of up to 30% v/v. The base gasoline has RON 85 (A, C, H) or RON 95 (B);
octane sensitivity ≤2 (A,B,C) or ≈10 (H), 5% (A, B, C) o 35% (H) of
aromatics content, and 5% (A,B) or 28% (C, H) of n-paraffins content.
The RVP range from 51 kPa (B, C) to 55 kPa (A). Ethanol specifications
are not mentioned in the report. This study is of special interest because
it uses some gasolines whose distillation curves are very different from
those of the other authors, allowing the model to be tested [40].
To solve the equations that model the distillation process the MAT­
LAB® R2020b licenced software (MathWorks Inc., USA) was used.
mixtures are far from ideal mixtures due to the formation of positive
azeotropes. This is the key for further study. Gasoline is composed of
hundreds of hydrocarbons (HC), each of which has a boiling tempera­
ture (THC). THC is therefore not a constant value but depends on the HC
that evaporates. Similarly, each of these hydrocarbons will (or will not)
form an azeotrope (Az) with ethanol, whose boiling temperature will be
TAz. For the same reason, TAz will not have a constant value but will
depend on the hydrocarbon that is part of the azeotrope, e.g. benzene,
with boiling temperature THC = 80.10 ◦ C, forms an azeotrope with
ethanol boiling at TAz = 67.90 ◦ C. In order to quantify how this azeo­
trope formation can affect distillation, and using published data
[51–54], a correlation is established between the temperature at which
any hydrocarbon boils (THC) and the temperature at which its corre­
sponding azeotrope with ethanol boils (TAz). In the same way, another
correlation is found between THC and the molar (mol) or volumetric
(vol) concentration of ethanol in the azeotrope ([EtOH]Az-mol or [EtO­
H]Az-vol). In all cases, using equations (1) to (3), a good regression co­
efficient R2 was found (Fig. 1). It shows that TAz and [EtOH]Az-vol depend
quadratically on THC with a correlation coefficient of 99.40% and
97.02% respectively while [EtOH]Az-mol depends linearly on THC with a
correlation coefficient of 98.12%. It should be highlighted that ETBE fits
the correlation as another hydrocarbon (Fig. 1) and that no azeotropes
are formed when hydrocarbons have boiling temperatures above 125.6
◦
C.
2
TAz = − 4.704 + 1.278⋅THC − 5.046⋅10− 3 ⋅THC
(1)
[EtOH]Az−
vol
2
= − 6.298⋅10− 2 + 1.649⋅10− 3 ⋅THC + 3.581⋅10− 5 ⋅THC
(2)
[EtOH]Az−
mol
= − 0.2583 + 9.042⋅10− 3 ⋅THC
(3)
2.2.2. Modelling of gasoline-ETBE mixtures
Contrary to ethanol, ETBE does not form azeotropes with hydro­
carbons. The T-x (temperature-composition) phase diagram of the
vapour-liquid equilibrium (VLE) corresponding to the blend of each of
the hydrocarbons in gasoline and ETBE consists of two lines. The lower
one (liquid line) represents the boiling temperature (T) of the liquid (L)
mixture as a function of the ETBE molar content in gasoline ([ETBE]Lmol). The upper one (vapour line) will indicate the molar concentration
of ETBE in the vapour (V) formed ([ETBE]V-mol) at that temperature (T).
These lines of each HC-ETBE blend are unknown and, therefore, they
must be assumed. In order to simplify the mathematical model,
[ETBE]vol is used instead of [ETBE]mol as an alternative for the compo­
sition (x). Nevertheless, it will be seen later that the model results are
accurate. The parametric functions chosen must meet certain conditions:
2.2. Methods
This section describes in detail the procedure followed for the
development and tuning of the mathematical model for predicting the
distillation curve of a specific blend. For this purpose, the distillation
curve of the base gasoline and the volumetric concentrations of ethanol
and/or ETBE must be known in advance. The process followed in an
abbreviated form is as follows.
• if [ETBE]L-vol = 1 then T = TETBE and [ETBE]V-vol = 1 (TETBE is
known)
• if [ETBE]L-vol = 0, then T = THC and [ETBE]V-vol = 0 (THC is known in
each distillation step)
• The vapour will always be richer in the more volatile component of
the mixture.
• Using information published in the literature, the azeotropic per­
formance of hydrocarbon (and ETBE) blends with ethanol is
modelled by first and second order polynomials.
