Abstract
Alcohol has already been widely used as an alternative fuel to blend with petroleum-based fuels.
Accurate knowledge of flash points and their reliable prediction methods is essential in hazard
identification, fire hazard reduction, process inherently safer design, and the risk management of
alcohol-based fuels. This work presents a model to predict the flash point for alcohol + petroleumbased fuel blends based on the Liaw model incorporated with the original UNIFAC model. The flash
point prediction model was modified by two steps: 1. applying a single vapor-temperature
relationship for the petroleum-based fuel; 2. obtaining the activity coefficients by UNIFAC model
using an average fuel structure for the petroleum-based fuel. The proposed model was verified
experimentally for five fuel blends of alcohol + kerosene (alcohol being n-butanol, n-hexanol, and
n-octanol) and alcohol + diesel (alcohol being n-butanol and n-hexanol). The flash point prediction
procedure for alcohol + petroleum-based fuel blends was reduced to that of a binary mixture. The
deviations between the predicted values and experimental data were mostly within 2℃ for the five
fuel blends.
Keywords: Flash point; Kerosene; Alcohol; UNIFAC model; Group structure
1
1 Introduction
Aviation fuel (kerosene and gasoline) is the main energy source in the aviation industry, and
the fuel demand is continuously growing. The kerosene demand is expected to increase annually by
2-3%. The aviation industry is responsible for around 3.6% of the greenhouse gas emission and
about 13.4% of the overall emission from transportation, and as such is under increasing global
pressure to reduce carbon emissions through increasingly strict targets [1, 2]. The combination of
increasing flight demand and fuel costs and pressure to reduce emissions has pushed the aviation
industry under considerable strain. One of the best options is to focus on alternative aviation fuels
blending with petroleum-based fuel, as the fuel blends, in most cases, have the advantage of
compatibility over other substitute fuels (e.g. ethanol) with the conventional engine and fuel system
[3, 4]. Alcohol becomes a well-known alternative fuel to blend with petroleum-based fuel since it
can be obtained from renewable sources such as grains, algae, woods, and grass, and the preparation
cost is expected to substantially reduce due to the improvement of the biological fermentation
method [5, 6]. The feasibility of the alcohol + fuel blends1 has been confirmed by investigating its
fuel properties, spray and combustion characteristics, energy release, and exhaust emissions on
engines. For example, it is shown that the addition of butanol in the Jet-A can yield positive effects
on the exhaust emission and small effects on engine performance in a gas turbine engine (Mendez
et al. [7]). Liu et al. [8] demonstrate that ethanol / n-propanol / n-butanol + kerosene (RP-3) blends
get higher efficiency and have lower emissions than aviation gasoline. It is observed that butanol
can enhance efficient combustion and reduce CO and NOx emissions of Jet A-1 in a swirl-stabilized
gas turbine-type combustor (Kumar and Karmakar [9]). Meanwhile, it is also shown that the aviation
kerosene exhibits a better spray performance by blending with alcohol (ethanol, 2-propanol, butanol,
and 1-pentanol) (Touazi et al. [10], and Li et al. [11]). Considering the general performance, npropanol and n-butanol are more suitable for blending with aviation kerosene than ethanol, as they
have higher energy content, fewer corrosive effects, lower vapor pressure, and higher miscibility
with fuel compared with ethanol [8, 9].
Although butanol blending with kerosene as an alternative fuel has shown excellent
1
alcohol + fuel blends refer to alcohol + petroleum-based fuel blends in this study
2
performance in the studies mentioned above, there was almost no report for its fire and explosion
(F&E) risk assessment. The fires in the fuel process plants normally cause severe damages due to
accompanied explosions [12]. The process with a low F&E risk must be designed in the fuel process
industry to prevent accidents and design mitigating measures against accidents [13-15]. The process
design of fuel storage plants, from layout to fire protection system setting, is related to the F&E
hazard classification of the fuels. The F&E hazards of materials are determined by safety-related
properties such as flash point, boiling point and range, flammability limits, auto-ignition
temperature, electrical resistivity, and minimum ignition energy [16]. Of the liquid fuels, the F&E
hazards are determined mainly by their flash point, which is used by organizations such as National
Fire Protection Agency (NFPA) to categorize flammability [17]. Flash point is an important criterion
of fuels because it drives the safe conditions of storage and transportation and influences the
operation temperature of the processes. To ensure the safe operation of aircrafts, the minimum flash
points are specified for different types of fuel (e.g. Jet A /A-1 stated in ASTM D1655, JP-5 fuel in
MIL-T-5624 [18]). Fire-safety precautions must be particularly taken for alcohol-hydrocarbons fuel
blends, as the dissociation of hydrogen bonding in alcohol due to the addition of the hydrocarbon
would cause the blends to present a large positive deviation to the ideal solution, which usually leads
to minimum flash-point behavior (MFPB) [19-22]. It implicates a particularly hazardous situation
because the flash point of the blends is lower than that of the individual fuels in a specific
composition range. The flash point data for pure chemicals can be obtained from various sources,
such as Lange’s Handbook of Chemistry (1999) [23], Handbook of Hazardous Chemical Properties
(2000) [24], the Merck Index (2006) [25] or NIOSH Pocket Guide to Chemical Hazards (NIOSH,
2020) [26]. Unfortunately, flash point for fuel blends as a function of the composition are scarce in
literature. Liquid mixtures, such as liquid blends of fuels with alcohols, are more commonly used
in industrial processes than pure liquids [22, 27]. Thus, accurate prediction is desirable for assessing
fuel blends F&E hazards and process safety improvement processes, such as inherently safer design
[13].
Correspondingly, there have been studies on prediction models of the flash point, summarized
as empirical, molecular structure-based, and vapor pressure-based models. Empirical models are
obtained by adjusting empirical parameters to experimental property data, mainly flash point to
3
volatility properties, such as the normal boiling point, density, vapor pressure and standard
vaporization enthalpy [28, 29]. Due to the simplicity of use, empirical models, such as the initial
boiling point-based (IBP) models, flash point blending index (FPBI) models, have been successfully
employed to predict flash point for pure hydrocarbons, petroleum fractions, diesel-biodiesel blends,
and biodiesel-FAME blends [29-31]. Molecular structure-based models include Group Contribution
Method (GCM) and Quantitative Structure Property Relationships (QSPR) based models [32, 33].
