Page 1
Handbook of Oil Spill Science and Technology, First Edition. Edited by Merv F. Fingas.
© 2015 John Wiley & Sons, Inc. Published 2015 by John Wiley & Sons, Inc.
207
7.1 IntroductIon
Evaporation is an important process for most oil spills. In a
few days, typical crude oils can lose up to 45% of their
volume [1]. Most oil spill models include evaporation as a
process and output of the model. Despite the importance of
the process, only little work has been conducted on the basic
physics and chemistry of oil spill evaporation [2]. The diffi-
culty with studying oil evaporation is that oil is a mixture of
hundreds of compounds and this mixture varies from source
to source and even over time. Much of the work described in
the literature focuses on “calibrating” equations developed
for water evaporation [2].
Evaporation plays a strong role in the fate of most oils.
Almost all oils must undergo evaporation before they form
water-in-oil emulsions [1]. Light oils will change very dra-
matically from fluid to viscous. Heavy oils will become
solid-like. Many oils after long evaporative exposure form
tar balls such as illustrated in Figure 7.1.
An important step to understanding evaporation is to
understand the mechanisms that regulate evaporation [3]. If
there were no regulation, evaporation would proceed nearly
instantly. Figure 7.2 shows a schematic of the air-boundary-
layer regulation mechanism. The liquid could evaporate at a
very high rate if it was not for the regulation caused by the
slow transfer of vapor into the air boundary layer. The most
common example of this type of regulation is applicable to
water. Evaporation of water can be increased by spreading it
out or by increasing the wind speed. The wind speed
increases the transfer of water across the air boundary layer.
Many liquids are not air-boundary-layer regulated pri-
marily because they evaporate too slowly to have the vapors
saturate the air boundary layer above them [1]. Many mix-
tures are regulated by the diffusion of molecules inside the
liquid to the surface of the liquid. This regulatory mecha-
nism is illustrated in Figure 7.3. Such a mechanism is true
for many slowly evaporating mixtures of compounds such as
oils and fuels. Some of the outcomes of this mechanism may
seem counterintuitive to some people such as that increasing
area may not increase evaporation rate. More importantly,
increasing wind speed does not increase evaporation.
It is possible to have combinations of the two regulation
mechanisms. For example, if a mixture has volatile compo-
nents, these may evaporate via an air-boundary-layer-regu-
lated mechanism, and then the remaining components
evaporate via a diffusion-regulated mechanism.
Scientific work on water evaporation is decades old
and forms the basis for early oil evaporation work [1,3,4].
There are several fundamental differences between the
evaporation of a pure liquid such as water and that of a
multicomponent system such as crude oil. The evaporation
rate for a single liquid such as water is a constant with
respect to time [3,4]. Evaporative loss, either by weight or
oIl And Petroleum evAPorAtIon
UNCORRECTED PROOFS
Merv F. Fingas
Spill Science, Edmonton, Alberta, Canada
7
7.1 Introduction
7.2 Review of Historical Concepts
7.3 Development of New Diffusion-Regulated Models
7.3.1 Wind Experiments
7.3.2 Variation with Area
7.3.3 Variation with Mass
7.3.4 Evaporation of Pure Hydrocarbons
7.3.5 Saturation Concentration
7.3.6 Development of Generic Equations
Using Distillation Data
7.4 Complexities to the Diffusion-Regulated Model
7.4.1 Oil Thickness
7.4.2 The Bottle Effect
7.4.3 Skinning
7.4.4 Jumps from the 0-Wind Values
7.5 Use of Evaporation Equations in Spill Models
7.6 Volatilization
7.7 Measurement of Evaporation
7.8 Summary
207
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213
213
214
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215
216
216
218
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OIL AND PETROLEUM EVAPORATION
volume, is not linear with time for crude oils and other
multicomponent fuel mixtures [5].
Evaporation of a liquid can be considered as the movement
of molecules from the surface into the vapor phase above it.
The immediate layer of air above the evaporation surface is
known as the boundary layer [6]. This boundary layer is the
intermediate phase between the air and the liquid and might
be viewed as very thin such as less than 1 mm. The charac-
teristics of this air boundary layer can influence evaporation.
In the case of water, the boundary layer regulates the evapo-
ration rate. Air can hold a variable amount of water, depend-
ing on temperature, as expressed by the relative humidity.
Under conditions where the boundary layer is not moving
(no wind) or has low turbulence, the air immediately above
the water quickly becomes saturated and evaporation slows.
In actuality, the actual evaporation of water proceeds at a
small fraction of the possible evaporation rate because of the
saturation of the boundary layer [6]. The air-boundary-layer
physics is then said to regulate the evaporation of water. This
regulation manifests as the increase of evaporation with
wind or turbulence. When turbulence is weak, evaporation
can slow down by orders of magnitude. The molecular diffu-
sion of water molecules through air is at least 103 times
slower than turbulent diffusion [6].
The rate of molecular diffusion for water is about 105
slower than the maximum rate of evaporation, purely from
thermodynamic considerations [6]. The rate for turbulent
diffusion, the combination of molecular diffusion and
movement with turbulent air, is in the order of 102 slower
than that for maximum evaporation. For air-boundary-
layer-regulated liquids, one can write the mass transfer
rate in semiempirical form (also in generic and unitless
form) as [4]
u
E K C T S
?
(7.1)
where E is the evaporation rate in mass per unit area; K is
the mass transfer rate of the evaporating liquid, presumed
constant for a given set of physical conditions, sometimes
denoted as kg (gas-phase mass transfer coefficient, which
may incorporate some of the other parameters noted here);
C is the concentration (mass) of the evaporating fluid as a
mass per volume; Tu is a factor characterizing the relative
intensity of turbulence; and S is a factor that relates to the
saturation of the boundary layer above the evaporating
liquid. The saturation parameter, S, represents the effects of
local advection on saturation dynamics. If the air is already
saturated with the compound in question, the evaporation
rate approaches zero. This also relates to the scale length of
an evaporating pool. If one views a large pool over which a
wind is blowing, there is a high probability that the air is
saturated downwind and the evaporation rate per unit area
is lower than that for a smaller pool. It is noted that there
are many equivalent ways of expressing this fundamental
evaporation equation.
FIgure 7.1 Photograph of tar balls on a beach on Louisiana
after the 2010 Deep Water Horizon spill. Oil on the seas often ends
up on beaches in the form of tar balls, a highly evaporated residual
of oil.
Air
Air
boundary
layer
Liquid
Diffusion into air is slowest process and limiting
FIgure 7.2 The diffusion into the air layer is the limiting factor
in this case and serves to regulate the evaporation rate. This is
called air-boundary-layer regulation. The evaporation rate is
affected by turbulence in the air which will increase the transfer of
the molecules across the boundary layer. This regulatory mecha-
nism is true for pure liquids that have a high evaporation rate. Water
is an example of such a liquid and is the most common concept held
for evaporation.
Air
Liquid
Liquid surface
FIgure 7.3 Diffusion-controlled regulation mechanism where
the diffusion rate through the evaporating liquid is the limiting
factor and thus the regulation mechanism. This mechanism is gen-
erally applicable to oils, fuels, and many other mixtures of liquids
that both evaporate more slowly than water and are mixtures.
0002215964.INDD 208 10/9/2014 3:00:13 PM
UNCORRECTED PROOFS
Page 3
REVIEW OF HISTORICAL CONCEPTS
209
Much of the pioneering work for water evaporation was
performed by Sutton, who proposed the following equation
based on empirical work [7]:
E K C Ud Sc
s
r
=
−−
7 9/ 1 9/
(7.2)
where E is the evaporation rate, Cs is the concentration of the
evaporating fluid (mass/volume), U is the wind speed, d is
the area of the pool, Sc is the Schmidt number, and r is the
empirical exponent assigned values from 0 to 2/3. Other
parameters are defined as above. The terms in this equation
are analogous to the very generic equation, (7.1), proposed
above. The turbulence is expressed by a combination of the
wind speed, U, and the Schmidt number, Sc. The Schmidt
number is the ratio of kinematic viscosity of air (ν) to the
molecular diffusivity (D) of the diffusing gas in air, that is, a
dimensionless expression of the molecular diffusivity of the
evaporating substance in air [7]. The coefficient of the wind
power typifies the turbulence level. The value of 0.78 (7/9),
as chosen by Sutton, represents a turbulent wind, whereas a
coefficient of 0.5 would represent a wind flow that was more
laminar. The scale length is represented by d and has been
given an empirical exponent of −1/9. This represents for
water a weak dependence on size. The exponent of the
Schmidt number, r, represents the effect of the diffusivity of
the particular chemical and historically was assigned values
between 0 and 2/3 [7].
Subsequently, boundary-layer regulation was also assumed
to be the primary regulation mechanism for oil and petroleum
evaporation. This assumption was never well tested by exper-
imentation [2]. The implications of these assumptions are that
evaporation rate for a given oil is increased by:
• Increasing turbulence
• Increasing wind speed
• Increasing the surface area of a given mass of oil
These factors can be verified experimentally to test whether
oil is boundary-layer regulated or not [1].