• The phase diagrams of the vapour-liquid equilibrium for the mixture
of each hydrocarbon with EtOH or ETBE have been modelled by
means of power functions of non-dimensional variables.
• Finally, a distillation process has been modelled whose equations
and process are fully described in the article following a sequential
order.
As a starting point, the experimental distillation data of the base
gasoline must be available (T0, T5, T10 … T95). From these data, a
i
polynomial is fitted to allow the curve THC
= f(EiHC− vol ) to be discretized
into much smaller distillation step, where EiHC− vol is the HC evaporated
i
volume at a temperature THC
.
The process starts by calculating the boiling temperature (T i ) using
as inputs [ETBE]iL− vol and the T-x phase diagram (HC-ETBE) corre­
sponding to each distillation step “i” (ΔE = 0.01%v/v). For this purpose,
an estimate of the liquid line of the corresponding T-x phase diagram is
used (Eq. (4)), since the actual line is unknown.
2.2.1. Modelling of azeotropic performance of hydrocarbon-ethanol and
ETBE-ethanol mixtures
First of all, it should be noted that hydrocarbon-ethanol (HC-EtOH)
T i = TETBE −
3
(
)
i
(1 − [ETBE]iL−
TETBE − THC
k1
vol )
(4)
L.M. Rodríguez-Antón et al.
Fuel 308 (2022) 122030
Fig. 1. Correlation found in the HC-EtOH azeotropes between TAz (right) or [EtOH]Az-vol (left) and THC (Data from [51–54]).
Where k1 is a constant to be optimised (Table 1).
The volume evaporated in a distillation step (Eivol ) at a temperature
(T i ) will be the sum of the volume of HC evaporated (EiHC− vol ) and the
volume of ETBE evaporated (EiETBE− vol ).
EiHC− vol (Eq. (5)) is constant in all distillation step:
(
i=1 )
i
(5)
EHC−
vol = ΔE⋅ 1 − [ETBE]L− vol
Once EiHC− vol (Eq. (5)) and EiETBE− vol (Eq. (8)) are known, their sum will
(
)
be the total volume evaporated Eivol in that distillation step. With these
data it is possible to calculate the volume evaporated until that distil­
(
( ))
(
( ))
lation step of HC EHC− vol T i , ETBE EETBE− vol T i or total: HC + ETBE
(
( i) )
i
Evol T , and also [ETBE]L− vol for that distillation step (Eqs. (9) to (11)).
EHC−
Where ΔE = 0.01% and [ETBE]i=1
L− vol is the initial [ETBE]L-vol in the
gasoline before distillation.
To calculate the EiETBE− vol it is first necessary to calculate the volu­
(
vol
i
) ∑
j
Ti =
EHC−
metric concentration of ETBE in the vapour
For this pur­
pose, an estimate of the vapour line of the corresponding T-x phase
diagram is used (Eqs. (6)–(7)), since the actual line is unknown. This
vapour line (Fig. 2) will allow
[ETBE]iL−
value:
(
(
to be obtained from
i
THC
> TETBE
)
[ETBE]iV−
)
[ETBE]iV−
vol
vol
(
= [ETBE]iL−
=1−
(
)k2
(6)
vol
1 − [ETBE]iL−
)k3
vol
(7)
Where k2 and k3 are constants to be optimised (Table 1).
Fig. 2 shows two examples of optimised VLE T-x phase diagrams for
HC-ETBE blends: the left one, using Eqs. (4) and (6), for THC(=34 ◦ C) <
TETBE and the right one, using Eqs. (4) and (7), for THC(=108 ◦ C) >
TETBE.
The volume evaporated of each component of the mixture will be
proportional to its concentration in the vapour:
i
EETBE−
vol
[ETBE]i−V− 1vol
=
i
EHC−
vol
[HC]i−V− 1vol
=
i
EHC−
vol
vol
=
[ETBE]i−V− 1vol
1−
[ETBE]i−V− 1vol
∙EiHC−
vol
i
i
Evol
= EHC−
vol
[ETBE]iL−
=
k2 = 1.242
k5 = 0.3053
k8 = 6
vol
i
+ EETBE−
vol
(9)
j=1
vol
( ) ∑i
& Evol T i =
Ej
j=1 vol
[ETBE]i=1
L− vol − EETBE−
( )
1 − Evol T i
(
vol
Ti
(10)
)
(11)
normalized temperature and evaporated volume modelled.
Additionally, other error variables have been used to calculate the
error in the estimation of the distillation temperature or the evaporated
volume. For this purpose the root mean square temperature error
(RMST) and the root mean square evaporated error (RMSE) are defined.