The GCM establishes linear or nonlinear model of the flash point as a function of the contribution
of all molecular functional groups, which is mainly established for pure ignitable liquids [32, 34,
35]. The QSPR models characterize the molecular structure information based on molecular
descriptors, and use a mathematical regression method or artificial neural network (ANN) approach
to correlate flash point with molecular structure [36, 37]. This kind of model is not only applicable
in flash point prediction for pure substance [13, 37] but also has been applied in mixtures such as
biodiesel blends [38-40]. Molecular structure-based models could be used to predict flash point
without detailed knowledge of the mechanisms of interaction and additional experiments but require
specialized software and a larger number of databanks to construct an efficient model. The vapor
pressure-based models are formulated using Le Chatelier’s rule and vapor-liquid equilibrium (VLE)
equation, such as the Affens and McLaren model, Gmehling and Rasmussen model, White model,
and Liaw model [28]. The activity coefficient models (e.g. Wilson, NRTL, UNIQUAC, and
UNIFAC models) may be employed in the vapor pressure-based models depending on the nonideality behavior of the liquid phase. Compared to empirical models, the vapor-pressure based
models usually give high prediction accuracy [28]. The vapor-pressure-based model most
commonly used today is the Liaw model [41]. The UNIFAC (Universal Quasi-Chemical
Functional-group Activity Coefficients) method has been more extensively adopted than others as
it is used in a fully predictive manner that does not require parameter fitting for each system under
study [28]. The Liaw model incorporated with the UNIFAC model has been proven as an efficient
flash point prediction model for miscible [27, 42-45] or partial miscible blends [46, 47], aqueous
solutions [20, 45], diesel and/or biodiesel blends [48-50]. However, detailed information about the
alcohol-diesel / biodiesel blends [48, 49] composition is required for the method, such as the flash
point, the group structure, and the vapor-temperature relationship of each fuel components, and the
4
calculation procedure for multi-component blends are complicated (Phoon et al. [48]). Besides, for
the Liaw-Gibbs-Duhem model as a kind of improved method, several components are needed to
formulate the fuel, and the surrogates should be carefully selected to emulate the target properties
[49]. In this paper, flash point data for aviation fuel (kerosene) blending with different alcohol were
firstly measured and discussed according to the safety regulations. Moreover, a new strategy to
predict the flash point was suggested for alcohol-fuel blends by using an average fuel structure to
the UNIFAC model. Therefore, the flash point prediction of the alcohol-fuel blend is reduced to that
of a two-component blend, leading to a simple prediction algorithm. Accurate knowledge of alcohol
+ fuel flash point and its reliable prediction methods can be applied in hazard identification, F&E
hazard reduction, process inherently safer design, and the risk management of alcohol-based fuels.
2 Experimental details
2.1 Materials and characterization
The n-butanol having a purity of more than 99.0% was purchased from Sinopharm Chemical
Reagent Co., Ltd. The n-hexanol and n-octanol having a purity of more than 99.0% were purchased
from Shanghai LingFeng Chemical Reagent Co., Ltd. The kerosene (reagent grade) was purchased
from Shanghai Macklin Biochemical Co., Ltd. Commercial 0# diesel [51] was purchased from a
local gas station. Table 1 shows the most relevant properties of the fuels used in this work.
Table 1 Fuel properties of kerosene and 0# diesel [52-54]
Properties
kerosene
0# diesel
Chemical formula
C10.8H19.9
C15.8H33.6
Molecular weight
149.8
223.7
Density at 20°C (g/cm3)
0.800
0.840
Boiling point range (°C)
175-325
180-360
The composition of the kerosene was analyzed by Agilent7890GC/5977B gas
chromatography/mass spectrometry (GC/MS). The peaks were identified with NIST 2017 Mass
Spectral Library. The experiment settings were displayed in Table 2 and Table 3.
5
Table 2 The experiment settings of GC/MS
Column
HP-5 MS, 30.0m×0.25mm×0.25μm
Carrier gas
helium
Carrier gas flow rate (mL/min)
0.7
Split ratio
100:1
Sample
0.1μL
Mass spectra m/z range (amu)
33.0-480.0
Table 3 The temperature program of GC/MS
Initial temperature (℃)
30
Isothermal process (min)
2 (initial hold)
Isothermal temperature (℃)
30
Heating process (℃/min)
2
Heating temperature (℃)
180
Heating process (℃/min)
10
Final temperature (℃)
280
Isothermal process (min)
5 (final hold)
2.2 Flash point measurements
2.2.1 Experimental apparatus
The flash point of the samples was measured using the Grabner Mini-FLASH TOUCH flash
point tester [55]. The setting of standard ASTM D 6450 [56] was applied. This test method is
suitable for testing samples with a flash point range from 10℃ to 250℃. Fig. 1 shows the schematic
diagram the main components and structure of the flash point apparatus. For the test, the sample
cup is lifted to the temperature-controlled oven, forming a metal-sealed test chamber. A
thermocouple is immersed into the sample to measure the temperature in real time. The
instantaneous pressure increase in the test chamber caused by ignition is detected by a built-in
pressure transducer. Peltier elements and an air-cooled heat sink are internally installed for accurate
6
temperature control of the oven. A high voltage arc inside the test chamber is used as the ignition
source. A rotating magnet inside the sample cup provides uniform stirring of the samples. A
stainless-steel cup with 1 ml of sample is placed in the oven.
⑪
P
P
④
⑩
②
⑨
①
P
③
⑫
⑤
⑥
⑦
⑧
① Metal lid of test chamber;
⑤ Sample cup;
⑨ Lifter cam device;
② Peltier element;
⑥ Stirring magnet;
⑩ Adjusting screw of lifter;
③ Sample temperature sensor;
⑦ Sample holder;
⑪ Front panel;
④ Pressure transducer;
⑧ Rotating magnet;
⑫ Sample delivery door
Fig. 1. Schematic diagram of the main components and structure of the flash point apparatus
2.2.2 Standard test procedure
The instrument automatically adjusts the oven to a temperature approximately 18℃ below the
anticipated flash point. The sample is heated at a rate of 5.5 ± 0.5℃ /min, where the voltage electric
arc is used for the ignition in equidistant steps of 1℃ rise in temperature of the sample. To have
enough oxygen for each arc to develop a flame, a small amount of air is blown into the measuring
7
chamber before each ignition. The flash point is determined as the temperature where the pressure
increase reaches a programmed threshold (default value 20 kPa) due to the hot flames or combustion.
The repeatability and reproducibility of the tester according to ASTM D 6450 [56] are 1.9 and 3.1℃,
respectively.
2.2.3 Experimental steps
The alcohol-fuel blends with various compositions were prepared by directly weighing the
individual components with an analytical balance. The blends were thoroughly mixed with a vortex
mixer. The flash point of every tested sample has adopted the criteria of the required repeatability
of ASTM D 6450 [56]. Each sample was tested at least three times and the experimental standard
deviation was always within 1℃.
