Copyright © 2013 by American Scientific Publishers
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Energy and Environment Focus
Vol. 2, pp. 171–175, 2013
(www.aspbs.com/efocus)
Comparative Study of Vapor Pressure Prediction
Methods for Alcohol–Gasoline Blends
Muhammad Muneeb Anwar1 , Faheem A. Sheikh1, 2, ∗ , and Hern Kim1, ∗
1
Department of Environmental Engineering and Energy, Energy and Environment Fusion Center,
Myongji University, Yongin, Kyonggi-Do 449-728, Korea
2
Department of Chemistry, University of Texas-Pan American, Edinburg, TX 78539, USA
ABSTRACT
KEYWORDS: Activity Coefficient, Vapor Pressure,
Alcohol,
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performance. Fernández et al.3 studied the fuel perfor1. INTRODUCTION
mance of higher alcohol (1-butanol,1-pentanol) blended
The emission of organic compounds in the environment
diesel. They found that the diesel engine run smoothly on
is influenced in part by the composition of gasoline
the blend up to 30% alcohol in diesel without any damthat is being used. As a result of growing environmental
age to the diesel engine. The performance improvement
concerns, regulations to reduce pollutant emissions from
of biodiesel by alcohol blending was studied by Yasin
vehicles have been imposed by Environmental Protection
et al.4 They concluded that the flow characteristic and denAgency (EPA) and state governments through the Clean
sity of mineral diesel improves whereas the Cetane numAir Act amendment of 1990. For this reason, various
ber (diesel performance parameter) of biodiesel improves
approaches from materials scientists had been put forby alcohol blending Bata et al.5 experimentally investiwards to have less use and no pollution in environment.
gated the exhaust emission (carbon monoxide, CO; carbon
For instance, cobalt based materials had been documented
dioxide, CO2 and unburned hydrocarbons, HC) of ethanol
to cover up this burning issue to address environmental
blended
gasoline. They found that the CO concentration
1
concerns. However, simulations programs are considered
is inversely proportional to the concentration of ethanol
to be best as they don’t require the experimental trials
in fuel blend and the concentration of CO was reduced
and methods based on predictions are considered to be
by about 40–50% at an equivalence ratio on the lean side
practically important. In line with this, several of gasoline
near stoichiometry. The influence of gasoline composition
types has been predicted and among these include; reforon air quality was studied by Unzelman.6 They concluded
mulated, conventional, oxygenated, low RVP (Reid Vapor
that oxygenates can improve air quality by reducing the
Pressure), low sulfur, and many others.2 Currently, alcoamount of exhaust emission. On the one hand, the use of
hol blended gasoline is most commonly used among the
blended gasoline reduces the pollutants in the vehicle glue
above listed gasoline. There are numbers of studied regardgases enhances the octane number and has better antiknock
ing the alcohol blended fuel characteristics, emissions and
properties as compared to the unblended gasoline.7 On the
∗
Authors to whom correspondence should be addressed.
Emails: [email protected], [email protected]
Received: 15 April 2013
Accepted: 18 May 2013
Energy Environ. Focus 2013, Vol. 2, No. 3
other hand, the high vapor pressure of alcohol blended
gasoline raised the problem of emission of fuel by evaporation. The accurate vapor pressure prediction of blended
gasoline is essential in environmental impact assessment
of blended gasoline.
2326-3040/2013/2/171/005
doi:10.1166/eef.2013.1045
171
ARTICLE
The main reason of blending alcohol with gasoline is to reduce fossil carbon dioxide emissions and thus to
have less load on environment. The fuels like methanol, ethanol and isopropanol are considered as important energy resources in today’s times. A intelligent system which can be used to forecast the consumption
and adequate blend system of these important fuels are the need of hour. In this study, we have used various simulation programs which will help to determine proper blend ratios of these important fuels in useful manners. For instance, different titrations have been predicted by using the Nelder-Mead pattern search
method and the Gibss free energy models such as Margules, van Larr, Wilson and NRTL equations. The
best correlations were obtained using the NRTL model; where the average vapor pressure deviations from
the experimental data reached as low as (0.52, 0.32, and 0.62) for methanol, ethanol, and isopropanol,
respectively.
ARTICLE
Comparative Study of Vapor Pressure Prediction Methods for Alcohol–Gasoline Blends
Anwar et al.
The thermodynamic behavior and vapor–liquid equiliba non-ideal binary system. In this case, Raoult’s Law is
rium data on oxygenate and multi-component hydrocarmodified to account for non-idealities by introducing an
bon mixtures are essential for predicting the vapor-phase
activity coefficient, . For each component, this can be
compositions. Distillation curves, vapor pressure, vaporrepresented as:
ization enthalpy and less frequently, the vapor/liquid ratio
(2)
yi P = i xi Pisat
are among the various methods that can be used to express
where is a function of the liquid phase composition and
a fuel’s volatility. Specifically in a gasoline supply system
many correlations exist for determining it. The simplest
and combustion process, the vapor pressure of a gasoline is
correlations are the Margules equation, the van Larr equaa fundamental physicochemical property that serves as an
tion, and the Wilson equation; while more complex methindication of the level of emission of volatile compounds.
ods include the NRTL, UNIQUAC, and UNIFAC models.