The RMST has units of Celsius degrees and is defined (Eq. (13)) as the
mean value of the quadratic differences of temperatures for the n
experimental values (T0, T5, … T95) and those provided by Eq. (10) for
the same Evol . The RMSE has units of percentage of volume evaporated
and is defined (Eq. (13)) as the mean value of the quadratic differences
(8)
Table 1
Optimized fitting parameters for liquid and vapour curves of T-x phase
diagrams.
k1 = 0.6960
k4 = 7
k7 = 9.906
i
) ∑
j
Ti =
EETBE−
Where n is the number of experimental data, Ti* and Ei are the normal­
ized experimental temperature and evaporated volume, m is the number
of steps of the modelled distillation curve, and Tj* and Ej are the
1 − [ETBE]i−V− 1vol
Therefore:
i
EETBE−
(
vol
The flow diagram followed to obtain the distillation curve of the
binary mixture gasoline/ETBE is detailed in Fig. 3.
Once the calculations have been performed for all distillation steps,
the simulated distillation curve (Eq. (10)) is obtained. However, it is
necessary to fit the constants k1, k2 and k3 first by minimizing the
discrepancy between the model and the experimental data. For this
purpose, the root mean square distance error (RMSD) is defined. The
RMSD (Eq. (12)) is performed on 0–1 normalized axes (Evaporated
volume: 0 → 0% and 1 → 100%; Distillation temperature: 0 → T0 and
0.95 → T95) so that its units do not correspond to any physical unit,
simply percentages. It aims to minimize the quadratic distance (dmin− i )
between the n experimental data and the modelled curve.
√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
∑n 2
((
)
)2 (
)2
i=1 dmin− i
T *i − T *j + Ei − Ej
(12)
RMSD=
&dmin− i =minj=1tom
n
i
vol . Different expressions are assumed depending on the THC
i
THC
< TETBE
& EETBE−
j=1
([ETBE]iV− vol ).
[ETBE]iV− vol
vol
k3 = 3.980
k6 = 2.427
k9 = 0.3262
4
L.M. Rodríguez-Antón et al.
Fuel 308 (2022) 122030
Fig. 2. Examples of T-x phase diagram of VLE for some HC-ETBE blends (Left: THC = 34 ◦ C; Right: THC = 108 ◦ C) estimated by parametric functions (Left: Eqs. (4) and
(6); Right: Eqs. (4) and (7)).
Fig. 3. Flow chart for the calculation of the distillation curve for gasoline/ETBE blends.
despite the fact that some gasoline hydrocarbons form azeotropes with
ethanol and the T-x phase diagrams differ. As in the case of HC-ETBE
blend, vapour and liquid lines are unknown and therefore they must
be assumed. In order to simplify the mathematical model, [EtOH]vol is
used instead of [EtOH]mol as an alternative for the composition (x).
Nevertheless, it will be seen later that the model results are accurate. The
parametric functions chosen must meet certain conditions:
of percentages evaporated for the n experimental values (T0, T5, … T95)
and those provided by Eq. (10) for the same Ti .
√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
∑n
∑n
2
2
i=1 (Ti − Ti− model )
i=1 (Ei − Ei− model )
RMST =
& RMSE =
(13)
n
n
2.2.3. Modelling of gasoline-ethanol mixtures
Up to this point, the process for obtaining the distillation curves of
gasoline-ETBE mixtures has been described. The methodology for pre­
dicting the gasoline-ethanol distillation curves is completely analogous,
• if [EtOH]L-vol = 1 then T = TEtOH and [EtOH]V-vol = 1 (TEtOH is
known)
5
L.M. Rodríguez-Antón et al.
Fuel 308 (2022) 122030
• if [EtOH]L-vol = 0, then T = THC and [EtOH]V-vol = 0 (THC is known in
each distillation step)
• if [EtOH]L-vol = [EtOH]Az-vol, then T = TAz and [EtOH]V-vol = [EtO­
H]Az-vol (TAz is known in each distillation step)
• The vapour will always be richer in the more volatile component of
the mixture.
