ARTICLE IN PRESS
Fire Safety Journal 44 (2009) 756–763
Contents lists available at ScienceDirect
Fire Safety Journal
journal homepage: www.elsevier.com/locate/firesaf
Changes in evaporation rate and vapor pressure of gasoline
with progress of evaporation
Katsuhiro Okamoto a,, Norimichi Watanabe a, Yasuaki Hagimoto a, Koji Miwa a, Hideo Ohtani b
a
b
National Research Institute of Police Science, 6-3-1, Kashiwanoha, Kashiwa, Chiba 277-0882, Japan
Yokohama National University, 79-7,Tokiwadai, Hodogaya-ku, Yokohama City, Kanagawa 240-8501, Japan
a r t i c l e in f o
a b s t r a c t
Article history:
Received 16 October 2008
Received in revised form
4 March 2009
Accepted 4 March 2009
Available online 8 April 2009
The evaporation properties of motor gasoline are expected to change markedly with the progress of
evaporation because gasoline is a multi-component fuel. The aim of this paper was to develop a
prediction model of the amount of vapor generated from gasoline spill. The risks associated with
gasoline spills can be accurately evaluated by the models. Degraded samples of regular gasoline and
high-octane gasoline were prepared by leaving them under conditions of no wind at 20 1C, and their
vapor pressures and flash points were measured. The evaporation rate was measured by determining
weight loss using an electronic balance, and the relation between the weight loss fraction and the
evaporation rate was investigated. ‘‘Weight loss fraction’’ was used as a parameter signifying the
progress of evaporation and expressed the changes in vapor pressure and evaporation rate as a function
of the weight loss fraction. The vapor pressure and the evaporation rate could be shown by exponential
functions of the weight loss fraction, and a prediction model of the amount of gasoline vapor was
obtained. Furthermore, the prediction model of the flash point of degraded gasoline was derived from
the relational expression of temperature and vapor pressure, and the predicted flash points were
compared with the measured values.
& 2009 Elsevier Ltd. All rights reserved.
Keywords:
Evaporation rate
Vapor pressure
Degraded gasoline
Fuel spill
Flash point
1. Introduction
Gasoline is highly volatile, and since volatile components
evaporate easily, a large amount of vapor is quickly generated
from the gasoline surface. The gasoline vapor mixes with air, and a
flammable gas zone is formed in the immediate surroundings.
If the flammable gas zone in an enclosure is ignited, the
gasoline vapor burns explosively, and causes extensive damage.
In cases in which motor gasoline is spilt deliberately in an
enclosed area for the purpose of arson, attention must be paid to
the fire hazard caused by not only the spilt gasoline but also the
released gasoline vapor [1]. It is necessary to predict the amount
of gasoline vapor to estimate its concentration in the enclosed
area. When gasoline evaporates, the low-boiling-point components are lost preferentially. Because gasoline is a multicomponent mixture, the chemical composition changes gradually
and the evaporation rate slows down gradually as the lighter
components are lost. This makes accurate prediction difficult. In
this paper, the composition change of gasoline by evaporation is
described as ‘‘degradation’’.
Corresponding author. Tel.: +81 4 71358001; fax: +81 4 71339169.
E-mail address: [email protected] (K. Okamoto).
0379-7112/$ - see front matter & 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.firesaf.2009.03.004
If the contribution of vapor at the surface of liquid spill is
ignored, the evaporation rate of spilt liquid is given by
N ¼ kAe P=ðRTÞ
(1)
where N is the evaporative molar flux (mol/s), Ae is the evaporative
area (m2), k is the mass transfer coefficient (m/s), P is the vapor
pressure of the bulk liquid (N/m2), R is the gas constant (8.314 J/
mol K), and T is the environmental temperature (K). Stiver et al. [2]
derived the relationship between the evaporated volume fraction of
oil spills and time from Eq. (1) and compared the relationship with
evaporative data of crude oil. Their equation has been modified by
many researchers, and the evaporation models of oil spills, such as
crude oil and gasoline at sea, have been reported [3–8]. Fingas
clarified empirically that most crude oil and petroleum products
evaporate at logarithmic rate with respect to time, and presented a
simple model for predicting the weight loss fraction considering the
temperature variations [9–11]. The depth of a fuel oil spill on a floor,
which is typically a few mm, changes depending on the floor
conditions [12]. The evaporation conditions, such as the thickness of
spill, spill area, and the amount of spill, are expected to influence the
evaporation rate. Fingas’ model cannot be applied to predict the
amount of gasoline vapor under different evaporation conditions
because it is an empirical model under limited conditions. Therefore,
it is necessary to develop a model considering the degradation
conditions for accurate prediction of the amount of gasoline vapor.