7.2 revIew oF HIstorIcAl concePts
The basis for most of the earlier evaporative work is the
extensive studies on the evaporation of water [3,4]. In fact,
some of the currently used equations still employ portions of
these equations. The pioneering work in the development of
evaporation equations was carried out by Sutton [7]. Sutton
proposed the following equation:
E C U
s
d Sc
r
=
−
Ms
7 9/ 1 9/
(7.3)
where E is the mean evaporation rate per unit area, Ms is the
mass transfer coefficient, Cs is the concentration of the evap-
orating fluid (mass/volume), U is the wind speed, d is the
area of the square or circular pool, Sc is the Schmidt number,
and r is an empirical exponent assigned values from 0 to 2/3.
Blokker was the first to develop oil evaporation equations
for oil evaporation at sea. His starting basis was theoretical
[8]. Oil was presumed to be a one-component liquid. The
distillation data and the average boiling points of successive
fractions were used as the starting point to predict an overall
vapor pressure. The average vapor pressure of these frac-
tions was then calculated from the Clausius–Clapeyron
equation to yield
log
.
p
p
qM
4 57
TT
s
s
=−
11
(7.4)
where p is the vapor pressure at the absolute temperature, T;
ps is the vapor pressure at the boiling point, Ts (for ps, 760 mm
Hg was used); q is the heat of evaporation in cal/g; and M is
the molecular weight.
The term qM/(4.57 Ts) was taken to be nearly constant
for hydrocarbons (=5.0 ± 0.2), and thus, the expression was
simplified to
log/.( )/[]
ppTTT
ss
=−
5 0 (7.5)
From the empirical data and Equation (7.5), the weathering
curve was calculated, assuming that Raoult’s law is valid for
this situation giving qM as a function of the percentage
evaporated. Pasquill’s equation was applied stepwise, and
the total evaporation time obtained by summation:
t
hD
U
PM
=
∑
∆
Kev
β
α
1
(7.6)
where t is the total evaporation time in hours; Δh is the
decrease in layer thickness in m; D is the diameter of the oil
spill; β is a meteorological constant (assigned a value of
0.11); Kev is a constant for atmospheric stability (taken to be
1.2 × 10−8); α is a meteorological constant (assigned a value
of 0.78); P is the vapor pressure at the absolute temperature,
T; and M is the molecular weight of the component or oil
mass [8].
Blokker constructed a small wind tunnel and tested this
equation against the evaporation of gasoline and a medium
crude oil [8]. The observed gasoline evaporation rate was
much higher than was predicted and the crude oil rate was
much lower than predicted. The times of evaporation, how-
ever, were relatively close and Equation (7.6) was accepted.
The aforementioned equations were then incorporated into
spreading equations to yield equations to predict the simul-
taneous spreading and evaporation of oil and petroleum
products.
Mackay and Matsugu approached the problem by using the
classical water evaporation and experimental work [9]. The
water evaporation equation was corrected to hydrocarbons
AQ1
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UNCORRECTED PROOFS
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OIL AND PETROLEUM EVAPORATION
using the evaporation rate of cumene. It was noted that the
difference in constants was related to the enthalpy differences
between water and cumene. Data on the evaporation of water
and cumene have been used to correlate the gas-phase mass
transfer coefficient as a function of wind speed and pool size
by the equation
UNCORRECTED PROOFS
KUX Sc
m=
−−
0 0292.
0 78. 0 11. 0 67.
(7.7)
where Km is the mass transfer coefficient in units of mass per
unit time and X is the pool diameter or the scale size of the
evaporating area. Note that the exponent of the wind speed,
U, is 0.78, which is equal to the classical water evaporation-
derived coefficient. Mackay and Matsugu noted that for
hydrocarbon mixtures the evaporation process is more com-
plex, being dependent on the liquid diffusion resistance
being present. Experimental data on gasoline evaporation
were compared with computed rates. The computed rates
showed fair agreement and suggested the presence of a liq-
uid-phase mass transfer resistance.
This work was subsequently extended by the same group
to show that the evaporative loss of a mass of oil spilled can
be estimated using a mass transfer coefficient, Km, as shown
earlier [10]. This approach was investigated with some labo-
ratory data and tested against some known mass transfer
conditions on the sea. The conclusion was that this mass
transfer approach could result in predictions of evaporation
at sea.
Butler developed a model to examine evaporation of
specific hydrocarbon components [11]. The weathering rate
was taken as proportional to the equilibrium vapor pressure,
P, of the compound and to the fraction remaining:
dx dt
/
kP x x
( /)
= −
o (7.8)
where x is the amount of a particular component of a crude
oil at time, t; xo is the amount of that same component pre-
sent at the beginning of weathering (t = 0); k is an empirical
rate coefficient; and P is the vapor pressure of the chosen oil
component.
Butler assumed that petroleum is a complicated mixture of
compounds; therefore, P is not equal to the vapor pressure of
the pure compound, but neither would there be large variation
in the activity coefficient as the weathering process occurs
[11]. For this reason, the activity coefficients were subsumed
in the empirical rate coefficient k. P and k were taken as
independent of the amount, x, for a fairly wide range of oils.
The equation was then directly integrated to give the fraction
of the original compound remaining after weathering as
x x
/
ktP x
exp(/)
oo
=−
(7.9)
The vapor pressure of individual components was fit using
a regression line to yield a predictor equation for vapor
pressure [11]:
PN
=−
exp(..) 10 94 1 06 (7.10)
where P is the vapor pressure in Torr and N is the carbon
number of the compound in question.
This combined with Equation (7.9) yielded the following
expression:
x x
/
t x
/k
N
exp[ () exp(.. )]
oo
=−−
10 94 1 06 (7.11)
where x/xo is the fraction of the component left after
weathering, k is an empirical constant, xo is the original
quantity of the component, and N is the carbon number of
the component in question [1].
Equation (7.11) predicts that the fraction weathered is a
function of the carbon number and decreases at a rate that is
faster than predicted from simple exponential decay [11]. If
the initial distribution of compounds is essentially uniform
(xo independent of N), then the aforementioned equation
predicts that the carbon number where a constant fraction
(e.g., half) of the initial amount has been lost (x = 0.5 xo) is a
logarithmic function of the time of weathering:
N t x
/k
1 2/
10 66. 2 17. log()
=+
o (7.12)
where N1/2 is half the volume fraction of the oil.
The equation was tested using evaporation data from
some patches of oil on shoreline, whose age was known
[11]. The equation was able to predict the age of the samples
relatively well. It was suggested that the equation was appli-
cable to open water spills; however, this was never subse-
quently applied in models.
Yang and Wang developed an equation using the Mackay
and Matsugu molecular diffusion process [12]. The vapor-
phase mass transfer process was expressed by
DkppT
miis
ie
R
=−
∞
( )/[] (7.13)
where Die is the vapor-phase mass transfer rate, km is a coef-
ficient that lumps all the unknown factors that affect the
value of Die, pi is the hydrocarbon vapor pressure of fraction
I at the interface, pi∞ is the hydrocarbon vapor pressure of
fraction I at infinite altitude of the atmosphere, R is the
universal gas constant, and Ts is the absolute temperature of
the oil slick.
The following functional relationship was proposed [12]:
k A e
m
qU
=α
γ
(7.14)
where A is the slick area; U is the overwater wind speed; and
α, q, and γ are empirical coefficients. This relationship was
based on the results of past studies, including, for instance,
those of MacKay and Matsugu who suggested the value of γ
to be in the range from −0.025 to −0.055 [9]. Further exper-
iments were performed by Yang and Wang to determine the
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REVIEW OF HISTORICAL CONCEPTS
211
values of “a” and “q.” The results were found to be twofold.
Experiments showed that a film formed on evaporating oils
and that this film severely retarded evaporation. Before the
surface film developed (ρt/ρo < 1.0078),
UNCORRECTED PROOFS
KAe
U
mb=
−
69
0 0055 0 42..
(7.15)
where Kmb is the coefficient that groups all factors affecting
evaporation before the surface film has formed and A is the
area.
After the surface film developed (ρt/ρo > 1.0078),
Kk
mamb
?1 5/ (7.16)
where ρo is the initial oil density, ρt is the weathered oil
density at time t, and Kma is the coefficient that groups all
factors affecting evaporation after the surface film has
formed [12]. The evaporation rate was found to be reduced
fivefold after the formation of the surface film.
Drivas compared the Mackay and Matsugu equation with
data found in the literature and noted that the equations
yielded predictions that were close to the experimental data
[13]. Reijnhart and Rose developed a simple predictor model
for the evaporation of oil at sea [14]. They proposed the fol-
lowing simple relationship:
QC
eio
=α
(7.17)
where Qei is the evaporation rate of the component of interest,
α is a constant incorporating wind velocity and other factors
(taken as 0.0009 m/s), and Co is the equilibrium concentration
of the vapor at the oil surface. Several pan experiments were
run to simulate evaporation at sea and the data used to test
the equation [13]. No method was given for calculating the
essential value, Co.
Brighton proposed that the standard formulation used by
many workers required refining [15]. His starting point for
water evaporation was similar to that proposed by Sutton:
E C U
s
d Sc
r
=
−−
Km
7 9/ 1 9/
(7.18)
where E is the mean evaporation rate per unit area; Km is an
empirically determined constant, presumably related to the
foregoing mass transfer constant; Cs is the concentration of
the evaporation fluid (mass/volume); d is the area of the
pool; and r is an empirical exponent assigned values from 0
to 2/3.