ETBE (Eqs. (18) and (19)):
(
)k
) [EtOH]iL− vol − 1 8
( i
− TEtOH
T i = TEtOH + THC
0− 1
[EtOH]iV−
( i
i
i
T i = TAz
+ THC
− TAz
=
< [EtOH]iAL−
(
) [EtOH]iL−
1−
⎛
[EtOH]iV− vol
vol
⎛
[EtOH]iAz− vol ⎝1 −
⎝1 −
vol
then:
vol
)k4
(14)
)k5 ⎞ ⎞
⎠⎠
(15)
− [EtOH]iAz−
vol
[EtOH]iAz− vol
(
[EtOH]iL− vol
[EtOH]iAz− vol
If
< 125.6 C &
◦
i
T i = TAz
+ (TEtOH
[EtOH]iV− vol
=
[EtOH]iAz− vol
<
[EtOH]iL− vol
(
[EtOH]iL− vol − [EtOH]iAz−
i
− TAz
)
1 − [EtOH]iAz− vol
[EtOH]iAz− vol
(
+ 1−
[EtOH]iAz− vol
then:
)k6
(16)
vol
(
) [EtOH]iL−
vol
− [EtOH]iAz−
1 − [EtOH]iAz−
)k9
vol
(19)
2.2.4. Modelling of gasoline-ETBE-ethanol mixtures
The modelling of gasoline-EtOH-ETBE ternary blends is treated
identically to the modelling of gasoline-EtOH blends except that instead
of using the base gasoline as starting information, the result of the
gasoline-ETBE blend will be used. This approach can be taken since the
azeotrope formed by ETBE and ethanol has a boiling temperature and
molar/volumetric composition that are very close to those offered by the
where k4 and k5 are parameters to be optimised (Table 1).
i
THC
(
= [EtOH]iL−
Where k8 and k9 are parameters to be optimised (Table 1).
Fig. 4 shows two examples of optimised VLE T-x phase diagrams for
HC-EtOH blends. The one on the left, obtained from Es. (14)–(17) for
THC(=82.8 ◦ C) < 125.6 ◦ C, shows the formation of an azeotrope with
TAz = 66.5 ◦ C and a with [EtOH]L-vol = 31.5%. The one on the right, built
from Eqs. (18) and (19) for THC(=148.0 ◦ C) > 125.6 ◦ C, shows no
azeotrope formation.
As in the case of ETBE, optimisation of parameters k4, k6 and k8 that
characterize the liquid curves, and parameters k5, k7 and k9 that char­
acterize the vapour curves, aims to minimize the RMSD, ensuring that
the distillation curves obtained by simulation are as close as possible to
the experimental data.
The rest of the parameters (EiHC− vol ; EHC− vol ; EiEtOH− vol ; EEtOH− vol ;
[EtOH]L− vol and Evol ), equivalent to those of the distillation process of the
gasoline-ETBE blends, will be obtained by equations completely analo­
gous to those already shown (Eqs. (8)–(11)).
If THC < 125.6 ◦ C (Fig. 4 left) positive azeotropes are formed [51–54]
and it will be necessary to define the T-x phase diagram with different
equations to the left ([EtOH]L-vol < [EtOH]Az-vol) and to the right
([EtOH]Az-vol < [EtOH]L-vol) of the azeotrope (Eqs. (14)–(15) and (16)–
(17) respectively). The vapour and liquid lines will be parametric power
functions similar to those seen in the case of ETBE but which are forced
to pass through the azeotrope since the concentration of the vapour and
the liquid coincide, that is, it behaves as a pure substance.
i
If THC
< 125.6 ◦ C & [EtOH]iL−
vol
(18)
)k7
(17)
vol
vol
corresponding correlations found for HC-EtOH blends (Eqs. (1)–(3)). In
other words, ETBE performs almost identically to gasoline HCs in terms
of azeotrope formation with ethanol (Fig. 1).
Fig. 3 shows the flow chart for calculating the distillation curve for
Where k6 and k7 are parameters to be optimised (Table 1).
If THC > 125.6 ◦ C no azeotropes are formed and the T-x phase dia­
gram (Fig. 4 right) will be analogous to those already seen in the case of
Fig. 4. Examples of T-x phase diagram of VLE for some HC-EtOH blends (Left: THC = 83 ◦ C < 125.6 ◦ C; Right: THC = 148 ◦ C > 125.6 ◦ C) estimated by parametric
functions (Left: Eqs. (14)–(17); Right: Eqs. (18) and (19)).
6
L.M. Rodríguez-Antón et al.