ARTICLE IN PRESS
K. Okamoto et al. / Fire Safety Journal 44 (2009) 756–763
Nomenclature
Ae
A, B
CA, CB
DA, DB
N
P
R
evaporative area (m2)
Clausius–Clapeyron constant ()
slopes of the approximate straight lines of constants A
and B (dimensionless)
intercepts of the approximate straight lines of
constant A and B (dimensionless)
evaporative molar flux (mol/s)
vapor pressure of a bulk liquid (N/m2)
gas constant (8.314 J/mol K)
In this study, vapor-pressure histories and evaporation-rate
histories of gasoline were measured in evaporation processes
under various conditions, and gasoline evaporation was examined
quantitatively. ‘‘Weight loss fraction’’ was used as a parameter to
identify the extent of degradation of gasoline. The weight loss
fraction a is given by
a ¼ ðw0 wÞ=w0
S
T
a
k
m, n
p
t
v
w0
w
757
evaporative area (m2)
ambient temperature (K)
weight loss fraction (dimensionless)
mass transfer coefficient (m/s)
constants of evaporation rate curve ()
vapor pressure (kPa)
time (s)
evaporation rate (kg/m2 s)
initial weight of gasoline (kg)
current weight of gasoline (kg)
reached 0.7. The experiments were conducted under a fume hood.
The fume hood fan was not operated, and gasoline was degraded
under conditions of no wind. The amounts of gasoline were 100,
150, and 200 mL (depth of gasoline spill d: 1, 1.5, and 2 mm,
respectively). A thermocouple of 80 m was placed on the base of
the pan, and the temperature of gasoline was measured.
(2)
where w0 is the initial weight of gasoline (kg) and w is the weight
of gasoline (kg) at the time of measurement. The relationships
between weight loss fraction and evaporation properties, such as
vapor pressure and evaporation rate, were clarified. The measured
vapor pressure was the saturated vapor pressure. The relation
between temperature and saturated vapor pressure was analyzed
using the Clausius–Clapeyron equation. In addition, a model for
prediction of the amount of gasoline vapor was derived.
Flash point is used to characterize the flammability of liquid
fuels. The vapor pressure of gasoline is so high that the flash point
is considerably lower than room temperature [13]. The flash point
of gasoline is expected to rise with evaporation of low-boilingpoint components. Therefore, changes in the flash point with
progress of degradation were also measured.
2.4. Flash point measurement
Flash point was measured using an automated closed-cup flash
point tester (AVP-30D; Tanaka Scientific Ltd.). A sample of 50 mL
of degraded gasoline was put into a sample cup, which was then
covered with a lid. A pilot flame was brought closer to the inner
2. Experimental
2.1. Degraded samples
Eight degraded samples with different weight loss fractions
from 0 to 0.7 in increments of 0.1 were prepared by leaving
regular and high-octane motor gasoline samples in a tray at 20 1C.
2.2. Vapor pressure measurement
Vapor pressure of the degraded samples was measured at
10–40 1C in steps of 5 1C using an automated vapor pressure tester
(AVP-30D; Tanaka Scientific Ltd.). A sample cylinder was filled
with 30 ml of degraded sample and submerged in a water bath
maintained at a predetermined temperature. The cylinder was
shaken in the water bath for 8 min until the sample inside the
cylinder reached a constant temperature, and then the pressure
rise in the cylinder was measured as vapor pressure.
2.3. Evaporation rate measurement
Evaporation rate was measured by weight loss using an
electronic balance (CP4202S; Sartorius) with an accuracy of
0.01 g. A tared square pan (base area: 0.1 m2) was loaded on the
balance, and regular gasoline or high-octane gasoline was poured
into the tray, and then the weight loss was measured. The data
were recorded on a PC every 10 s until the weight loss fraction
Fig. 1. Temperature changes in vapor pressure of degraded samples of gasoline: (a)
regular gasoline and (b) high-octane gasoline.
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K. Okamoto et al. / Fire Safety Journal 44 (2009) 756–763
space of the cup through an observation hatch in steps of 0.5 1C,
while heating the sample at an increasing rate of 1 1C/min. Flash
point is defined as the lowest temperature where a flash was
observed. Flash point was determined automatically. Each sample
was examined three times. A flash point below 30 1C could not
be measured because the refrigerator of the flash point tester
cannot cool samples to less than 30 1C.
a straight line (Fig. 2). Constants A and B of the Clausius–Clapeyron equation were obtained from the intercept and the slope of the
experimental linear plots, respectively. These constants are
plotted against the weight loss fraction a in Fig. 3. The results
indicated that A and B are linearly related to the weight loss
fraction. The slopes and intercepts of the approximate straight
lines of A and B are expressed by CA, DA, CB, and DB, respectively.
A and B are then given by
3. Results and discussion
A ¼ C A a þ DA
(4)
3.1. Changes in vapor pressure of gasoline with progress of
evaporation
B ¼ C B a þ DB
(5)
Substitution of Eqs. (4) and (5) into the Clausius–Clapeyron
equation yields
The vapor pressures of degraded regular and high-octane
gasoline varied with temperature as shown in Fig. 1. The vapor
pressure increased as the temperature rose. The relation between
vapor pressure p and temperature T in a multi-component fuel
mixture can be explained by the Clausius–Clapeyron equation
[3,14]
ln p ¼ A B=T
ln p ¼ ðC A C B =TÞa þ ðDA DB =TÞ
(6)
p ¼ expðDA DB =TÞ expðC A C B =TÞa
(7)
(3)
The logarithm of vapor pressure was plotted against the reciprocal
of the absolute temperature, and they were shown to lie almost on
Fig. 3. Correlation of weight loss fraction with constants of Clausius–Clapeyron
equation: (a) regular gasoline and (b) high-octane gasoline.