Brighton suggested that this equation should conform to
the basic dimensionless form involving the parameters U
and z0 (wind speed and roughness length, respectively),
which define the boundary-layer conditions [15]. The key
factor in Brighton’s analysis was to use a linear eddy diffu-
sivity profile. This feature implied that concentration pro-
files become logarithmic near the surface, which is suspected
to be more realistic compared with the more finite values
previously used. Using a power profile to provide an
estimation of the turbulence, Brighton was able to substitute
the following identities into the classical relationship:
U
u
k
n
?
*
(7.19)
n
z
z
=
ln
1
0
(7.20)
where u* is the friction velocity, z1 is the reference height
above the surface, z0 is the roughness length, and n is the
power law dimensionless term.
The evaporation equation now became
U
z
z
X
x
ku z X
σ
z
z
1
=
δ
δ
δ
δ
δ
δ
*
(7.21)
where z is the height above the surface, Χ is the concentration of
the evaporating compounds, x is the dimension of the evapo-
rating pool, k is given by K/u*z and is the von Karman constant,
and σ is the turbulent Schmidt number (taken as 0.85).
Brighton subsequently compared his model with experi-
mental evaporation data in the field and in the laboratory,
which included laboratory oil evaporation data [16]. The model
only correlated well with laboratory water evaporation data,
and the reason given was that other data sets were “noisy.”
Tkalin proposed a series of equations to predict evapora-
tion at sea [17]:
E
K M P x
RT
i
ii
=
α
oi
(7.22)
where Ei is the evaporation rate of component i (or the sum
of all components) (kg/m2∙s),
Ka is the mass transfer coefficient (m/s), Mi is the molec-
ular weight, Poi is the vapor pressure of the component i, and
xt is the amount of component i at time t.
Using empirical data, relationships were developed for
some of the factors in the equation
PeA
oi?103
(7.23)
where
ATTTTT
= −+−−
( .4 4log ) .[1 803{/}.ln(/ )]10 803
bbb
(7.24)
where Tb is the boiling point of the hydrocarbon, given as
Ka=
−
1 25.10
3
U (7.25)
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OIL AND PETROLEUM EVAPORATION
The equations were verified using empirical data from the
literature [17].
The most frequently used work in older spill modeling is
that of Stiver and Mackay [18]. It is based on some of the
earlier work by Mackay and Matsugu [9]. Additional
information is given in a thesis by Stiver [19]. The formula-
tion was initiated with assumptions about the evaporation
of a liquid. If a liquid is spilled, the rate of evaporation is
given by
UNCORRECTED PROOFS
N KAP RT
?
/() (7.26)
where N is the evaporative molar flux (mol/s), K is the mass
transfer coefficient under the prevailing wind (m/s), A is the
area (m2), and P is the vapor pressure of the bulk liquid.
This equation was arranged to give
dF dt KAPV RT
/(
o
v/)
=ν
(7.27)
where Fv is the volume fraction evaporated, v is the liquid’s
molar volume (m3/mol), and Vo is the initial volume of the
spilled liquid (m3).
By rearranging, we obtain
dFP RT KAdt V
θ
v=[ /( )](/)
ν
o
(7.28)
orH
dFd
v=
(7.29)
where H is Henry’s law constant and θ is the evaporative
exposure (defined in the following).
The right-hand side of the second last equation has been
separated into two dimensionless groups. The group,
KAdt/Vo, represents the time rate of what has been termed the
“evaporative exposure” and was denoted as dθ. The evapora-
tive exposure is a function of the time, the spill area and
volume (or thickness), and the mass transfer coefficient
(which is dependent on the wind speed). The evaporative
exposure can be viewed as the ratio of exposed vapor volume
to the initial liquid volume [18].
The group Pν/(RT) or H is a dimensionless Henry’s law
constant or ratio of the equilibrium concentration of the sub-
stance in the vapor phase [P/(RT)] to that in the liquid (l/ν).
H is a function of temperature. The product θH is thus the
ratio of the amount that has evaporated (oil concentration in
vapor times vapor volume) to the amount originally present.
For a pure liquid, H is independent of Fv and Equation 7.29
was integrated directly to give
FH
v=θ (7.30)
If K, A, and temperature are constant, the evaporation rate is
constant and evaporation is complete (Fv is unity) when θ
achieves a value of 1/H [18].
If the liquid is a mixture, H depends on Fv and the basic
equation can only be integrated if H is expressed as a function
of Fv; that is, the principal variable of vapor pressure is
expressed as a function of composition. The evaporation rate
slows as evaporation proceeds in such cases.
Equation (7.28) was replaced with a new equation devel-
oped using laboratory empirical data:
FTTT
v=+−
( / )ln/ exp/()()KKKK
1123
1
θ
(7.31)
where Fv is the volume fraction evaporated and K1,2,3 are
empirical constants [18].
A value for K1 was obtained from the slope of the Fv
versus log θ curve from pan or bubble evaporation experi-
ments. For θ greater than 104, K1 was found to be approxi-
mately 2.3 T divided by the slope. The expression
exp(K2 − K3/T) was then calculated, and K2 and K3 deter-
mined individually from evaporation curves at two different
temperatures.
Hamoda and coworkers performed theoretical and exper-
imental work on evaporation [20]. An equation was devel-
oped to express the effects of American Petroleum Institute
gravity (APIo—a unit of density) of the crude oil, tempera-
ture, and salinity on the mass transfer coefficient K:
KTe
=×
−
1 68 10.
5 1 253
)
1 80. 0 1441.
( ( )
.
APIo
(7.32)
where K is the mass transfer coefficient, cm/h; APIo is the
density in API units, unitless; and e is the water salinity in
degrees salinity or parts per thousand. The exponents of the
equation were determined by multiple linear regression on
experimental data.
Quin and coworkers weathered oils in a controlled envi-
ronment and correlated the data with equations developed
starting with Fick’s diffusion law and the Clausius–
Clapeyron equation [21]. Crude oil was divided into a series
of pseudofractions by boiling point. Each fraction was taken
to be equivalent to an n-paraffin. The n-paraffin distributions
of a number of naturally weathered crude oils were deter-
mined by capillary gas–liquid chromatography. The actual
measured evaporation was compared with those generated
by computer simulation of weathering. Good agreement was
obtained for oil film thicknesses between 10 µm and 1 mm,
weathered for periods of up to 4 weeks.
Brown and Nicholson studied the weathering of a heavy
oil, bitumen [22]. They compared experimental data using a
large-scale weathering tank with two spill model outputs. In
the Fate Of Oil Spills model, the evaporative exposure con-
cept is used in which the fraction of oil evaporated is given
by a variant of the Mackay equation:
FPEP C
/ ]/
=++
[ln( ) ln()C1 (7.33)
where F is the fraction evaporated, C is an empirical constant,
and E is a measure of the evaporative exposure, defined as
E K Avt
m
RTV
? ()/()
o (7.34)
AQ2
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DEVELOPMENT OF NEW DIFFUSION-REGULATED MODELS
213
where
Km = 0.0048 U0.78Z− 0.11Sc0.67 (7.35)
and where Km is the mass transfer coefficient, A is the slick
area, v is the oil molar volume, Vo is the initial slick volume,
Z is the pool size scale factor, and Sc is the Schmidt number
(taken as 2.7) [22].
Brown and Nicholson compared the measured evapora-
tion for a 5 m/s wind at an ambient temperature of 20°C, and
evaluation was done with the equation earlier. A spill volume
of 100 m3 was assumed. A value of about 10−5 m3/mol was
used for the average molar volume. The model generally
described the observed evaporation quite well, particularly
during the first few hours. Later however, it was found that
the model consistently overpredicted the evaporation rate. A
simple method of correcting the equation was implemented
by assuming that the vapor-phase Schmidt number decreases
slightly as the skin on the oil thickens. Subsequently, the
evaporative exposure was modified to
K t U
)
m=−
( . 0 0025 0 000021.
. 0 78 (7.36)
The predicted evaporation then compared favorably with the
measured values.
A commercial model was also compared with the experi-
mental data [22]. This model assumed that the oil consists of
a series of components each with a distinct boiling point,
API gravity, and molecular weight. A mass transfer rate from
the slick was then written for each component as
dm dtK P AF
mi
RT
ii
//
?
Mass (7.37)
where dm/dt is the mass transfer rate, Km is the mass transfer
coefficient of Mackay, Pi is the vapor pressure of each com-
ponent, Fi is the fraction of each component remaining, and
Massi is the mass of each component.
For this simulation, boiling points, volume percents, and
API gravities were input for 13 boiling ranges. The general
shape of the model curve agreed well with the measured data
but the model predicts a higher overall evaporation rate.
Bobra conducted laboratory studies on the evaporation of
crude oils [23]. The evaporation curves for several crude oils
and petroleum products were measured under several differ-
ent environmental conditions. These data were compared to
the equation developed by Stiver and Mackay [19]. The
equation used was
FTT T T
o
TT
V=+−
ln[/ exp( / )]{ /} 1 B()ABB
GG
θ
(7.38)
where FV is the fraction evaporated, TG is the gradient of
the modified distillation curve, A and B are dimensionless
constants, To is the initial boiling point of the oil, and θ is the
evaporative exposure as previously defined.