Fuel 308 (2022) 122030
gasoline/ETBE blends. For the case of gasoline/EtOH blends, the flow
diagram is the same but substituting the input data and equations for
those for ethanol (e.g. Eqs. (15), (17) and (19) instead of Eqs. (6) and
(7)). In the case of ternary blends, the same would be done as for binary
gasoline/EtOH blends, except that the starting point is not the base
gasoline, but the distillation curve resulting from the previously calcu­
lated binary gasoline/ETBE blend, which does not require polynomial
fitting as it is already discretised.
Table 3
RMSE (%v/v) of the modelled distillation curves for gasoline/EtOH/ETBE
blends (exp. data from [32]).
ETBE (% v/v)
3. Results and discussion
The model’s parameters k1 to k9 have been fitted by using detailed
experimental data and by minimizing RMSD. The optimal k1 to k3 values
have been fitted by using binary gasoline/ETBE blends containing up to
100% ETBE, while the optimal k4 to k9 values have been fitted by using
gasoline/ETBE/EtOH blends containing up to 30% ETBE and up to
100% ethanol. The k-values are the same for all mixtures, which adds
robustness to the method. It can therefore be expected that the model
will perform reliably at least within these limits. The results are reported
in Table 1. In order to validate the model, the results are compared with
experimental data obtained for different binary and ternary blends of
gasoline, ETBE and ethanol. These blends use different types of base
gasoline, some of whose distillation curves differ greatly from the ones
used to fit the model.
Once the fitting parameters for the T-x phase diagrams are known,
we proceed with the simulations of all the binary and ternary gasoline/
EtOH/ETBE blends mentioned in the Materials section. The large num­
ber of samples analysed do not allow all the distillation curves to be
reported in this work. Therefore, tables with the errors obtained for all
the cases will be presented and the graphs of only some of them will be
shown to visualize the numerical errors.
The first three error tables show the RMST (Table 2), RMSE (Table 3)
and RMSD (Table 4) values for binary and ternary gasoline/EtOH/ETBE
blends. The distillation curves used for these validations were previously
published by authors of this work [32].
In the following paragraphs and figures, gasoline/EtOH/ETBE blends
will be referred to by indicating the volumetric percentage of ethanol
after the letter “E” and the volumetric percentage of ETBE after the letter
“T”. For example, E20T30 represents a blend of gasoline with 20% v/v
ethanol and 30% v/v ETBE.
The highest values for the RMST (Table 2) are observed for the
average ethanol concentrations (20% to 45% v/v). For these blends, the
RMST has values of between 2.4 and 6.6 ◦ C, much higher than those of
the rest of the blends, with an average of 2.1 ◦ C and rarely exceeding 3
◦
C. This is due to the fact that the distillation curves undergo a sharp
jump and small errors in the abscise position of the jump imply large
values for the RMST. Despite these high RMST values (E30T30,
E45T15), it can be seen (Fig. 5) that the experimental values are very
0
5
10
15
20
25
30
Average
0,4
1,5
1,8
1,8
2,3
2,5
2,6
5,0
5,1
2,4
1,7
2,3
2,5
1,5
1,3
1,7
2,0
1,6
2,0
3,2
5,1
5,4
4,5
1,4
1,5
2,6
0,9
2,1
2,4
2,0
1,9
1,9
2,8
3,4
3,7
5,4
1,6
1,2
2,4
1,3
1,6
1,7
1,7
1,9
1,8
2,8
3,3
4,6
6,6
1,5
1,9
2,5
1,3
1,9
1,8
1,8
2,0
2,1
2,6
3,4
4,0
5,8
1,7
–
2,6
1,9
2,0
2,1
2,3
3,8
3,6
2,9
3,3
3,7
5,3
2,1
–
3,0
2,4
2,4
2,2
2,4
2,3
3,1
4,0
4,4
6,1
4,2
2,5
–
3,3
1,4
1,8
1,9
2,0
2,3
2,4
3,0
4,0
4,7
4,9
1,8
1,7
2,7
5
10
15
20
25
30
Average
0
2
4
6
8
10
15
20
30
45
60
85
Average
0,3
1,0
1,5
1,7
2,2
2,5
2,2
3,5
3,7
3,7
8,5
26,4
4,8
1,3
1,1
1,4
1,7
1,6
1,9
3,2
4,4
4,2
4,2