3 Theory
3.1 Mathematical formulation
At the flash point of multi-component mixtures, the Liaw model [57, 58] based on Le
Chatelier’s rule must be satisfied. For the alcohol-fuel blends, the Liaw model can be applied as
follows [48, 49]:
𝑥
𝛾
𝑃𝑠𝑎𝑡
𝑂𝐻 𝑂𝐻
1 = 𝑂𝐻 𝑠𝑎𝑡
+ ∑𝑖
𝑃𝑂𝐻,𝐹𝑃
𝑠𝑎𝑡
𝑥𝑓,𝑖 𝛾𝑓,𝑖 𝑃𝑓,𝑖
𝑠𝑎𝑡
𝑃𝑓,𝑖,𝐹𝑃
(1)
where x and γ are the mole fraction and liquid phase activity coefficient, respectively; 𝑃𝑖𝑠𝑎𝑡 is the
𝑠𝑎𝑡
saturated vapor pressure of pure component i at the flash point of the mixture, and 𝑃𝑖,𝐹𝑃
is the
saturated vapor pressure of pure component i at its flash point. The subscripts OH and f,i refer to
the alcohol and the fuel component i present in the alcohol + fuel blends, respectively.
Petroleum-based fuel is a complex blend of a large number of compounds with similar
functional groups and chain length, and is known as the continuous mixture. A discrete compound
(such as alcohol) blending with a continuous mixture forms a semi-continuous blend. To predict the
flash point behavior for semi-continuous blends by using conventional thermodynamic methods, it
is most important to characterize the petroleum-based fuel by accurately representing its vaportemperature relationship and the non-ideal behavior (deviations from Raoult’s law) of the fuel blend.
The vapor-temperature relationship of fuel can be estimated by using the Antoine equation or the
8
Clausius-Clapeyron equation. The non-ideality of the blends is commonly expressed by activity
coefficients. The UNIFAC method was used to predict non-ideal behavior for fuel blends.
When the Liaw model is applied to the semi-continuous blend, its continuous constituent is
always treated as an ideal mixture on the basis that the interaction among the molecules with similar
functional groups and chain length can be neglected [49]. In this work, the continuous fuel (kerosene
and diesel) was considered a pseudo component that has the average fuel structure, from which the
activity coefficient was simply derived using the original UNIFAC model.
Therefore, the Liaw model was transformed from Eq. (1) into the form of Eq. (2) to predict the
flash point of the alcohol-fuel blends as:
𝑥
𝑃𝑠𝑎𝑡
𝛾
𝑂𝐻 𝑂𝐻
1 = 𝑂𝐻 𝑠𝑎𝑡
+
𝑥𝑓 𝛾𝑓 𝑃𝑓𝑠𝑎𝑡
𝑃𝑂𝐻,𝐹𝑃
𝑠𝑎𝑡
𝑃𝑓,𝐹𝑃
(2)
where subscript f is referring to the petroleum-based fuel. Two simplification steps were made in
the proposed model: 1. the petroleum-based fuel has a single vapor-temperature relationship; 2. the
activity coefficients for alcohol and petroleum-based fuel can be derived from a two-component
mixture by the UNIFAC model. The temperature that satisfies Eq. (2) is considered the flash point
of the fuel blends.
3.2 Calculation procedure
A Matlab-based program was developed to calculate the flash point. The calculation procedure
of the proposed method to predict the flash point of the alcohol-fuel blends is shown in Fig. 2. Since
the flash point temperature is determined as that which simultaneously fits the vapor-temperature
equations and UNIFAC model, the problem is to solve the complex nonlinear equation of
temperature (Eq. (2)). Function Le was defined to allow for the determination of the flash point
under a simple loop procedure:
𝑥
𝛾
𝑃𝑠𝑎𝑡
𝑂𝐻 𝑂𝐻
𝐿𝑒 = 𝑂𝐻𝑃𝑠𝑎𝑡
+
𝑂𝐻,𝐹𝑃
𝑥𝑓 𝛾𝑓 𝑃𝑓𝑠𝑎𝑡
𝑠𝑎𝑡
𝑃𝑓,𝐹𝑃
(3)
This procedure starts assuming flash point equal to a temperature Tpred that below the actual
flash point for alcohol-fuel blend (Tpred = min(FPOH, FPf) -10K), and then the Tpred is updated by
equidistant steps of temperature rise (ΔT = 0.1K). The vapor-temperature equations, the UNIFAC
model and Le are successively updated under each temperature of Tpred. In the following temperature
9
steps, the calculation has to sweep increasing number of Le until reaching 1. When the temperature
is high enough that sufficient vapor emits to form a combustible mixture (the function Le reaches
1), it breaks the calculation loop and prints the flash point results T. The vapor-temperature
equations accounting for vapor pressure of each component are shown in Section 4.2. The UNIFAC
model accounting for non-ideality effects of the blends is shown in Section 4.3.
Assume flash point of fuel blend, Tpred
𝑠𝑎𝑡
Calculate 𝑃𝑖𝑠𝑎𝑡 /𝑃𝑖,𝐹𝑃
Calculate γOH and γf by UNIFAC
model using average fuel structure
Composition xOH and xf
Calculate Le
Is Le ≥ 1?
No
Tpred =Tpred + ΔT
Yes
Print results: flash point T
Fig. 2. The procedure of the flash point prediction model for alcohol + fuel blends
4 Results and discussion
4.1 Average fuel structure
For the proposed model, knowing the average fuel structure will simply enable the use of the
UNIFAC model without detailed information about the fuel composition, such as the mole fraction
and the group structure of each fuel component. For pure components, the number of each type of
functional group can simply be counted from the chemical structure. Therefore, the average fuel
structure of petroleum-based fuel (Table 4) can be deduced from the structure of all fuel components.
𝑓
The number of each functional group k in the “average fuel structure” 𝑣𝑘 is linearly averaged from
𝑓,𝑖
those of its components 𝑣𝑘 as:
10
𝑓
𝑥
𝑓,𝑖
𝑣𝑘 = ∑𝑖 ∑ 𝑓,𝑖 𝑣𝑘
𝑖 𝑥𝑓,𝑖
(4)
The subscript f,i refers to the fuel component i present in the alcohol + fuel blends. The GC/MS
experiment was conducted to determine the average kerosene structure from its composition. To
reduce the complexity to obtain the average fuel structure, only the most representative components
present in kerosene (10 components for paraffins, 9 for naphthenes, and 7 for aromatics) are
accounted to represent each kerosene component with the same carbon number. The detailed
composition proposed for each family is given as Supplementary material (A1). When not enough
information about the fuel components is available experimentally, the composition data obtained
from literature is useful to calculate the average fuel structure. The composition data is available in
[59] for 0# diesel. The molecular structure of pure components and the average structure of
petroleum-based fuels are shown in Table 4.