The results from several comparison runs were carried out
to evaluate evaporation models [23]. The agreement between
the experimental data and the equation results were good in a
few cases, but poor in most. This comparison showed that the
Stiver and Mackay equation predicts the evaporation of most
oils relatively well until time approaches 8 h, after which it
overpredicted the evaporation. The “overshoot” could be as
much as 10% evaporative loss at the 24 h mark. This is espe-
cially true for very light oils. The Stiver and Mackay equation
was also found to underpredict or overpredict the evaporation
of oils in the initial phases. Bobra also noted that most oil
evaporation follows a logarithmic curve with time and that a
simple approach to this was much more accurate than using
Equation (7.38) [23].
In summary, it is difficult to develop a theoretical approach
to oil evaporation for several reasons. First, oil consists of
many components, and thus, there is no constant boiling point,
vapor pressure, or other essential properties used in typical
evaporation models. Further, oil evaporation proceeds by dif-
fusion regulation and not by air-boundary-layer regulation.
Water evaporation models cannot be accurately modified to
oil evaporation for these reasons.
7.3 develoPment oF new
dIFFusIon-regulAted models
A review of the predictive and theoretical work in Section 7.2
reveals that air-boundary-layer concepts are limited and
cannot accurately explain long-term evaporation. Fingas
conducted a series of experiments over several years to
examine the concepts further [1,24].
The results of the boundary-layer regulation experiments
are presented in the order of the experimental series.
7.3.1 wind experiments
A simple experiment to determine whether or not oil evapora-
tion is air-boundary-layer regulated is to measure if the evap-
oration rate increases with wind as would be predicted by
Equations (7.2 and 7.7) [24]. Experiments on the evaporation
of oil with and without winds were conducted with Alberta
Sweet Mixed Blend (ASMB), gasoline, and water. Water
formed a baseline data set since this is the substance being
compared [3]. Regressions on the data were performed and
the equation parameters calculated. Curve coefficients are the
constants from the best-fit equation [Evap = a ln(t)], t = time in
minutes, for logarithmic equations or Evap = a √ t, for square
root equations. Oils such as diesel fuel with few subcompo-
nents evaporating at one time have a tendency to fit square
root curves [5,25]. While data were calculated separately for
percentage of weight lost and absolute weight, the latter is
usually used because it is more convenient. The plots of wind
speed versus the evaporation rate (as a percentage of weight
lost) for each oil type are shown in Figures 7.4, 7.5, and 7.6.
These figures show that the evaporation rates for oils and even
the light product, gasoline, are not increased with increasing
wind speed. In most cases, there is a small rise from the
0002215964.INDD 213 10/9/2014 3:00:27 PM
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214
OIL AND PETROLEUM EVAPORATION
0-wind level to the 1-m/s level, but after that, the rate remains
relatively constant. The evaporation rate after the 0-wind
value is nearly identical for all oils. This is due to the stirring
effect on the oil, which increases the diffusion rate to the
surface. The oil evaporation data can be compared to the evap-
oration of water, as illustrated in Figure 7.6. These data show
the classical relationship of the water evaporation rate with the
wind speed (evaporation varies as U0.78, where U is the wind
speed). This correlation shows that the oils studied here not
boundary-layer regulated.
Figure 7.7 shows the rates of evaporation compared to the
wind speed for all the liquids used in this study. This figure
shows the evaporation rates of all test liquids versus wind speed.
The lines shown are those calculated by linear regression. This
clearly shows that water evaporation rate increased, as expected,
with increasing wind velocity. The oils, ASMB and gasoline, do
not show increases with increasing wind speed.
All the aforementioned data show that oil is not air-
boundary-layer regulated.
7.3.2 variation with Area
Air-boundary-layer-regulated liquids evaporate much faster if
one increases the area [24]. A small spill of water on the kitchen
floor can be evaporated quickly by spreading it out. A test of
this tendency will also give confirmation on the proposition that
oil is diffusion regulated. ASMB was also used to conduct a
series of experiments with varying evaporation area. The mass
of the oil was kept constant so that the thickness of the oil would
also vary. However, the greater the area, the lesser the thickness
and both factors would increase oil evaporation if it were
boundary-layer regulated. The experiments showed no correla-
tion between area and evaporation rate. One can conclude that
evaporation rate is not highly correlated with area and thus the
evaporation of oil is not air-boundary-layer regulated.
Time (min)
Wind = 0 m/s
Wind = 1 m/s
Wind = 1.6 m/s
Wind = 2.1 m/s
Wind = 2.6 m/s
0 500 10001500 20002500
Percent evaporated
0
10
20
30
40
50
FIgure 7.4 Evaporation of a crude oil with varying wind veloc-
ities. This figure shows that there is little variation with wind
velocity except in going from the 0-wind level up to high wind
levels. This is due to the stirring effect of wind and not air-bound-
ary-layer regulation.
Time (min)
0 20 4060 80100 120 140 160 180
Percent evaporated
0
20
40
60
80
100
Wind = 0 m/s
Wind = 1 m/s
Wind = 1.6 m/s
Wind = 2.1 m/s
Wind = 2.6 m/s
FIgure 7.5 Evaporation of gasoline subjected to varying wind
velocities. This figure also shows that there is little variation with
wind velocity except in going from the 0-wind level up to the
higher wind levels. This again is because of the stirring effect of
wind and not air-boundary-layer regulation.
Time (min)
0 20 40 6080 100 120 140 160 180
Percent evaporated
0
20
40
60
80
100
Regression line
Wind = 0 m/s
Wind = 1 m/s
Wind = 1.6 m/s
Wind = 2.1 m/s
Wind = 2.6 m/s
FIgure 7.6 Evaporation of water with varying wind velocities.
This figure shows the large differences in the evaporation rate of
water with wind velocity. This is typical of air-boundary-layer reg-
ulation. Compare Figure 7.6 with oil evaporation in Figures 7.4 and
7.5 which do not show this trend of variance with wind velocity.
0002215964.INDD 214 10/9/2014 3:00:30 PM
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DEVELOPMENT OF NEWDIFFUSION-REGULATED MODELS
215
7.3.3 variation with mass
Air-boundary-layer liquids showed no correlation between
the mass of oil evaporated and the evaporation rate; however,
diffusion-regulated liquids do [24]. ASMB oil was again used
to conduct a series of experiments with volume as the major
variant. Alternatively, thickness and area were held constant
to ensure that the strict relationship between these two vari-
ables did not affect the final regression results. Figure 7.8
illustrates the relationship between evaporation rate and
volume of evaporation material (also equivalent to mass of
evaporating material). This figure shows the strong correla-
tion between oil mass (or volume) and evaporation rate. This
again proves that there is no boundary-layer regulation.
7.3.4 evaporation of Pure Hydrocarbons
A study of the evaporation rate of pure hydrocarbons was
conducted to test the classic boundary-layer evaporation
theory as applied to the hydrocarbon constituents of oils [24].
The evaporation rate data are illustrated in Figure 7.9. This
figure shows that the evaporation rates of the pure hydrocar-
bons have a variable response to wind. Heptane (hydrocarbon
number 7) shows a large difference between evaporation rate
in wind and no wind conditions, indicating boundary-layer
regulation. Decane (carbon number 10) shows a lesser effect,
and dodecane (carbon number 12) shows a negligible
difference between the two experimental conditions. This
experiment shows the extent of boundary-layer regulation
and the reason for the small or negligible degree of bound-
ary-layer regulation shown by crude oils and petroleum prod-
ucts. Crude oil contains very little material with carbon
numbers less than dodecane, often less than 3% of its compo-
sition. Even the more volatile petroleum products, gasoline
Wind velocity (m/s)
012
Evaporation rate (%/min or %/ln min)
0
5
10
15
20
25
Water
Gasoline
FCC heavy cycle
ASMB
FIgure 7.7 Correlation of evaporation rates and wind velocity.
The lines are drawn through the data points from experimental values.
This clearly shows no correlation of oil evaporation rates with wind
velocity and the strong and expected high correlation of water with
wind velocity. The water evaporation line has been moved to fit on the
vertical scale. ASMB is Alberta Sweet Mixed Blend crude oil.
AQ3
Weight (g)
020406080 100120140
Evaporation rate (g/ln min)
0
1
2
3
4
5
FIgure 7.8 Correlation of oil mass with evaporation rate. The
plots are the equation factors from the evaporation equation which
is approximately equivalent to evaporation rate. This shows a direct
relationship between evaporation rate of oil and mass of oil. This
indicates that oil is diffusion regulated.
Hydrocarbon number
6810121416
Hexadecane
Evaporation rate (g/min)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Hexane
No wind
Wind
FIgure 7.9 Evaporation rate of pure hydrocarbons. This shows
that hydrocarbons up to about C12 (dodecane) show some air-
boundary-regulated behavior whereas those above C12 show no
air-boundary-regulated behavior. As most compounds in oil are
higher than dodecane, the bulk oil would not show air-boundary-
regulated behavior.
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OIL AND PETROLEUM EVAPORATION
and diesel fuel, only have limited amounts of compounds
more volatile than decane and thus are also not strongly
boundary-layer regulated if at all.