Results from research geared towards the discovery of a
In this article, the models to be used each contain an
correlation between evaporative losses and vapor pressure
equation represented as a function of x1 , x2 and two or
found that even for vehicles with the newest fuel injection
three coefficients as (A12 and A21 for Margules, A12 and
system, a 0.1 psi reduction in the water pressure resulted
8
A21 for Van Larr, 12 and 21 for the Wilson equation,
in an average of 4.3% evaporative losses.
and G12 , G21 and for the NRTL equation).11
Attempts to measure the vapor pressure of fuelMargules equation
oxygenate mixtures involved both experimental and
numerical methods. The latter method requires rigorous
(3)
ln 1 = x22 A12 + 2A21 − A12 x1 information collection from distillation data or from actual
fuel composition. On the other hand, direct experimental
(4)
ln 2 = x12 A21 + 2A12 − A21 x2 measurement requires infinite dilution activity co-efficient
9
to fit data, which makes it practically impossible.
Van Larr equation
In order to overcome this problem, experimental vapor
9
2
pressure data from the work of Pumphrey et al. on gasoA x
line blended with methanol, ethanol, and isopropanol were
(5)
ln 1 = A12 21 2 A12 x1 + A21 x2
used to determine the theoretical constantsDelivered
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ity coefficients of the different models
used. In general,
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a comparative study on the accuracy of
the various
predic- Scientific Publishers
(6)
ln 2 = A21 12 1 A21 x1 + A21 x2
tion methods for vapor pressure of gasoline-alcohol binary
systems was carried out. The predicted vapor pressures
Wilson equation
were correlated with experimental data using the NelderMead pattern optimization to obtain the parameter coeffiln 1 = − lnx1 + x2 12 cients. This method provides one of the most widely used
12
21
algorithms for unconstrained optimization of non-smooth
(7)
+ x2
−
x1 + x2 12 x2 + x1 21
functions and can be implemented in various ways such
as for the reduction of VLE experimental data.10 Good
ln 2 = − lnx2 + x1 21 vapor pressure correlations were obtained by using this
method.
21
12
+ x1
(8)
−
x2 + x1 21 x1 + x2 12
2. RESULTS AND DISCUSSION
2.1. Theoretical Procedure
Considering the ideal case of vapor–liquid equilibrium, for
an ideal solution the vapor pressure of each component is
proportional to the mole fraction of that component in the
liquid phase. This relationship is known as Raoult’s law
and is stated mathematically as:
yi P = xi Pisat
(1)
where xi is the mole fraction of component i in the liquid
phase, Pisat is the vapor pressure of pure component i, P is
the total pressure of the system, and yi is the mole fraction of component i in the vapor phase. Typically, Raoult’s
Law is valid when the components in solution are very
similar to each other. It is more common however, to have
172
NRTL equation
ln 1 = x22 21
ln 2 =
x12
12
G21
x1 + x2 G21
G12
x2 + x1 G12
2
2
G12 12
+
x2 + x1 G12 2
G21 21
+
x1 + x2 G21 2
(9)
(10)
Whereas, G12 = exp−12 and G21 = exp−21 .
From Pumphrey et al., work, the vapor pressures of
mixtures of gasoline with each of the three alcohols
were measured at 37.8 C (100 F). The vapor pressures
for the methanol–gasoline, ethanol–gasoline, isopropanol–
gasoline systems were examined from 0 to 100% gasoline
composition.
Energy Environ. Focus, 2, 171–175, 2013
Anwar et al.
Fig. 1.
Comparative Study of Vapor Pressure Prediction Methods for Alcohol–Gasoline Blends
Flow Chart of present computational procedure.
The parameter coefficient values were determined from
vapor pressure experimental data using nonlinear regression via the Nelder-Mead pattern search method which is
one of the most widely used optimization methods.12
Fig. 2. Flow chart of previous14 computational procedure.
Table I. Comparison between thermodynamic models with optimized parameter estimation.