Table 4 UNIFAC group assignment in this study
compound
group assignment
n-butanol
1 × CH3, 3 × CH2, 1 × OH
n-hexanol
1 × CH3, 5 × CH2, 1 × OH
n-octanol
1 × CH3, 7 × CH2, 1 × OH
0# diesel
2.0 × CH3, 13.8 × CH2
kerosene
1.4 × CH3, 5.6 × CH2, 0.6 × CH,
1.2 × ACH, 0.3 × ACCH2, 0.7 × ACCH3
4.2 Vapor pressure
The saturated vapor pressure of the alcohol at various temperatures was calculated by using
the Antoine equation (Table 5). Since the petroleum-based fuel composition changes with its origin
and processes, each fuel has a unique thermodynamic behavior. Hence, it usually requires detailed
information on the composition of the fuel to obtain its vapor-temperature relationship.
11
Table 5 Antoine coefficients for alcohols
Antoine coefficients
compound
A
B
C
Temperature range/K
n-butanola
9.54607
1351.555
-93.34
273/391[60]
n-hexanola
9.617
1547
-94.6
313/393[61]
b
13.73
3017.81
-137.1
343/468[62]
n-octanol
alog(P/Pa)=A-B/[(T/K)+C].
bln(P/kPa)=A-B/[(T/K)+C].
A single vapor-temperature relationship for continuous fuels can make its flash point prediction
rapid and straightforward. The Clausius-Clapeyron equation can express the vapor pressure of fuel
with the vaporization enthalpy [63]. The value of vaporization enthalpy is related to the strength of
the intermolecular actions. There are several empirical approaches to determine the vaporization
enthalpy of petroleum fractions, which correlates the vaporization enthalpy with its thermo-physical
properties [64]. Fang et al. [65] proposed an empirical approach based on the molecular weight Mw,
specific gravity SG, and normal boiling point temperature Tb. The correlations proposed by
Mohammadi and Richon [66], and Parhizgar et al. [67] are just based on Tb and SG. Their results
illustrate that the correlation is able to calculate the vaporization enthalpy that has good agreement
with experiment data. The empirical approach proposed by Parhizgar et al. is relatively more
accurate and has an average absolute relative deviation (AARD%) of 1.32% for petroleum fractions
over a boiling point range from 355.5 to 646.8K [67]. The ratio of the saturated vapor pressure of
𝑃𝑓𝑠𝑎𝑡
petroleum-based fuel at the flash point of blend and of pure fuel 𝑃𝑠𝑎𝑡 is needed to solve Eq. (2),
𝑓,𝐹𝑃
and it is given by:
𝑃𝑓𝑠𝑎𝑡
𝑠𝑎𝑡
𝑃𝑓,𝐹𝑃
= exp (−
∆𝐻𝑣𝑎𝑝 1
𝑅
(𝑇 − 𝑇
1
𝑓,𝐹𝑃
))
(5)
The fuel vaporization enthalpies ΔHvap derived by Parhizgar’s method were 40.24kJ/mol for
kerosene and 40.51kJ/mol for 0# diesel. The fuel flash points Tf,FP measured by the experiment were
12
323K for kerosene and 351K for 0# diesel. By applying a single vapor-temperature relationship of
petroleum-based fuel with its vaporization enthalpy, the experiments and complicated calculations
to obtain the vapor pressure from the fuel composition can be saved.
4.3 Activity coefficient
The UNIFAC model is widely applied to describe mixtures’ non-ideality (activity coefficient)
[28]. The UNIFAC model [42, 68] expresses the activity coefficient as the sum of a combinatorial
and a residual contribution.
ln𝛾𝑖 = ln𝛾𝑖𝐶 + ln𝛾𝑖𝑅
(6)
The combinatorial contribution, ln𝛾𝑖𝐶 , accounts for differences in size and shape of
the molecules, and the residual contribution, ln𝛾𝑖𝑅 , accounts for differences in
intermolecular interaction. The UNIFAC model treats the molecular mixture as a mixture of the
functional groups. The molecules in a mixture are divided into several groups as shown in Table 4,
and then the activity coefficient 𝛾𝑖 of component i is calculated by the shape parameters of the
groups and the interaction parameters between different groups.
To obtain the activity coefficient of component i in a multi-component mixture, the
combinatorial contribution is obtained by using the following relations:
ln𝛾𝑖𝐶 = ln
𝜑𝑖
𝑧
𝜃
𝜑𝑖
2
𝜑𝑖
𝑥𝑖
+ 𝑞𝑖 ln 𝑖 + 𝑙𝑖 −
∑𝑗 𝑥𝑗 𝑙𝑗
(7)
𝑙𝑖 = (𝑟𝑖 − 𝑞𝑖 ) − (𝑟𝑖 − 1); 𝑧 = 10
(8)
𝑥𝑖
where
𝑧
2
x i is a mole fraction of component i, and the summation of j in Eq. (7) is over all
components j, including component i. 𝜑𝑖 , the segment fraction of component i, 𝜃𝑖 ,
the surface area fraction of component i, are defined as:
𝑥𝑟
𝜑𝑖 = ∑ 𝑥𝑖 𝑖𝑟
𝑗 𝑗 𝑗
𝑥𝑞
𝜃𝑖 = ∑ 𝑥𝑖 𝑖𝑞
𝑗 𝑗 𝑗
(9)
(10)
where ri and qi are the measures of molecular van der Waals volumes and molecular surface areas
for pure components, respectively.
The residual contribution is expressed as:
13
ln𝛾𝑖𝑅 = ∑𝑘 𝑣𝑘𝑖 [𝑙𝑛𝑍𝑘 − 𝑙𝑛𝑍𝑘𝑖 ]
(11)
where
𝜃 𝜓
ln𝑍𝑘 = 𝑄𝑘 [1 − ∑𝑚 ln(𝜃𝑚 𝜓𝑚𝑘 ) − ∑𝑚 ∑ 𝑚𝜃 𝜓𝑘𝑚 ]
𝑛 𝑛
𝑛𝑚
𝜃𝑖 𝜓
𝑖
ln𝑍𝑘𝑖 = 𝑄𝑘 [1 − ∑𝑚 ln(𝜃𝑚
𝜓𝑚𝑘 ) − ∑𝑚 ∑ 𝑚 𝑖 𝑘𝑚 ]
𝑛 𝜃𝑛 𝜓𝑛𝑚
(12)
(13)
𝑣𝑘𝑖 is the number of groups of type k in molecule i. 𝑍𝑘 is the group residual activity
coefficient and 𝑍𝑘𝑖 is the residual activity coefficient of group k in a reference
solution containing only molecules of type i. The sums in Eqs. (12) and (13) are over
all different groups. Q k is a group parameter obtained from the van der Waals group
𝑖
surface areas. 𝜃𝑚 and 𝜃𝑚
are the area fractions of group m in the mixture and the
reference solution, and they are calculated as follows:
𝑄 𝑋
𝜃𝑚 = ∑ 𝑚 𝑚
(14)
𝑛 𝑄𝑛 𝑋𝑛
𝑄 𝑋𝑖
𝑖
𝜃𝑚
= ∑ 𝑚𝑄 𝑚
𝑋𝑖
𝑛
(15)
𝑛 𝑛
𝑖
where X m and 𝑋𝑚
are the mole fractions of group m in the mixture and the reference
solution, and they are given by:
𝑗
𝑋𝑚 =
∑𝑗 𝑣𝑚 𝑥𝑗
(16)
𝑗
∑𝑗 ∑𝑘 𝑣𝑘 𝑥𝑗
𝑣𝑖
𝑖
𝑋𝑚
= ∑ 𝑚𝑖
(17)
𝑘 𝑣𝑘
where x j is a mole fraction of components j, and the sums of j are over all components.