7.3.5 saturation concentration
Another evaluation of evaporation regulation is that of satu-
ration concentration, the maximum concentration soluble in
air. The saturation concentrations of water and several oil
components are listed in Table 7.1 [26]. This table shows
that saturation concentration of water is less than that of
common oil components. The saturation concentration of
water is in fact about two orders of magnitude less than the
saturation concentration of volatile oil components such as
pentane. This further explains why even light oil compo-
nents have little boundary-layer limitation. Further, the satu-
ration concentration of water is so regulating that with a high
relative humidity, there is little that can be added to the air.
7.3.6 development of generic equations using
distillation data
The evaporation equations for oils show unique differences
for oils under the same conditions. This implies that unique
equations may be needed for each oil and this fact is a
significant disadvantage to practical end use. A method to
accurately predict evaporation using other readily available
data is necessary [27]. Findings show that distillation data
can be used to predict evaporation. Distillation data are very
common and are often the only data used to characterize
oils. This is because the data are crucial in operating refin-
eries. Crude oils are sometimes priced on the basis of their
distillation data.
It was noted that oils and fuels evaporated as two distinct
types, those that evaporated as a logarithm of time and those
that evaporated as a square root of time [5]. Most oils typi-
cally evaporated as a logarithm (natural) of time. Diesel fuel
and similar oils, such as jet fuel, kerosene, and the like, evap-
orate as a square root of time [1, 25]. The reasons for this are
simply that diesel fuel and such like have a narrower range
of compounds that evaporate at similar yield rates, which
sum as a square root [5].
The empirically measured parameters at 15°C were cor-
related with both the slopes and the intercepts of the temper-
ature equations. Full details of this correlation are given in
the literature [28–30]. For the variation with temperature, the
resulting equation is
Percentage evaporated =
where B is the equation parameter at 15°C, T is the tempera-
ture in degree Celsius, and t is the time in minutes.
Distillation data were correlated to the evaporation rates
determined by experimentation. The optimal point was found
to be 180°C by using peak functions. The percent mass
distilled at 180° was used to calculate the relationship bet-
ween the distillation values and the equation parameters. The
equations used were derived from correlations of the data.
The data from those oils that were better fitted with square
root equations—diesel, Bunker C light, and FCC heavy
cycle—were calculated separately.
The equations derived from the regressions are as follows:
For oils that follow a logarithmic equation,
+−
[.()]ln( )15
BTt
0 045
(7.39)
For oils that follow a square root equation,
Percentage evaporated ? 0 165. (% )ln( )
Dt (7.40)
where %D is the percentage (by weight) distilled at 180°C.
These equations can be combined with the equations
generated in previous work as shown in Equation (7.39) to
account for the temperature variations:
For oils that follow a logarithmic equation,
Percentage evaporated =√
0 0254.(% )
Dt (7.41)
Percentage evaporated =
+−
[ .0 165
0 045
(% )
(
T
.)]ln( )15
D
t (7.42)
For oils that follow a square root equation,
Percentage evaporated=+−√
[ .0 0254(% ).()]0 0115
DTt
(7.43)
where %D is the percentage (by weight) distilled at 180°C.
A large number of experiments were performed on oils to
directly measure their evaporation curves. The empirical
equations that result are given in Table 7.2.
Since the equations described earlier require only time
and temperature (or at the very worst, the percentage of oil
distilled at 180°C), it is relatively simple to apply these
forms of equations. They can also be applied in models as
increments where t, the time, becomes the total time and the
previous evaporation is subtracted, for example, if one was
modeling the evaporation of ASMB oil in the time step from
12 to 15 h. The equation is (from Table 7.2)
Percentage evaporation =+
( .3 24.)ln( )0 054Tt (7.44)
tAble 7.1 saturation concentration of water and hydrocarbons
Substance
UNCORRECTED PROOFS
Saturation concentrationa
in g/m3 at 25°C
Water
n-Pentane
Hexane
Cyclohexane
Benzene
n-Heptane
Methylcyclohexane
Toluene
Ethylbenzene
p-Xylene
m-Xylene
o-Xylene
20
1689
564
357
319
196
192
110
40
38
35
29
a Values taken from Ullmann’s Encyclopedia [26].
0002215964.INDD 21610/9/2014 3:00:34 PM
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DEVELOPMENT OF NEWDIFFUSION-REGULATED MODELS
217
tAble 7.2 equations for predicting evaporation
Oil typeEquation Oil typeEquation
Adgo, Beaufort Sea
Adgo—long term
Alaminos Canyon Block 25
Alaska North Slope (2002)
Alberta Sweet Mixed Blend
Amauligak, Beaufort Sea
Amauligak—f24
Anadarko H1A-376
Arabian Medium
Arabian Heavy
Arabian Heavy
Arabian Light
Arabian Light
Arabian Light (2001)
ASMB—standard #5
ASMB (offshore)
Av Gas 80
Avalon, NL, Canada
Avalon J-34
Aviation Gasoline 100 LL
Azeri—long term, Azerbaijan
Azeri—short term
Barrow Island, Australia
BCF-24, Venezuela
Belridge Crude, CA, USA
Bent Horn A-02, NS, Canada
Beta, CA, USA
Beta—long term
Boscan, Venezuela
Brent, UK
Bunker C—light (IFO ~ 250)
Bunker C—long term
Bunker C (2002)
Bunker C (short term)
Bunker C anchorage
Bunker C anchorage (long term)
California API 11
California API 15
Cano Limon, Colombia
Canola oil
Carpinteria, CA, USA
Cat Cracking Feed
Chayvo, Russia
Cold Lake Bitumen, AB, Canada
Combined oil/gas
Compressor lube oil—new
Cook Inlet—Granite Point
Cook Inlet—Swanson River
Cook Inlet New Batch
Cook Inlet Trading Bay
Corrosion Inhibitor Solvent
Crude Castor oil
Cusiana, Colombia
Delta West Block 97, USA
Diesel—anchorage—long
Diesel—anchorage—short
Diesel—long term
Diesel Mobile 1997
Diesel (2002)
Diesel (regular stock)
Diesel fuel—Southern—long term
Diesel fuel—Southern—short term
Diesel Fuel 2002
%Ev = (0.11 + 0.013T) √(t)
%Ev = (0.68 + 0.045T)ln(t)
%Ev = (2.01 + 0.045T)ln(t)
%Ev = (2.86 + 0.045T)ln(t)
%Ev = (3.24 + 0.054T)ln(t)