8,5
30,4
5,3
0,7
2,0
2,3
1,9
1,9
2,2
3,8
4,7
5,3
5,0
11,0
34,1
6,2
1,1
1,5
1,6
1,8
2,0
1,9
4,9
6,0
6,3
5,9
14,2
37,8
7,1
1,1
1,7
1,8
1,8
2,1
2,4
5,0
7,1
7,7
6,7
14,7
–
4,7
1,5
2,0
2,0
2,4
3,7
3,1
6,3
6,9
8,5
8,0
17,1
–
5,6
2,0
2,3
2,1
2,5
2,8
4,4
7,5
9,4
9,8
8,7
17,5
–
6,3
1,1
1,7
1,8
2,0
2,4
2,6
4,7
6,0
6,5
6,0
13,1
32,2
5,7
ETBE (% v/v)
EtOH (%v/v)
0
5
10
15
20
25
30
Average
0
2
4
6
8
10
15
20
30
45
60
85
Average
0,2
0,7
1,0
1,0
1,3
1,4
1,1
1,8
1,4
0,9
1,0
1,8
1,1
0,8
0,7
0,9
1,1
0,9
1,1
1,5
1,9
1,5
1,2
0,9
1,1
1,1
0,5
1,3
1,4
1,1
1,0
1,1
1,6
1,7
1,7
1,2
1,0
0,9
1,2
0,7
0,9
1,0
1,1
1,1
1,0
1,8
1,8
1,9
1,4
1,1
1,2
1,2
0,7
1,1
1,0
1,0
1,2
1,2
1,6
2,0
2,1
1,6
1,3
–
1,4
1,1
1,1
1,2
1,4
2,1
1,9
1,8
1,8
2,2
1,9
1,5
–
1,6
1,4
1,4
1,3
1,4
1,4
1,8
2,2
2,3
2,4
1,9
1,8
–
1,7
0,8
1,0
1,1
1,2
1,3
1,4
1,7
1,9
1,9
1,4
1,2
1,3
1,3
close to the modelled curves, as evidenced by the low RMSD values for
the same ethanol percentages (Table 4). In this case, the RMSD values
are similar to those for the rest of the blends.
In the case of RMSE, the error increases according to the increasing
ethanol and ETBE content (Table 3) as this leads to a flattening of the
distillation curve. This flattening leads to higher errors in the percentage
of volume evaporated for a given distillation temperature. However, in
view of the graphs (Fig. 5), higher RMSE values (E85T15, E60T15) do
not imply higher model error, which is consistent with the RMSD values
remaining within normality.
These are the reasons why the model’s parameters are fitted by
minimizing RMSD rather than RMST or RMSE. To better understand the
numerical errors shown in the tables above, some graphs relating to
blends with the highest, lowest and average errors are shown. In Fig. 5,
the graphs corresponding to the E30T30, E20T20 and E15T30 blends
show the case of high RMSD values while the graphs corresponding to
the E85T15, E60T15, E10T15 and E45T0 blends illustrate the case of
low RMSD values (Table 4). In all cases the high degree of approxima­
tion between the experimental data and the modelled curves can be
appreciated.
Once the distillation curves have been obtained for all the samples
shown in the tables above, it is possible to determine the values of some
of the parameters controlled by the European (UNE-EN228) and
American (ASTM D4814) standards. To do so, it is sufficient to check the
values of the percentage of evaporates at 70, 100 and 150 ◦ C (E70/
E100/E150) or the distillation temperature at 10, 50 and 90% of
ETBE (% v/v)
0
2
4
6
8
10
15
20
30
45
60
85
Average
0
Table 4
RMSD (%) of the modelled distillation curves for gasoline/EtOH/ETBE blends
(experimental data from [32]).
Table 2
RMST (oC) of the modelled distillation curves for gasoline/EtOH/ETBE blends
(experimental data from [32]).
EtOH (% v/v)
EtOH (% v/
v)
7
L.M. Rodríguez-Antón et al.
Fuel 308 (2022) 122030
Fig. 5. Distillation curves of base gasoline [32], fitted by a polynomial (▬), and of gasoline/EtOH/ETBE blends (see at the top of each graph) from experimental [32]
(*), and from the mathematical model (⋅⋅⋅⋅⋅⋅).
8
L.M. Rodríguez-Antón et al.
Fuel 308 (2022) 122030
Table 5
Differences between experimental and modelled values of E70, E100, E150 and
T10, T50 and T90.
Mean
Std.
deviation
E70 (%
v/v)
E100 (%
v/v)
E150 (%
v/v)
T10
(oC)
T50
(oC)
T90
(oC)
− 1,3
4,0
0,4
2,1
− 0,8
2,5
3,0
1,7
0,3
1,5
0,6
3,8
Table 7
RMST, RMSE and RMSD of the modelled distillation curves for gasoline/ETBE
blends.
distilled volume (T10/T50/T90). The differences obtained between the
experimental data and those obtained from the distillation curves show
distributions with average values and standard deviations reported in
Table 5. These values reveal again the accuracy and usefulness of the
model.