In the Eqs. (12) and (13) the group interaction parameter 𝜓𝑛𝑚 is given by:
𝑎
𝜓𝑛𝑚 = exp(− 𝑛𝑚
)
𝑇
(18)
where anm measures the energy of interaction between groups n and m, and anm ≠ amn. Parameters
anm and amn and the shape parameters of the groups R and Q (given in Supplementary Materials
(A2)) are obtained from [69]. As mentioned before, to obtain activity coefficients of alcohol and
petroleum-based fuel, the average fuel structure of petroleum-based fuel instead of its complete
composition was used in the UNIFAC model. The theoretical analysis was provided to demonstrate
the appropriation of the proposed model.
14
4.3.1 Verification of activity coefficient of alcohol
The UNIFAC model based on molecular thermodynamics is a group contribution method. In
the group contribution methods, mixtures are considered to consist of different functional groups.
The system’s properties are the contribution of the groups, regardless of to which molecule the
groups belong. In the UNIFAC model, the activity coefficient of component i in the mixtures is
considered an additive function of parameters that are related to each of the groups that describe
them [70]. For a multi-component mixture, replacing all the components except i with a single
component that has their average group structure does not change the total composition of the groups,
thus does not change the obtained activity coefficient of component i. In this study, the component
i was assigned to alcohol in the alcohol-fuel blends, and the complete composition of fuel was
replaced by its average group structure. The alcohol activity coefficient is an additive function of
group parameters in the UNIFAC model; therefore, its obtained value by using the average fuel
structure should be the same as that using the complete fuel composition.
As shown in Table 6, the independent variables (input parameters) in the UNIFAC model can
be divided into four types:(1) functional groups properties; (2) properties of pure component i; (3)
group interaction properties; (4) properties of components j. Compared with the UNIFAC model
using the complete fuel composition, the use of the average group structure only changes the type
(4) parameters. Note that other types of input parameters, for example, group interaction properties
that affect the activity coefficient through T and anm, do not play a role in the properties of each
component. In other words, the types (1), (2), (3) parameters are independent of petroleum-based
fuel composition, whose values are the same whether the average fuel structure or the complete fuel
composition is used in the UNIFAC model.
Table 7 shows which of the terms of the UNIFAC equation are influenced by the type (4)
parameters. The type (4) parameter-related terms are all calculated in a manner of summations over
j, which can be written in the form of ∑𝑗 𝑥𝑗 𝑌𝑗 , where xj is the mole fraction of component j, and Yj
𝑗
𝑗
represents molecular property l j , r j , q j , and ∑𝑘 𝑣𝑘 . It is acknowledged that l j , r j , q j , and ∑𝑘 𝑣𝑘
are additive functions of group properties, therefore the values of the sums ∑𝑗 𝑥𝑗 𝑌𝑗 are determined
by the contribution of the total groups [68]. Compared with using complete fuel composition in the
15
UNIFAC model, the use of the average fuel structure does not change the total composition of the
groups, thus does not change the values of ∑𝑗 𝑥𝑗 𝑌𝑗 . It can be concluded that in the proposed model
the input parameters of the “properties of components j” changed, but the values of the resulting
terms were the same as that using the complete fuel composition. Thereby, the activity coefficient
of the alcohol obtained by the proposed model is the same as that using the actual fuel composition.
Table 6 Input parameters for the UNIFAC model
Type
Symbol
Parameter
functional groups
Q
group area parameter
R
group volume parameter
T
temperature
anm
the group interaction parameter
xi
the mole fraction of components i
ri
volume parameter of component i
qi
area parameter of component i
𝑣𝑘𝑖
the number of groups of type k in a
group interaction
pure component i
molecule of component i
components j
xj
the mole fraction of components j, over
all components, including component i
𝑗
𝑣𝑘
the number of groups of type k in a
molecule of component j
rj
volume parameter of components j
qj
area parameter of components j
lj
defined in Eq. (8)
16
Table 7 Terms influenced by properties of components j in the UNIFAC model and source for the
term
Molecular property of j
Symbol
Term
Source
a linear function of rj and qj
𝑙𝑗
∑ 𝑥𝑗 𝑙𝑗
Eq. (7)
𝑗
∑ 𝑥𝑗 𝑟𝑗
𝑟𝑗
volume parameter of molecule j
Eq. (9)
𝑗
∑ 𝑥𝑗 𝑞𝑗
𝑞𝑗
area parameter of molecule j
Eq. (10)
𝑗
the total number of groups in a molecule j
𝑗
𝑗
∑ 𝑣𝑘
∑ ∑ 𝑣𝑘 𝑥𝑗
𝑘
𝑗
Eq. (16)
𝑘
4.3.2 Verification of activity coefficient of petroleum-based fuel
The activity coefficient measures the deviation from ideality for a component present in a
mixture. The petroleum-based fuel itself is a continuous mixture; thereby, its activity coefficient
lacks physical meaning. For non-ideal mixtures, the components have activity coefficients smaller
or greater than 1 [20]. A definition of petroleum-based fuel activity coefficient can be useful to
represent its non-ideality in the alcohol + fuel blends. By considering petroleum-based fuel as a
single component of its average group structure, the activity coefficients of petroleum-based fuel γf
can be calculated by the UNIFAC model along with alcohol. The use of “average fuel structure” to
obtain the alcohol activity coefficient γOH of alcohol-fuel blends has been justified with rigorous
expressions. The obtained fuel activity coefficients γf should also be analyzed to examine its validity.