%Ev = (1.63 + 0.045T)ln(t)
%Ev = (1.91 + 0.045T)ln(t)
%Ev = (2.66 + 0.013T) √(t)
%Ev = (1.89 + 0.045T)ln(t)
%Ev = (1.31 + 0.045T)ln(t)
%Ev = (2.71 + 0.045T)ln(t)
%Ev = (2.52 + 0.037T)ln(t)
%Ev = (3.41 + 0.045T)ln(t)
%Ev = (2.4 + 0.045T)ln(t)
%Ev = (3.35 + 0.045T)ln(t)
%Ev = (2.2 + 0.045T)ln(t)
%Ev = (15.4 + 0.045T)ln(t)
%Ev = (1.41 + 0.045T)ln(t)
%Ev = (1.58 + 0.045T)ln(t)
ln(%Ev) = (0.5 + 0.045T)ln(t)
%Ev = (1.3 + 0.045T)ln(t)
%Ev = (−0.09 + 0.013T) √(t)
%Ev = (4.67 + 0.045T)ln(t)
%Ev = (1.08 + 0.045T)ln(t)
%Ev = (0.01 + 0.013T) √(t)
%Ev = (3.19 + 0.045T)ln(t)
%Ev = (−0.08 + 0.013T) √(t)
%Ev = (0.29 + 0.045T)ln(t)
%Ev = (−0.15 + 0.013T) √(t)
%Ev = (3.39 + 0.048T)ln(t)
%Ev = (0.0035 + 0.0026T) √(t)
%Ev = (−0.21 + 0.045T)ln(t)
%Ev = (−0.16 + 0.013T) √(t)
%Ev = (0.35 + 0.013T) √(t)
%Ev = (−0.13 + 0.013T) √(t)
%Ev = (0.31 + 0.045T)ln(t)
%Ev = (−0.13 + 0.013T) √(t)
%Ev = (−0.14 + 0.013T) √(t)
%Ev = (1.71 + 0.045T)ln(t)
Litte
%Ev = (1.68 + 0.045T)ln(t)
%Ev = (−0.18 + 0.013T) √(t)
%Ev = (3.52 + 0.045T)ln(t)
%Ev = (−0.16 + 0.013T) √(t)
%Ev = (−0.08 + 0.013T) √(t)
%Ev = (−0.68 + 0.045T )ln(t)
%Ev = (4.54 + 0.045T)ln(t)
%Ev = (3.58 + 0.045T)ln(t)
%Ev = (3.1 + 0.045T)ln(t)
%Ev = (3.15 + 0.045T)ln(t)
%Ev = (−0.02 + 0.013T) √(t)
Litte
%Ev = (3.39 + 0.045T)ln(t)
%Ev = (6.57 + 0.045T)ln(t)
%Ev = (4.54 + 0.045T)ln(t)
%Ev = (0.51 + 0.013T) √(t)
%Ev = (5.8 + 0.045T)ln(t)
%Ev = (0.03 + 0.013T) √(t)
%Ev = (0.02 + 0.013T) √(t)
%Ev = (0.31 + 0.018T) √(t)
%Ev = (2.18 + 0.045T)ln(t)
%Ev = (−0.02 + 0.013T) √(t)
%Ev = (5.91 + 0.045T)ln(t)
Jet 40 Fuel
Jet A1
Jet Fuel (Anch)
Jet Fuel (Anch) short term
Komineft, Russia
Lago, Angola
Lago Treco, Venezuela
Lucula, Angola
Main Pass Block 306
Main Pass Block 37
Malongo, Angola
Marinus Turbine Oil
Marinus Valve Oil
Mars TLP, GOM, USA
Maui, New Zealand
Maya, Mexico
Mayan crude
Mississippi Canyon Block 807
Mississippi Canyon Block 72
Mississippi Canyon Block 194
Mississippi Canyon Block 807
Morpeth, LA, USA
Nektoralik, Beaufort Sea
Neptune Spar (Viosca Knoll 826)
Nerlerk, Beaufort Sea
Ninian, UK
Norman Wells, Canada
North Slope—middle pipeline
North Slope—northern pipeline
North Slope—southern pipeline
Nugini, New Guinea
Odoptu, Russia
Olive oil
Oriente, Ecuador
Oriente
Orimulsion 400—dewater
Orimulsion plus water
Oseberg, Norway
Panuke, NS, Canada
Petronius VK981A
Pitas Point, CA, USA
Platform Gail (Sockeye)
Platform Holly, CA, USA
Platform Irene—long term
Platform Irene—short term
Point Arguello—comingled
Point Arguello heavy
Point Arguello light
Point Arguello light—b
Polypropylene Tetramer
Port Hueneme, CA, USA
Prudhoe Bay—old stock
Prudhoe Bay (new stock)
Prudhoe stock b
Rangely, CO, USA
Sahara Blend, Algeria
Sahara Blend (long term)
Sakhalin, Russia
Santa Clara, CA, USA
Scotia light
Scotia light
Ship Shoal Block 239
Ship Shoal Block 269
%Ev = (8.96 + 0.045T)ln(t)
%Ev = (0.59 + 0.013T) √(t)
%Ev = (7.19 + 0.045T)ln(t)
%Ev = (1.06 + 0.013T) √(t)
%Ev = (2.73 + 0.045T)ln(t)
%Ev = (1.13 + 0.045T)ln(t)
%Ev = (1.12 + 0.045T)ln(t)
%Ev = (2.17 + 0.045T)ln(t)
%Ev = (2.86 + 0.045T)ln(t)
%Ev = (3.04 + 0.045T)ln(t)
%Ev = (1.67 + 0.045T)ln(t)
%Ev = (−0.68 + 0.045T)ln(t)
%Ev = (−0.68 + 0.045T)ln(t)
%Ev = (2.18 + 0.045T)ln(t)
%Ev = (−0.14 + 0.013T) √(t)
%Ev = (1.38 + 0.045T)ln(t)
%Ev = (1.45 + 0.045T)ln(t)
%Ev = (2.28 + 0.045T)ln(t)
%Ev = (2.15 + 0.045T)ln(t)
%Ev = (2.62 + 0.045T)ln(t)
%Ev = (2.05 + 0.045T)ln(t)
%Ev = (1.58 + 0.013T) √(t)
%Ev = (0.62 + 0.045T)ln(t)
%Ev = (3.75 + 0.045T)ln(t)
%Ev = (2.01 + 0.045T)ln(t)
%Ev = (2.65 + 0.045T)ln(t)
%Ev = (3.11 + 0.045T)ln(t)
%Ev = (2.64 + 0.045T)ln(t)
%Ev = (2.64 + 0.045T)ln(t)
%Ev = (2.47 + 0.045T)ln(t)
%Ev = (1.64 + 0.045T)ln(t)
%Ev = (4.27 + 0.045T)ln(t)
Litte
%Ev = (1.32 + 0.045T)ln(t)
%Ev = (1.57 + 0.045T)ln(t)
%Ev = (3.6)ln(t) (at 15°C)
%Ev = (3 + 0.045T)ln(t)
%Ev = (2.68 + 0.045T)ln(t)
%Ev = (7.12 + 0.045T)ln(t)
%Ev = (2.27 + 0.013T) √(t)
%Ev = (7.04 + 0.045T)ln(t)
%Ev = (1.68 + 0.045T)ln(t)
%Ev = (1.09 + 0.045T)ln(t)
%Ev = (0.74 + 0.045T)ln(t)
%Ev = (−0.05 + 0.013T) √(t)
%Ev = (1.43 + 0.045T)ln(t)
%Ev = (0.94 + 0.045T)ln(t)
%Ev = (2.44 + 0.045T)ln(t)
%Ev = (2.3 + 0.045T)ln(t)
%Ev = (0.25)(t) (at 15°C)
%Ev = (0.3 + 0.045T)ln(t)
%Ev = (1.69 + 0.045T)ln(t)
%Ev = (2.37 + 0.045T)ln(t)
%Ev = (1.4 + 0.045T)ln(t)
%Ev = (1.89 + 0.045T)ln(t)
%Ev = (0.001 + 0.013T) √(t)
%Ev = (1.09 + 0.045T)ln(t)
%Ev = (4.16 + 0.045T)ln(t)
%Ev = (1.63 + 0.045T)ln(t)
%Ev = (6.87 + 0.045T)ln(t)
%Ev = (6.92 + 0.045T)ln(t)
%Ev = (2.71 + 0.045T)ln(t)
%Ev = (3.37 + 0.045T)ln(t)
(Continued)
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UNCORRECTED PROOFS
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OIL AND PETROLEUM EVAPORATION
Substituting for the temperature of 15°C and with a time of
12 h or 720 min, we get a percentage of 26.65. With 18 h, we
get a percentage of 27.72 with a difference of 1.07%, the
amount evaporated in the interval between 15 and 18 h.
The variation of evaporation is illustrated in Figure 7.10,
which shows the evaporation of two oils, diesel fuel and
North Slope Crude, at two temperatures [1].
7.4 comPlexItIes to tHe dIFFusIon-
regulAted model
7.4.1 oil thickness
Studies show that under diffusion regulation very thick slicks
(much more than 4 mm) evaporate slower than other slicks
[1]. This is due to the increased path length that volatile com-
ponents must diffuse in a thicker slick. This can certainly be
confused with air-boundary-layer regulation. Figure 7.11
shows the evaporation rate of various thicknesses of oil by the
volume-to-thickness ratio. As can be seen, there is very little
difference in this standard presentation. Figure 7.12 shows
the concept of slower evaporation with increased path length,
that is, increased oil thickness. As noted, there are insufficient
data to fully evaluate this at this time; however, most slicks at
sea do not reach this thickness. Earlier experiments by the
present author studied the effect of thickness on the evapora-
tion of a light crude oil, ASMB. The equations noted in
Table 7.2 were all measured at a slick thickness of 1.5 mm,
which is typical of sea values. The results of this are shown in
Figure 7.13. The best curve fit from these is a square root
function from which a correction can be given for thickness:
Corrected equation factor equation factor
= + −
1 0 78
×√
.