Margules (Eq. (3))
Avg. VP dev. (%)
Max VP dev. (%)
a1
b1
c1
Van Larr (Eq. (4))
Wilson (Eq. (5))
MeOH
EtOH
Isopropanol
MeOH
EtOH
Isopropanol
MeOH
EtOH
Isopropanol
3
18
10
35
2
0779
2
2216
–
1
52
3
84
1
974
1
7182
–
1
8
4
58
1
7956
1
3986
–
3
11
10
47
2
0654
2
2347
–
1
49
3
96
1
9984
1
716
–
1
74
4
62
1
8541
1
3999
–
1
18
4
66
0
1475
0
1916
–
0
35
1
02
0
178
0
3546
–
1
03
2
75
0
2014
0
5023
–
Table I. Continued
Previous work15
NRTL (Eq. (6))
Avg. VP dev. (%)
Max VP dev. (%)
a1
b1
c1
MeOH
2
MeOH
EtOH
isoPropanol
LS
0
53
1
52
1
8764
2
2505
0
5112
0
32
1
36
1
1528
1
6881
0
5041
0
62
2
39
1
0033
1
7115
0
6176
2.87
4.82
EtOH
LI
3
1.79
3.35
2
Isopropanol
3
LS
LI
0.67
1.84
0.82
1.67
LS2
LI3
5.64
9.3
4.41
7.77
Notes: Comments: 1 for Margules equation, a refers to A12 while b refers to A21, for van Larr Equation, a refers to A’12 while b refers to A’21, for Wilson equation, a
refers to A12 while b refers to A21, for NRTL equation, a refers to T12, b refers to T21, while c refers to; 2 LS: east square fitting, 3 LI: Lagrange interpolating polynomials.
Energy Environ. Focus, 2, 171–175, 2013
173
ARTICLE
Data on vapor–liquid equilibria of binary and ternary
systems
of additives and gasoline blends can be corre2.2. Computational Procedure
lated using Gibbs free energy models such as Margules,
Figure 1 shows the computation procedure block diagram.
van Larr, Wilson, and NRTL.8 13–17 The activity coeffiPumpherery and co-workers’ experimental data (vapor
cients calculated using the Nelder-Mead method was used
pressure Versus molar concentration) was optimized by
to obtain the parameters for the Gibbs free energy modNelder-Mead method to yield the activity coefficients of
els. As can be seen in (Table I), the highest average
applied models. The excess Gibbs free energy coefficients
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deviations
were calculated by the optimizedIP:
coefficients
calculated
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two-parameter
Margules equation for all alcohol–gasoline
in about step. Finally the vapor pressures
wereAmerican
calcu- Scientific Publishers
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blends. On the other hand, the best correlations were
lated by using the activity coefficients and the calculated
obtained using the NRTL model where the average deviavapor pressure data was compared with the experimental
tions reached as low as (0.5211, 0.3190 and 0.6153%) for
data.
methanol, ethanol, and isopropanol, respectively. The same
Comparative Study of Vapor Pressure Prediction Methods for Alcohol–Gasoline Blends
Anwar et al.
is true for the maximum vapor pressure deviations
obtained at (1.5179, 1.3591 and 2.3893%) for methanol,
ethanol and isopropanol, respectively. Furthermore, our
procedure has fewer steps (Fig. 1) than that of procedure
described by Pumphrey et al.9 (Fig. 2).
Furthermore, the deviation of all the models is presented
in plots (Figs. 3–5) for Methanol, Ethanol and isopropanol,
respectively. Commercially the alcohol percentage in the
alcohol–gasoline blend is now a day limited to about
25%.18 The absolute maximum vapor pressure error by
NRTL model is nearly 1 percent for considered alcohol–
gasoline blends in the above composition range.
3. CONCLUSIONS
From this research, a simple way to work out the simulation program can be used to predict the perfect blends
which are environmentally safe and highly efficient. Using
the combination of Nelder-Mead pattern search method
and the NRTL model presented the best correlation to predict vapor pressure experimental data for alcohol–gasoline
blends. Using the Nelder-Mead method provided a simple
and accurate estimation of the activity coefficients since
although other methods3 may require the use of limited
vapor pressure data, estimation using limited concentration regions such as low and high concentrations may not
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adequate
properly characterize the behavior of the
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04:17:21
systems
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accuracy of the prediction method is comCopyright: American Scientific Publishers
promised. Although the NRTL model required the calculation of three parameters, it provided the best correlation
compared to the van Larr, Wilson, and Margules models.
ARTICLE
Fig. 3. Model Equation (Wilson, van Larr, Margules, and NRTL) Error
of vapor pressure data for Methanol–Gasoline mixtures.
Fig. 4. Model Equation (Wilson, van Larr, Margules, and NRTL) Error
of vapor pressure data for Ethanol–Gasoline mixtures.
Acknowledgments: This research was supported by
2013 research fund of Myongji University, by International
Research & Development Program (2011-0030906) and by
Basic Science Research Program (2009-0093816) through
the National Research Foundation of Korea (NRF) funded
by the Ministry of Education, Republic of Korea.
References and Notes
Fig. 5. Model Equation (Wilson, van Larr, Margules, and NRTL) Error
of vapor pressure data for Isopropanol–Gasoline mixtures.
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