Since the activity coefficient of binary blends is under the constraint of thermodynamic consistency,
the petroleum-based fuel activity coefficient γf must satisfy the Gibbs-Duhem equation to be valid.
The Gibbs-Duhem equation relates the partial molar quantity of components in a mixture to one
another [71]. The UNIFAC model, like several other well-known excess Gibbs energy models,
including the Wilson, Margules, van Laar, NRTL, and UNIQUAC equations, is constructed by
17
relating the activity coefficient term ln 𝛾𝑖 to a partial molar quantity of nT GE/RT [72] . Therefore,
the activity coefficients γf and γOH derived by UNIFAC model satisfy the Gibbs-Duhem equation,
which can be written in terms of activity coefficients for the pseudo-binary blend of alcohol + fuel
as [49]:
𝜕 ln 𝛾𝑂𝐻
𝑥𝑂𝐻 (
𝜕𝑥𝑓
𝜕 ln 𝛾𝑓
)
+ 𝑥𝑓 (
𝑇.𝑃
𝜕𝑥𝑓
)
=0
(19)
𝑇.𝑃
In the proposed model, using the average fuel structure, the calculation procedure of activity
coefficient for alcohol + fuel blend is reduced to that for a binary mixture. It can obtain the activity
coefficient for alcohol representing its non-ideality in the actual alcohol + fuel blends. The activity
coefficient of petroleum-based fuel can be obtained by considering petroleum-based fuel as a single
component in the blend that follows thermodynamic consistency.
4.4 Comparison of predicted and measured flash points
4.4.1 Flash point variation for alcohol + fuel blends
The flash point values of the pure components were obtained experimentally (Table 8). The
experimentally derived flash points were close to the values reported in literature. Kerosene is a
very complex hydrocarbon mixture that majorly composes paraffin, aromatic hydrocarbon, and
naphthene compounds [63]. The flash point for a complex mixture such as kerosene is not fixed but
is characterized by a specific range of flash points. To keep the kerosene vapor in the tanks of aircraft
below the explosive limit, the aviation fuel standards set the minimum flash points for aviation fuel,
thereby limiting the use of highly volatile fuels. The target value set for Jet A / A-1 fuel by ASTM
D1655-17a is 38°C, JP-5 fuel by MIL-T-5624 is 60°C [18]. The fire hazard classifications of the
fuels drive the conditions for the safe process, storage, and transportation, which are designated
Class I liquids having flash points below 38℃, Class II having flash points in the range of 38-60℃,
and Class III having flash points in the range of 60-93℃[17]. The fire hazard classifications of the
five materials are ranked Class I for n-butanol, Class II for kerosene, Class III for diesel, n-hexanol,
and n-octanol.
18
Table 8 Comparison of flash point values adopted from the literature with experimentally
derived data.
Experimental
Reference
Absolute
data (℃)
data (℃)
deviation (℃)
37.0
37[23]
0.0
36-38[25]
-
78[53]
0.0
≥60[51]
-
38-72[26]
-
41-63 [73]
-
60[48]
0.9
63[24]
2.1
86[74]
2.0
87 [75]
3.0
compound
n-butanol
0# diesel
kerosene
n-hexanol
n-octanol
78.0
50.0
60.9
84.0
It was shown in Fig. 3 and Fig. 4 that the n-butanol + kerosene and n-hexanol + kerosene blends
exhibit minimum flash point behavior. The flash points of the fuel blends decrease rapidly to 37℃
or less once the mole fraction of n-butanol mixed with kerosene was more than 0.10, which is lower
than the target value set for Jet fuel. Due to the appearance of MFPB, the blending ratio of butanol
should be limited with flash point to ensure the resulting fuel blends conform to safety regulations.
Otherwise, higher fire safety requirements should be specified, and the fire protection configuration
should be enhanced accordingly. The flash points of n-hexanol and n-octanol are relatively high and
consequently have a low risk. The flash points of n-hexanol + kerosene blends are lower than 60℃
over almost the entire composition range. The flash points of the n-octanol + kerosene blends (Fig.
5) are lower than 60℃ when the mole fraction of n-octanol is not more than 0.70. The flash points
of the alcohol + kerosene blends are lower than ideal analogues due to strong non-ideality with
19
positive deviation. The flash point results showed that the presence of n-hexanol and n-octanol in
the fuel blends cannot effectively elevate the flash point and the fire hazard classification of
kerosene over a wide concentration range, which means that the non-ideality is more important to
the flash point of the blends than the flash point of individual components.
Fig. 3. Comparison of predicted flash point and
Fig. 4. Comparison of predicted flash point and
experimental data for n-butanol + kerosene blends
experimental data for n-hexanol + kerosene blends
Fig. 5. Comparison of predicted flash point and experimental data for n-octanol + kerosene blends
It was shown in Fig. 6 and Fig. 7 that alcohol + diesel blends have a flash point variation similar
20
to the alcohol + kerosene blends. The flash point of n-butanol + diesel and n-hexanol + diesel blends
are lower than ideal analogues due to strong non-ideality with positive deviation. The flash point of
blends decreases sharply along with the quantity of alcohol in the alcohol-lean region (<0.1) and
decreases smoothly in the region where the alcohol mole fraction ranges between 0.1 and 1. The
results showed that the blends have flash points approaching that of alcohols in a wide range of
concentration.
Fig. 6. Comparison of predicted flash point and
Fig. 7. Comparison of predicted flash point and
experimental data for n-butanol + diesel blend
experimental data for n-hexanol + diesel blend
4.4.2 Evaluation of the flash point prediction
The flash point predictions of alcohol-kerosene blends made by the Raoult’s law, Hu-Burns
model, and the proposed model were shown in Fig. 3-5. The “Raoult’s law” method is the Liaw
model for ideal mixture, and the “Hu-Burns model” is a conventional blending index approach
commonly used in the petroleum refining flash point calculation for blends. It has been reported in
[29] that Hu-Burns model can calculate flash points with good accuracy for biofuel blends such as
diesel-biodiesel and biodiesel-biodiesel blends. This model is established based on the index of the
blend Ib, which is obtained by summing the value of the flash point indices (Ii) with the volume
fraction (νi) of each compound i. The flash point index Ii is determined based on the flash point of
21
the pure component FPi (expressed in Kelvin). Hu-Burns model to calculate the flash point of blend
(FPb) is expressed as:
1
𝐼𝑖 = 𝐹𝑃𝑖−0.06
(20)
𝐼𝑏 = ∑ 𝑣𝑖 𝐼𝑖
(21)
𝐹𝑃𝑏 = 𝐼𝑏−0.06
(22)
It is observed that the Hu-Burns model and Raoult’s law overestimate the flash point for three
alcohol + kerosene blends. The predictions made by the proposed model using average fuel structure
are generally in good agreement with the experimental data. The Average Absolute Relative
Deviation (AARD) for three fuel blends of alcohol + kerosene (alcohol being n-butanol, n-hexanol,
and n-octanol) are 2.4%, 0.8%, and 1.2%, respectively. It has been reported in [29] that blending
index approaches, such as Hu-Burns model, and Liaw’s method for ideal mixture can calculate flash
points of fuel blends with slight differences. In these methods, the non-ideality of the liquid phase
is not taken into account for flash point prediction. However, the alcohol-kerosene blends are more
complex systems in terms of diversity of functional groups, non-ideality evaluation must be
considered for accurate prediction. Therefore, the blending index approach is not a preferred flash
point prediction method for the blends under study.