t
(7.45)
tAble 7.2 (Continued)
Oil type Equation Oil typeEquation
Diesel Fuel 2002 short
Diesel Mobile 1997 long-term
Dos Cuadras, CA, USA
Ekofisk, Norway
Empire Crude, LA, USA
Endicott, AK, USA
Esso Spartan EP-680 industrial oil
Eugene Island 224—condensate
Eugene Island Block 32
Eugene Island Block 43
Everdell, AB, Canada
FCC heavy cycle
FCC light
FCC medium cycle
FCC-VGO
Federated, AB, Canada
Federated (new—1999)
Fuel oil #5
Garden Banks 387, GOM, USA
Garden Banks 426
Gasoline
Genesis, GOM, USA
Green Canyon Block 109
Green Canyon Block 184
Green Canyon Block 200
Green Canyon Block 65
Greenplus hydraulic oil
Greenplus hydraulic oil
Gullfaks, Norway
Heavy reformate
Hebron MD-4, NL, Canada
Heidrun, Norway
Hibernia, NL, Canada
High-viscosity fuel oil
Hondo, CA, USA
Hout, Kuwait
IFO-180
IFO-30 (Svalbard)
IFO-300 (old Bunker C)
Iranian Heavy
Issungnak, Beaufort Sea
Isthmus, Mexico
%Ev = (0.39 + 0.013T) √(t)
%Ev = (−0.02 + 0.013T) √(t)
%Ev = (1.88 + 0.045T)ln(t)
%Ev = (4.92 + 0.045T)ln(t)
%Ev = (2.21 + 0.045T)ln(t)
%Ev = (0.9 + 0.045T)ln(t)
%Ev = (−0.66 + 0.045T)ln(t)
%Ev = (9.53 + 0.045T)ln(t)
%Ev = (0.77 + 0.045T)ln(t)
%Ev = (1.57 + 0.045T)ln(t)
%Ev = (3.38 + 0.045T)ln(t)
%Ev = (0.17 + 0.013T) √(t)
%Ev = (−0.17 + 0.013T) √(t)
%Ev = (−0.16 + 0.013T) √(t)
%Ev = (2.5 + 0.013T) √(t)
%Ev = (3.47 + 0.045T)ln(t)
%Ev = (3.45 + 0.045T)ln(t)
%Ev = (−0.14 + 0.013T) √(t)
%Ev = (1.84 + 0.045T)ln(t)
%Ev = (3.44 + 0.045T)ln(t)
%Ev = (13.2 + 0.21T)ln(t)
%Ev = (2.12 + 0.045T)ln(t)
%Ev = (1.58 + 0.045T)ln(t)
%Ev = (3.55 + 0.045T)ln(t)
%Ev = (3.11 + 0.045T)ln(t)
%Ev = (1.56 + 0.045T)ln(t)
%Ev = (−0.68 + 0.045T)ln(t)
%Ev = (−0.68 + 0.045T)ln(t)
%Ev = (2.29 + 0.034T)ln(t)
%Ev = (−0.17 + 0.013T) √(t)
%Ev = (1.01 + 0.045T)ln(t)
%Ev = (1.95 + 0.045T)ln(t)
%Ev = (2.18 + 0.045T)ln(t)
%Ev = (−0.12 + 0.013T) √(t)
%Ev = (1.49 + 0.045T)ln(t)
%Ev = (2.29 + 0.045T)ln(t)
%Ev = (−0.12 + 0.013T) √(t)
%Ev = (−0.04 + 0.045T)ln(t)
%Ev = (−0.15 + 0.013T) √(t)
%Ev = (2.27 + 0.045T)ln(t)
%Ev = (1.56 + 0.045T)ln(t)
%Ev = (2.48 + 0.045T)ln(t)
Sockeye, CA, USA
Sockeye (2001)
Sockeye comingled
Sockeye sour
Sockeye sweet
South Louisiana
South Louisiana (2001)
South Pass Block 60
South Pass Block 67
South Pass Block 93
South Timbalier Block 130
Soybean oil
Statfjord, Norway
Sumatran Heavy, Indonesia
Sumatran Light
Taching, China
Takula, Angola
Tapis, Malaysia
Tchatamba Crude, Gabon
Terra Nova, NL, Canada
Terresso 150
Terresso 220
Terresso 46 industrial oil
Thevenard Island, Australia
Troll, Norway
Turbine oil STO 90
Turbine oil STO 120
Udang, Indonesia
Udang (long term)
Vasconia, Colombia
Viosca Knoll Block 826
Viosca Knoll Block 990
Voltesso 35
Waxy Light and Heavy
West Delta Block 143
West Delta Block 30 w/water
West Texas Intermediate
West Texas Intermediate
West Texas Sour
White Rose, NL, Canada
Zaire
%Ev = (2.14 + 0.045T)ln(t)
%Ev = (1.52 + 0.045T)ln(t)
%Ev = (1.38 + 0.045T)ln(t)
%Ev = (1.32 + 0.045T)ln(t)
%Ev = (2.39 + 0.045T)ln(t)
%Ev = (2.39 + 0.045T)ln(t)
%Ev = (2.74 + 0.045T)ln(t)
%Ev = (2.91 + 0.045T)ln(t)
%Ev = (2.17 + 0.045T)ln(t)
%Ev = (1.5 + 0.045T)ln(t)
%Ev = (2.77 + 0.045T)ln(t)
Litte
%Ev = (2.67 + 0.06T)ln(t)
%Ev = (−0.11 + 0.013T) √(t)
%Ev = (0.96 + 0.045T)ln(t)
%Ev = (−0.11 + 0.013T) √(t)
%Ev = (1.95 + 0.045T)ln(t)
%Ev = (3.04 + 0.045T)ln(t)
%Ev = (3.8 + 0.045T)ln(t)
%Ev = (1.36 + 0.045T)ln(t)
%Ev = (−0.68 + 0.045T)ln(t)
%Ev = (−0.66 + 0.045T)ln(t)
%Ev = (−0.67 + 0.045T)ln(t)
%Ev = (5.74 + 0.045T)ln(t)
%Ev = (2.26 + 0.045T)ln(t)
%Ev = (−0.68 + 0.045T)ln(t)
%Ev = (−0.68 + 0.045T)ln(t)
%Ev = (−0.14 + 0.013T) √(t)
%Ev = (0.06 + 0.045T)ln(t)
%Ev = (0.84 + 0.045T)ln(t)
%Ev = (2.04 + 0.045T)ln(t)
%Ev = (3.16 + 0.045T)ln(t)
%Ev = (−0.18 + 0.013T) √(t)
%Ev = (1.52 + 0.045T)ln(t)
%Ev = (2.18 + 0.045T)ln(t)
%Ev = (−0.04 + 0.013T) √(t)
%Ev = (2.77 + 0.045T)ln(t)
%Ev = (3.08 + 0.045T)ln(t)
%Ev = (2.57 + 0.045T)ln(t)
%Ev = (1.44 + 0.045T)ln(t)
%Ev = (1.36 + 0.045T)ln(t)
0002215964.INDD 218 10/9/2014 3:00:36 PM
UNCORRECTED PROOFS
Page 13
COMPLEXITIES TO THE DIFFUSION-REGULATED MODEL
219
where the corrected equation factor is the factor corrected
for the appropriate slick thickness, the equation factors are
noted in Table 7.2, and the t is the slick thickness in mm.
This equation is true for values above 1.5 mm at which the
original equations were measured.
7.4.2 the bottle effect
Another confusing phenomenon to understanding evapora-
tion is the bottle effect. This is illustrated in Figure 7.14. If all
the evaporating oil mass is not exposed, such as in a bottle,
more oil vapors than can readily diffuse through the air layer
at the bottle mouth may yield a partial air-boundary-layer
regulation effect. This air-boundary-layer regulatory effect
may end when the evaporation rate of the oil mass is lower
than the rate at which the vapors can readily diffuse through
the opening. Such effects could occur in reality in situations
such as oil under ice, partially exposed to air, or when a thick
skin forms over parts of the oil, blocking evaporation.
Time (h)
0 20 406080 100 120
Percent evaporated
0
10
20
30
40
50
60
70
Diesel at 20°
Diesel at 5°
North slope at 5°
North slope at 20°
FIgure 7.10 Comparison of evaporation curves for diesel and
a crude oil, Alaska North Slope oils at two different temperatures.
Thickness (mm)
02468 10
(Volume/thickness)/evap. rate
2.0
2.5
3.0
3.5
4.0
4.5
FIgure 7.11 The relationship of volume over thickness (area)
to evaporation rate (given as the equation parameter) for one light
crude oil. This shows that there is little relationship up to about 4
mm. Volume largely dictates the evaporation rate; however, for
thick slicks of thickness more than about 4 mm, the evaporation rate
slows due to the increased diffusion distance through the liquid.
Air
Air
Liquid
Liquid
Evaporation limited by diffusion rate through liquid
and surface layer; thickness is not very important
in thin layer
In thick layers, evaporation
limited by diffusion rate
through liquid and after
about 20–40 mm, diffusion
slows signifcantly
Liquid surface
Liquid surface
Thin
layer
Thick oil
layer
FIgure 7.12 The effect of great thicknesses of oil. The evapo-
ration rate is slower because of the longer diffusion difference. The
difference becomes measurable after about 4 mm of oil thickness.
This is greater than typical slicks at sea.
AQ4
02468 10
Thickness (mm)
2.5
3
3.5
4
4.5
5
5.5
6
Formula
FIgure 7.13 The difference in evaporation formulas for ASMB
oil evaporated at different thicknesses. The data show scatter, because
these early measurements lacked good temperature control.
0002215964.INDD 219 10/9/2014 3:00:38 PM
UNCORRECTED PROOFS
Page 14
220
OIL AND PETROLEUM EVAPORATION
During a recent experiment in ice, decreasing evaporation
rate in smaller test pools was observed [31]. This phenomenon
was probably caused by a combination of the bottle effect
and partially as a result of the increased thickness in the
more confined ice situations.
7.4.3 skinning
Several workers have noted that some crude oil and petro-
leum products form “skins” on their surfaces [32,33]. These
are largely due to the accumulation of compounds like resins
on the surface, some possibly created by photooxidation.
These can retard the evaporation of the compounds to a great
extent. Figure 7.15 shows the results of some evaporation
experiments carried out on two oils, Terra Nova crude and
Statfjord crude. Simultaneous experiments were carried out
on the oils; one was stirred and the other not [1]. As can be
seen in Figure 7.15, the stirred oils evaporated to a greater
extent than the unstirred oils. The relevance of this at sea may
not be great as wind and waves may accomplish the stirring
and skin formation may thus be slowed or prevented. During
the experiments shown in Figure 7.15, one could see the skin
formation on the unstirred oil and this skin was much more
evident closer to the end of the 200-h experiments.
Grose used the Mackay and Matsugu equations with
some modification to account for the skinning factor [34]:
=(
C
o
where L is the mass of oil evaporated with time (kg/s), C is
the environmental transfer constant, U is the wind speed at
the surface (m/h), Do is the diameter of the oiled area (m), K
is the oil temperature in Kelvin, Pi is the vapor pressure of
the particular component, Sk is the skin factor, and Mi is the
molecular weight equivalent of the particular oil fraction.