The standard deviation corresponding to the value of E70 is higher
than the remainder as a consequence of the proximity of the distillation
temperature of ethanol (78.3 ◦ C) and ETBE (73.0 ◦ C) to the temperature
of 70 ◦ C. In the case of T90 it is due to the verticality of the distillation
curve in that distillation percentage. Even so, it can be seen that the
mean values are in all cases really low.
The following two tables show the RMST, RMSE and RMSD values for
binary gasoline/EtOH blends (Table 6) and for binary gasoline/ETBE
blends (Table 7). The distillation curves used for these validations were
previously published by these and other authors [30,36,37,39,40].
The results shown in Tables 6 and 7 have been calculated using
gasolines other than the one used to fit the model. Some of them are
greatly different in terms of composition and distillation curve ([37,40]
FACE types A, B and H). In spite of this, the results are accurate in a way
that is practically the same, which shows the pertinence and relevance of
the model. Fig. 5 shows the high level of approximation achieved be­
tween the experimental data of the different authors and the results of
the predictive model presented in this work for gasoline/EtOH/ETBE
blends. It can also be seen that the RMSD is more suitable for assessing
the accuracy achieved, e.g. comparing the first two graphs that have a
similar degree of approximation, the RMST of the one on the left has a
value three times higher than the one on the right. However, the RMSD
value is similar in both.
With regard to the modelling of the binary blends with ETBE (Fig. 6),
as expected, no abrupt jump in the distillation curve is observed as a
consequence of the fact that ETBE does not form azeotropes with gas­
oline. The degree of approximation achieved in all cases is very high. On
average, the RMST achieved is 2.3 ◦ C, the RMSE 3.3% and the RMSD
1.4%, values more than adequate for this type of modelling.
Reference
%ETBE
RMST
RMSE
RMSD
[31]
[31]
[31]
[31]
[31]
[31]
[31]
[31]
[31]
[31]
0
5
10
15
20
25
30
45
60
85
1,2
0,6
1,0
1,2
1,7
1,9
2,8
3,4
4,1
4,3
1,0
0,4
1,1
1,0
1,6
1,6
2,5
3,3
5,4
12,5
0,7
0,3
0,6
0,7
1,0
1,1
1,7
2,1
2,4
2,6
4. Conclusions
The main contribution of this work is based on the discovery of two
simple empirical correlations for ethanol-hydrocarbons azeotrope per­
formances. One between the boiling point of the azeotrope (TAz) and the
temperature at which the corresponding gasoline hydrocarbons boil
(THC) and the other between the volumetric or molar ethanol concen­
tration of the azeotrope formed and the THC.
Ethers such as ETBE or MTBE have, in this respect, very similar
properties to gasoline hydrocarbons and fit perfectly into the abovementioned correlations.
A simple mathematical model has been developed which, using the
above correlations and optimized parametric power functions for the T-x
phase diagram of the VLE, is able to model the distillation curves of
binary and ternary gasoline/EtOH/ETBE blends with a high degree of
accuracy. Blends of ethanol and ETBE with other fossil fuels, as in the
much more interesting case of future synthetic fuels of renewable origin,
could be modelled in the same way, assuming the mixture to be ho­
mogeneous and using the appropriate coefficients k1 to k9.
It has been found that the minimization of the RMSD parameter,
instead of the RMST or RMSE, allows a better optimization of the
mathematical model, especially for mixtures with ethanol or high con­
centrations of oxygenates.
The model has been fitted and validated using previously published
distillation curves: 11 binary gasoline/EtOH blends (2–85% v/v), 9 bi­
nary ETBE/gasoline blends (5–85% v/v) and 51 ternary gasoline/EtOH/
ETBE blends (EtOH up to 85% v/v and ETBE up to 30% v/v), obtaining
mean values of RMST, RMSE and RMSD of 2.6 ◦ C, 5.7% v/v and 2.4%
respectively. Additionally, the model has been validated with distilla­
tion curves of blends with different base gasolines: 31 binary gasoline/
EtOH blends, obtaining mean values of RMST, RMSE and RMSD of 3.7
◦
C, 4.5% v/v and 1.4%, as well as with 10 binary gasoline/ETBE blends
whose mean values of RMST, RMSE and RMSD are 2.2 ◦ C, 3.0% v/v and
Table 6
RMST, RMSE and RMSD of the modelled distillation curves for gasoline/EtOH blends.