The experiment and prediction flash point results of alcohol + diesel blends were shown in Fig.
6 and 7. The predictions made by the Liaw-UNIFAC model are generally in good agreement with
the experimental data, which not only have a similar flash point variation with the experimental data
but also have a predictive slope of flash point vs. composition close to the experimental result in the
region where the flash point varies significantly with composition. The AARD of Liaw-UNIFAC
model for alcohol + diesel (alcohol being n-butanol, and n-hexanol) are 2.5% and 0.8%, respectively.
Hence, when not enough information about the fuel composition is available experimentally, the
composition data obtained from literature could give reasonable flash point prediction by the
proposed model.
5 Conclusions
The flash point variation of five fuel blends of alcohol + kerosene (alcohol being n-butanol, n22
hexanol, and n-octanol) and alcohol + diesel (alcohol being n-butanol and n-hexanol) was
determined experimentally. Experimental results showed that the flash points of all examined fuel
blends are lower than ideal analogues or even exhibited minimum values due to strong non-ideality
with positive deviation. The minimum flash point behavior (MFPB) has been observed for two
different alcohol + kerosene blends (alcohol being n-butanol, n-hexanol), which present greater fire
risks because their flash points within a particular composition range are lower than those of
individual fuel. The flash points of the fuel blends decrease rapidly to 37℃ or less once the mole
fraction of n-butanol mixed with kerosene was more than 0.1. The blending ratio of butanol must
be limited to attain the safety level.
A simplified model of predicting flash point for alcohol + fuel blends was proposed based on
the Liaw model. The proposed prediction model was derived using the average fuel structure in the
UNIFAC model to obtain the activity coefficients. A theoretical justification was provided for the
proposed model, which was able to reduce the input parameters of fuel composition, and simplify
the calculation procedure, while preserving strong description of fuel. Conventional flash point
estimation methods for fuel blends, such as Hu-Burns model and Liaw’s method for ideal mixture,
overestimates the flash point for five blends due to lack of non-ideality evaluation. The proposed
model can identify MFPB for alcohol + fuel blends and estimate the flash points with average
absolute relative deviation (AARD%) lower than 2.5% for five blends. The proposed method shows
great potential to obtain accurate results for the flash point prediction of the alcohol + fuel blends.
This work is helpful to ensure the safe design and the risk management of butanol blending with
petroleum-based fuel as an alternative fuel to guarantee safety in application.
23
Nomenclature
A, B, C Antoine coefficients
anm
the UNIFAC group interaction parameter
FP
flash point (K)
𝐺𝐸
the excess Gibbs energy per mole of mixture (J/mol)
∆𝐻𝑣𝑎𝑝,𝐾 vaporization enthalpy of kerosene(kJ/mol)
I
blending index
Le
defined in Eq. (3)
l
defined in Eq. (8)
n
the number of moles
nT
the total number of moles
P
pressure (kPa)
Psat
saturated vapor pressure (kPa)
𝑠𝑎𝑡
𝑃𝑖,𝐹𝑃
saturated vapor pressure of component i, at flash point (kPa)
Qk
group area parameter
q
pure component area parameter
R
gas constant (without subscript)(8.314J/mol K)
Rk
group volume parameter (with subscript)
r
pure component volume parameter
𝑣𝑘𝑖
number of groups of type k in a molecule of component i
T
temperature (K)
24
X
defined in Eq. (16)
x
liquid-phase composition
Z
defined in Eq. (12)
Greek letters
γ
activity coefficient
θ
defined in Eq. (10)
φ
defined in Eq. (9)
𝜓
defined in Eq. (18)
Superscripts
C
the combinatorial part of activity coefficient
R
the residual part of activity coefficient
Subscripts
b
blend
D
diesel
FP
flash point
i
component i
j
components j, over all components, including component
OH
alcohol
f
the complex fuel as a single component
f,i
i th compound inside the fuel
K
kerosene
k, m, n group k, m, n
Acknowledgments
This work was supported by the National Science and Technology Major Project (J2019-VIII0010-0171); and the Fundamental Research Funds for the Central Universities (WK2320000052).
25
Appendix A. Supplementary material
A1 The detailed composition proposed for each family of petroleum-based fuel
To apply the proposed method, the average fuel structure of petroleum-based fuel is necessary.
The detailed composition proposed for 0# diesel obtained from literature is shown in Tables A.1.
The composition of the kerosene was analyzed by an Agilent7890GC/5977B gas
chromatography/mass spectrometry (GC/MS). The detailed composition proposed for each family
of kerosene is shown in Tables A.2-A.4. The mass spectrum of each peak in the total ion current
chromatogram of kerosene was searched and compared with the mass spectrum in the provided
standard mass spectrum library (NIST 2017 Mass Spectral Library). When the matching degree is
higher than 60, it was considered that the compound structure given by the software can be used.
When the matching degree is too low, the compound structures were considered unidentified. The
total mass fraction of identified components is equal to 91.62%. To reduce the complexity to obtain
the average fuel structure, only the most representative components present in kerosene (10
components for paraffins, 9 for naphthenes, and 7 for aromatics) are accounted in this study to
represent each kerosene component with the same carbon number.
26
Table A.1 Representative constituents obtained for the 0# diesel
Paraffins
Compound
Functional groups
C.N.