The skin factor, Sk, ranges from 0.1 to 8 and accounts for
the effect of skinning (the formation of a semipermeable sur-
face layer). Yang and Wang suggested a value of Sk = 0.2
after the density of their test oils had increased by 0.78%
[12]. A value of 1.0 was used in testing the model. In
addition, mass loss rate depends on the vapor pressure, Pi,
and the molecular weight, MWi, of each fraction. C is a
dimensionless environmental transfer constant whose mag-
nitude depends on the units used. The value used by Yang
and Wang for C (0.00024) includes the constant 0.015 after
Mackay and Matsugu [9].
LUD RKPM
ii
) (
/
)
−
Sk
0 78. 0 11.
(7.46)
7.4.4 Jumps from the 0-wind values
Experimentation shows that studies of oil evaporation at no
turbulence or airflow show a slight decrease in evaporation
rate from those experiments carried out with slight air
movement such as found in an ordinary room [24]. This is
due to the slight stirring of the oil mass, which increases the
diffusion rate somewhat. Tests of this phenomenon show
that further increases in evaporation rate do not occur with
increased air movement or turbulence, thus confirming that
this is a phenomenon only at 0-wind or turbulence condi-
tions. These are seen only during capped vessel experiments,
and the “jump” in evaporation rate is seen when the condi-
tions are removed.
7.5 use oF evAPorAtIon eQuAtIons
In sPIll models
Evaporation equations are the prime physical change
equations used in spill models. A review of the use of evapo-
ration algorithms in oil spill models is given in Fingas (2011)
[1]. This is because evaporation is often the most significant
change that occurs in an oil’s composition. Many models in
the decade after 1984 use the Stiver and Mackay approach
Air
Air
Opening
Liquid
Evaporation limited by
diffusion rate through
liquid and surface layer
More vapor than can easily diffuse
through opening—therefore partially
air-boundary-layer regulated
Liquid surface
UNCORRECTED PROOFS
FIgure 7.14 An illustration of the bottle effect. If all the evap-
orating oil mass is not exposed, more oil vapors than can readily
diffuse through the air layer at the bottle mouth may yield a partial
air-boundary-layer regulation effect. This regulatory effect may
end when the evaporation of the oil mass lowers past the rate at
which the vapors can readily diffuse through the opening.
Time (h)
0 50
100 150200
% Evaporated
0
10
20
30
40
Terra nova
Terra nova–stirred
Statfjord
Statfjord–stirred
Stirred
Stirred
Not stirred
Not stirred
Terra nova crude
Statfjord crude
FIgure 7.15 Results of an experiment to show the effect of
“skinning” on oil evaporation. The upper curves in each case is the
evaporation of the oil shown with stirring, thus preventing or retard-
ing skin formation. The lower curve is the evaporation without stir-
ring. The effect of skinning for these two oils amounts to several
percent differential in evaporation over 200 h. At sea, wind and
waves may mix the oil sufficiently to minimize the skinning effect.
0002215964.INDD 220 10/9/2014 3:00:40 PM
Page 15
SUMMARY
221
[18]. Currently, more models are moving to equations such
as found in Table 7.2.
There are three major errors resulting from the use of air-
boundary-layer-regulated models: first and most important
is that they cannot accurately deal with long-term evapora-
tion; second, the wind factor results in unrealistic values;
and finally, they have not been adjusted for the different cur-
vature for diesel-like evaporation. Some modelers have
adjusted their air-boundary-layer models to avoid very high
values at long evaporation times by setting a maximum
evaporation value. This does avoid very unrealistic high
values after a point in time, but does so artificially. Most
models of any type will require that one sets a maximum rate
to avoid overprediction or values more than 100% for
example. This can be best illustrated using a long-term
example. A spill in northern Alberta of Pembina oil was
sampled 30 years after its spill. Chemical analysis shows
that this was weathered to the extent of 58% [35, 36]. An air-
boundary-layer-regulated predicted value overshoots the
estimate by over 60%, despite using only two low wind
values of 2 and 7 m/s [1]. Use of higher wind values increases
the evaporation to well over 100%. These high evaporation
values are physically impossible.
7.6 volAtIlIzAtIon
There is another phenomenon that has not been investigated
thoroughly. It is the volatilization of light components of
oils when submerged, dispersed, or released under water. It is
known that dispersed oils, rapidly lose their volatile compo-
nents, in fact, much more rapidly that the same oil evaporated
on the surface [37]. This accelerated weathering has been
studied somewhat for dispersants, but not much otherwise.
The recent Deep Water Horizon spill involved the
high-pressure injection of oil into water, and much of the oil
arrived on the surface as emulsion and having been weathered
to 40–50% [38]. A similar situation was observed during the
IXTOC spill, and the oil was found to emulsify directly at the
wellhead [39]. In both cases, most of the volatile components
were lost at the wellhead or in very close proximity. It appears
that most of the volatile compounds rose to the surface in the
form of small bubbles and in the case of the IXTOC blowout
were burned [39]. This involves a loss of 40–50% in a very
short time, not exceeding a few seconds.
7.7 meAsurement oF evAPorAtIon
Laboratory evaporation measurement has been carried
out over many years. Comparison of field methodologies
and laboratory experiments indicated that pan evapora-
tion studies are probably the best methodology, although
very few quantitative studies were carried out. Recently,
Fieldhouse and Hollebone carried out a study comparing
the rotary evaporator to pan evaporation. They found that
the rotary evaporator cannot be used to measure the rate
of evaporation, as would be expected [40]. They found
that the percent by volume extent of evaporation matched
very closely between pan and rotary evaporator with
respect to oil composition. Composition was analyzed by
gas chromatography.
The percentage of evaporation of an actual sample can be
determined using gas chromatographic–mass spectrometric
methods [41]. The current method is to measure the content
of the starting oil’s biomarker terpanes that are weather resis-
tant. Common substances used are C29 and C30 αβ-hopanes.
Application of this measurement in both the starting oil and
the weathered oil can yield the following equation [41]:
Oilevaporation % =−
×
1 100
0
1
H
H
(7.47)
where Ho is the hopane concentration in the original oil and
H1 is the hopane concentration in the weathered oil.
Researchers in the past tried to use ratios of the oil’s
alkanes such as
Evap
C
C
C
C
C
C
C
C
% =
+
+
+
+
+
+
×
1214 1618
20 2224 26
100 (7.48)
This approach does not function well as the alkanes in the
subscript of Equation (7.42) also evaporate to a certain degree.
Modern analysis is also capable of differentiating bet-
ween evaporation and biodegradation [42].
7.8 summAry
A review of the physics of oil evaporation shows that oil
evaporation is not air-boundary-layer regulated. The results
of the following experimental series have shown the lack of
boundary-layer regulation.
1. A study of the evaporation rate of several oils with
increasing wind speed shows that the evaporation
rate does not change past the 0-level wind. Water,
known to be boundary-layer regulated, does show
the predicted increase with wind speed, U (Ux, where
x varies from 0.5 to 0.78, depending on the turbu-
lence level).
2. Increasing the area does not change the oil evaporation
rate. This is contrary to the prediction resulting from
boundary-layer regulation.
3. The volume or mass of oil evaporating correlates
with the evaporation rate. This is a strong indicator
of the lack of boundary-layer regulation because
with water, volume (rather than area) and rate do not
correlate.
The fact that oil evaporation is not strictly boundary-layer
regulated implies that a simplistic evaporation equation will
0002215964.INDD 221 10/9/2014 3:00:41 PM
UNCORRECTED PROOFS
Page 16
222
OIL AND PETROLEUM EVAPORATION
suffice to describe the process. The following factors do not
require consideration: wind velocity, turbulence level, area,
and scale size. The factors important to evaporation include
time and temperature.
A comparison of the various models used for oil spill
evaporation shows that air-boundary-layer models result in
erroneous predictions. There are three issues: first, air-
boundary-layer models cannot accurately deal with long-term
evaporation; second, the wind factor results in unrealistic
values; and finally, they have not been adjusted for the differ-
ent curvature for diesel-like evaporation. There has been
some effort on the part of modelers to adjust air-boundary-
layer models to be more realistic for longer-term evapora-
tion, but these may be artificial and result in other errors such
as underestimation for long-term prediction.
A diffusion-regulated model has been presented along
with many empirically developed equations for many oils.
The equations are found to be of the following form:
Percentage evaporated =+−
[.( )]ln
BTt
0 04515
(7.49)
where B is the equation parameter at 15°C, T is the tempera-
ture in degree Celsius, and t is the time in minutes.
It is also noted that in diesel fuel and similar oils, the
curve is different and follows a generic curve such as
The most accurate predictions are carried out using the
empirical equations as noted in Table 7.2. If these are not
available, the parameters can be estimated using distillation
data as follows:
For oils that follow a logarithmic equation,
Percentage evaporated =+−√
[.( )]
BTt
0 0115
(7.50)
Percentage evaporated =
+−
[ . 0 165
0 045
(% )
(
T
. )ln( )15
D
t (7.51)
For oils that follow a square root equation,
Percentage evaporated =
+−√
[ .0 0254
0 01
(% )
(
T
. )] 15
D
t (7.52)
where D is the percentage distilled at 180°C, T is the temper-
ature in Celsius, and t is the time in minutes. Equations are
also given that allow estimation of evaporation from density,
viscosity, or SARA data; however, these are much less accu-
rate again.
In addition, an estimator for the variation in evaporation
for thick slicks was developed and given in Equation (7.45.)
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