Reference
%EtOH
RMST
RMSE
RMSD
[37]
[37]
[37]
[37]
[37]
[37]
[37]
[37]
[36]
[36]
[36]
[39]
[39]
[39]
[39]
0
5
10
15
20
25
50
85
0
10
40
0
10
20
30
1,2
2,4
3,3
4,6
5,5
6,2
9,2
3,0
1,1
3,5
6,8
1,5
3,3
7,7
3,9
1,1
1,8
2,8
3,4
3,3
3,1
6,9
33,3
0,6
2,8
10,4
0,6
3,0
11,2
2,8
0,6
1,2
1,7
2,2
2,1
2,3
1,5
2,2
0,6
1,5
1,4
0,9
1,5
3,5
1,1
Reference/FACE (type)
[40] (A)
[40] (A)
[40] (A)
[40] (A)
[40] (B)
[40] (B)
[40] (B)
[40] (B)
[40] (C)
[40] (C)
[40] (C)
[40] (C)
[40] (H)
[40] (H)
[40] (H)
[40] (H)
9
%EtOH
RMST
RMSE
RMSD
0
10
15
30
0
10
15
30
0
10
15
30
0
10
15
30
0,5
4,9
4,7
5,8
0,5
3,7
4,0
1,7
1,7
3,0
2,8
5,2
1,3
3,5
3,8
3,5
0,8
4,8
5,3
13,3
1,4
3,6
5,0
11,4
1,2
2,6
2,6
5,1
0,5
2,7
2,4
1,5
0,4
2,4
2,5
1,3
0,2
1,8
2,1
1,0
0,6
1,1
1,0
0,9
0,3
1,1
1,1
0,7
L.M. Rodríguez-Antón et al.
Fuel 308 (2022) 122030
Fig. 6. Distillation curves of base gasoline [31,36,37,39,40], fitted by a polynomial (▬) and of binary blends (see at the top each graph) from experimental
[31,36,37,39,40] (*) and from the mathematical model (⋅⋅⋅⋅⋅).
10
L.M. Rodríguez-Antón et al.
Fuel 308 (2022) 122030
1.3% respectively. All these values demonstrate the accuracy of the
model.
By means of this model, the boiling temperature of the gasoline
hydrocarbons that are evaporating, the concentration of ethanol in the
vapour that is being formed, the concentration of ethanol in the
remaining liquid, etc. can all be known at each step of the distillation
process. All these variables can be very interesting to study and under­
stand the processes of mixture formation in SI engines.
Being able to model with accuracy the influence that the addition of
renewable alcohols and ethers has on the distillation curve of gasoline
(for any base gasoline composition), helps significantly in fine-tuning
the distillation cuts in the refinery in order to meet the quality stan­
dards of biogasolines. In this respect, the prediction of the values of E70,
E100, E150, T10, T50 and T90 has been performed with considerable
accuracy.
There are other methods that estimate distillation curves, e.g. the
UNIFAC method. Despite its good results, this method requires prior
knowledge of the chemical composition of the fuel as well as a number of
properties of its components. UNIFAC method needs to solve a complex
system of differential equations with a significant computational cost.
The proposed method also achieves excellent results with a small
computational cost, however, only requires prior knowledge of the
distillation curve, which could even be accurately modelled from some
bulk properties following the method proposed by Hosseinifar [46].
Similar studies with other renewable alcohols or ethers should be
performed to verify whether, as expected, the same model can be used
with accuracy.
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
CRediT authorship contribution statement
[19]
Luis Miguel Rodríguez-Antón: Conceptualization, Methodology,
Software, Validation, Formal analysis, Investigation, Resources, Data
curation, Writing – original draft, Writing – review & editing, Supervi­
sion, Project administration. Mathieu Legrand: Formal analysis, Data
curation, Writing – review & editing. Fernando Gutiérrez-Martín:
Validation, Investigation, Resources, Writing – review & editing. Álvaro
Serrano-Corroto: Software, Validation, Data curation, Visualization.
[20]
[21]
[22]
[23]
Declaration of Competing Interest
[24]
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.
[25]
Acknowledgments
The authors would like to thank James E. Anderson [37], Robert L.
McCormick [39] and Saeid A. Shirazi [36] for sharing their experimental
data in order to perform the validation of the mathematical models.
[26]
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