Mass fraction
Mole
(%)
fraction
Molecular weight
CH2
CH3
n-Octane
8
114.24
0.50
0.00975
6
2
n-Nonane
9
128.27
1.89
0.03282
7
2
n-Decane
10
142.30
1.64
0.02567
8
2
n-Undecane
11
156.33
5.81
0.08279
9
2
n-Dodecane
12
170.36
6.69
0.08748
10
2
n-Tridecane
13
184.39
8.25
0.09967
11
2
n-Tetradecane
14
198.42
7.30
0.08196
12
2
n-Pentadecane
15
212.45
7.06
0.07403
13
2
n-Hexadecane
16
226.48
13.52
0.13298
14
2
n-Heptadecane
17
240.47
10.62
0.09838
15
2
n-Octadecane
18
254.49
5.03
0.04403
16
2
n-Nonadecane
19
268.52
4.21
0.03493
17
2
n-Eicosane
20
282.55
6.00
0.04730
18
2
n-Heneicosane
21
296.57
5.70
0.04282
19
2
n-Docosane
22
310.60
4.94
0.03543
20
2
n-Tricosane
23
324.63
3.49
0.02395
21
2
n-Tetracosane
24
338.65
2.59
0.01704
22
2
n-Pentacosane
25
352.68
2.73
0.01724
23
2
n-Hexacosane
26
366.71
0.00
0.00000
24
2
n-Heptacosane
27
380.73
1.31
0.00767
25
2
n-Octacosane
28
394.76
0.72
0.00406
26
2
Total value
100
1
—
—
Average value
—
—
13.74
2.00
27
Table A.2
Representative constituents obtained for the paraffin family of kerosene
Functional
Paraffins
groups
Compound
C.N.
Mass fraction
Mole
(%)
fraction
Molecular weight
CH2
CH3
n-Heptane
7
100.20
0.13
0.00211
5
2
n-Octane
8
114.23
0.36
0.00511
6
2
n-Nonane
9
128.26
1.36
0.01721
7
2
n-Decane
10
142.28
6.70
0.07642
8
2
n-Undecane
11
156.31
8.18
0.08492
9
2
n-Dodecane
12
170.33
8.84
0.08422
10
2
n-Tridecane
13
184.36
4.30
0.03785
11
2
n-Tetradecane
14
198.39
2.46
0.02012
12
2
n-Pentadecane
15
212.41
1.39
0.01062
13
2
n-Hexadecane
16
226.44
0.35
0.00251
14
2
Total value
34.07
0.34109
—
—
Average value
—
—
3.21
0.68
28
Table A.3 Representative constituents obtained for the Naphthene family of kerosene
Naphthenes
Functional groups
Compound
C.N.
Molecular weight
Mass fraction (%)
Mole fraction
CH2
CH3
-CH- ©
-CH2- ©
Cyclohexane, methyl-
7
98.19
0.14
0.00231
0
1
1
5
Cyclohexane, ethyl-
8
112.21
0.49
0.00709
1
1
1
5
cis-1-Ethyl-3-methyl-cyclohexane
9
126.27
2.92
0.03753
1
2
2
4
Cyclohexane, butyl-
10
140.27
10.81
0.12505
3
1
1
5
trans-Decalin, 2-methyl-
11
152.28
9.71
0.10345
0
1
3
7
trans, cis-3-Ethylbicyclo[4.4.0]decane
12
166.30
0.40
0.00390
1
1
3
7
Heptylcyclohexane
13
182.35
1.04
0.00925
6
1
1
5
Cyclopentane, decyl-
15
210.40
0.69
0.00532
9
1
1
4
Cyclohexane, 1,1'-(1,5-pentanediyl)bis-
17
236.44
0.89
0.00611
5
0
2
10
Total value
27.09
0.30001
—
—
—
—
Average value
—
—
0.56
0.33
0.56
1.70
29
Table A.4 Representative constituents obtained for the Aromatic family of kerosene
Aromatics
Compound
Functional groups
Molecular
Mass fraction
weight
(%)
C.N.
Mole fraction
CH
CH2
CH3
AC
ACH
ACCH2
ACCH3
Toluene
7
92.14
0.21
0.00370
0
0
0
0
5
0
1
p-Xylene
8
106.17
0.67
0.01024
0
0
0
0
4
0
2
Benzene, 1,2,4-trimethyl-
9
120.19
3.95
0.05334
0
0
0
0
3
0
3
Benzene, 2-ethyl-1,3-dimethyl-
10
134.22
13.45
0.16264
0
0
1
0
3
1
2
Benzene, 1-methyl-4-(2-methylpropyl)-
11
148.24
7.93
0.08682
1
0
2
0
4
1
1
Benzene, 1-(2-butenyl)-2,3-dimethyl-
12
162.32
3.77
0.03769
0
2
1
0
3
1
2
Naphthalene, 1,2,3,4-tetrahydro-1,6,8-trimethyl-
13
174.28
0.48
0.00447
1
2
1
1
2
1
2
30.46
0.35890
—
—
—
—
—
—
—
—
—
0.09
0.08
0.38
0.00
1.18
0.29
0.68
Total value
Average value
30
A2 The shape parameters and the interaction parameters in the original UNIFAC model
The shape parameters of the groups (Table A.5) and the interaction parameters between
different groups (Table A.6) are need for original UNIFAC model. It should be noted that each group
has its own values of R and Q; the subgroups within the same main group (for example, subgroups
CH3, CH2, and CH) have identical group energy-interaction parameters.
Table A.5
Main groups, subgroups and the corresponding van der Waals parameters for the
original UNIFAC model
Main group
Sub group
Rk
Qk
CH2
CH3
0.9011
0.8480
CH2
0.6744
0.5400
CH
0.4469
0.2280
ACH
ACH
0.5313
0.4000
ACCH2
ACCH3
1.2663
0.9680
ACCH2
1.0396
0.6600
OH
1.0000
1.2000
OH
Table A.6 Matrix of the original UNIFAC interaction parameters anm
CH2
ACH
ACCH2
OH
CH2
0
61.1300
76.5000
986.5000
ACH
-11.1200
0
167.0000
636.1000
ACCH2
-69.7000
-146.8000
0
803.2000
OH
156.4000
89.6000
25.8200
0
31
A3 Experimental flash point data of alcohol + petroleum-based fuel
Table A.7 Experimental flash point data of alcohol-kerosene blends
Mole fraction
Flash point/℃
xOH
Exp
0.020
44.0
0.040
40.1
0.098
37.1
0.340
35.1
0.578
35.1
0.755
35.1
0.892
36.1
0.143
48.0
0.274
47.0
0.392
48.0
0.501
48.0
0.601
49.0
0.858
54.0
0.230
50.8
0.443
53.8
0.544
54.8
0.642
57.8
0.827
65.9
alcohol-kerosene blends
n-butanol + kerosene
n-hexanol + kerosene
n-octanol + kerosene
32
Table A.8 Experimental flash point data of alcohol-kerosene blends
Mole fraction
Flash point/℃
xOH
Exp
0.028
53.1
0.055
46.1
0.126
41.1
0.224
40.0
0.293
38.0
0.420
37.0
0.743
37.0
0.920
37.0
0.953
37.0
0.967
37.0
0.096
63.0
0.175
59.9
0.347
58.9
0.680
58.9
alcohol-diesel blends
n-butanol + diesel
n-hexanol + diesel
33
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