Table 1
Slopes and intercepts of the approximate straight lines of A and B.
Fig. 2. Clausius–Clapeyron plots of degraded samples: (a) regular gasoline and (b)
high-octane gasoline.
Type of gasoline
Slope of A
CA
Intercept of A
DA
Slope of B
CB
Intercept of B
DB
Regular gasoline
High-octane gasoline
2.51
3.40
14.0
14.1
2.23 103
2.14 103
2.96 103
3.10 103
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K. Okamoto et al. / Fire Safety Journal 44 (2009) 756–763
Thus, if the temperature is constant, the vapor pressure p can be
expressed as an exponential function of the weight loss fraction a.
The values of CA, DA, CB, and DB are shown in Table 1. The change in
vapor pressure of gasoline can be determined from these values
using Eq. (7) as shown in Fig. 4. Low-boiling-point components
are lost and chemical composition of gasoline changes gradually
with the progress of evaporation, as gasoline is a multicomponent fuel mixture. Consequently, the vapor pressure
decreases exponentially as the weight loss fraction increases.
At the boiling point, vapor pressure is equal to atmospheric
pressure. The boiling points of degraded gasoline were predicted
using Eq. (6), which expresses the relation between temperature
and vapor pressure. The predicted boiling points of degraded
gasoline are shown in Fig. 5. These show the range of boiling
points when gasoline is distilled.
759
decreased rapidly over time. The decrease was more rapid in the
case of gasoline depth d ¼ 1 mm than d ¼ 2 mm. The reason is
that the amount of low-boiling-point component is less, and the
3.2. Change in evaporation rate of gasoline with progress of
evaporation
Time-related variations in the amount of gasoline vapor in
each evaporation experiment are shown in Fig. 6. Evaporation rate
v (kg/m2 s) was obtained from the weight loss at intervals of 10 s
in a 0.3 and 60 s in a 0.3. Time-related variations in evaporation rate are shown in Fig. 7. The evaporation rate of gasoline
Fig. 4. Variation of vapor pressure with progress in evaporation: (a) regular
gasoline and (b) high-octane gasoline.
Fig. 5. Variation of boiling point with progress in evaporation.
Fig. 6. Weight loss curves during evaporation of different layer depths: (a) regular
gasoline and (b) high-octane gasoline.
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K. Okamoto et al. / Fire Safety Journal 44 (2009) 756–763
Fig. 7. Variation of evaporation rates with time: (a) regular gasoline and (b) highoctane gasoline.
chemical composition changes more rapidly at 1 mm than at
2 mm. The vapor pressure at each measured weight loss fraction
was calculated from the measured gasoline temperature using Eq.
(7). The evaporation rate was plotted against the vapor pressure as
shown in Fig. 8. From the results of the plots, it was clear that the
evaporation rate was proportional to the vapor pressure
v/p
(8)
i.e.
v1 ¼ ðp1 =p2 Þv2
(9)
The evaporation rate can be calculated from the ratio of the
vapor pressure using Eq. (9). The temperature of gasoline was
influenced by the ambient temperature and decreased by the
latent heat of evaporation during the evaporation experiments.
Therefore, the temperature differed between the experiments. In
order to simplify comparisons between the experiments, the
measured evaporation rate, vmeas, was converted to the evaporation rate at 20 1C, v20 C , using the following equation:
v20 C ¼ ðp20 C =pmeas Þvmeas
(10)
The vapor pressure at the measured temperature of gasoline
was calculated from the weight loss fraction using Eq. (7).
The relation between weight loss fraction and v20 C is shown
in Fig. 9. The difference in the evaporation rate curves was
small between the experiments. The evaporation rate was
Fig. 8. Correlation of vapor pressure with evaporation rate: (a) regular gasoline
and (b) high-octane gasoline.
independent of the evaporation conditions, such as the depth of
gasoline, and was expected to be determined only by the weight
loss fraction.
If the temperature of gasoline is constant, Eqs. (7) and (8) can
be replaced by
v ¼ m expðnaÞ
(11)
The evaporation rate as well as the vapor pressure can be
expressed as an exponential function of the weight loss fraction
if the temperature is constant. The logarithms of the evaporation
rate at 20 1C were plotted against the weight loss fractions as
shown in Fig. 10, and the constants m and n were obtained from
the intercepts and slopes of the linear plots. The evaporation rates
at 20 1C of the regular gasoline and high-octane gasoline in this
study are given by
v20 C; reg ¼ 0:000496 expð5:13aÞ
(12)
v20 C; hi-oc ¼ 0:000407 expð4:68aÞ
(13)
The evaporation rates of the regular gasoline and high-octane
gasoline from 10 to 30 1C were predicted using Eqs. (9), (12) and
(13). The evaporation rate curves with varying temperature are
shown in Fig. 11.