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Most weather in g models use the approach
of
Mackay el al. [5 ), modified to
account fo r emulsion fonnation (Buchanan and Hurfo
rd
[61 , to forecast the
change in oil density,
Here,
Cl
and l are empirically fitted constants that will vary somewhat for
differe
nt
oils. Reasonable values are 0 .008
X-I
and 0.18 re spectively.
2.2 Pou r point
Another field
in
many oil property databases is the pour point of the oi l. This is
defined as the lowest temperature at which an oil will flow under specified
cond
iti
ons. Pour point is a difficu lt quantity to quantify and measu
re
ments of
pour point vary widely. For example, Environment Canada (Jokuty el al [2])
reports Khafj i crude oil as hav ing a pour point of either -35 C or -48 C.
depending upon the reference. While vagucly equivalent to melting point for
pure substances, th e pour point for oi l, unlike th e melting point of a pure
chemical, w
ill
increase as th e o il wcathers. The most commonl y used fonnula
to describe this change is an algorithm proposed by Mackay et al 71.
= Pp 1
c,j ., (2)
Here,
Cs is an
empirically determined constant. Mackay et
al.
[7) used the value
0.35 for Prudhoe B
ay
crud e. Others (Daling [8)) use an exponent i
al
curve fit
instead of the linear relationship assumed
in
eqn 2 ). Rasmussen el al [9]
in
clude a linear correction tenn
in
water content to acco unt fo r th e pour point
of
emu lsions as well as pure oi l
s.
2.3 Viscos ity
Somewhat related to pour point is the viscosity of the oi l, which is a measure of
its resistance
to
flow. Roofing tar, for example, is much more viscous than
kerosene. There a
re
actually two closely
re
lated physical propert ies that bear the
name viscosity: the kinematic viscosity which has units of length squared
divide d by time, and the dynamic viscosity which is the kinematic viscosity
mu
lti
p lied by th e density.The respective SI units are the stoke and poise. These
are large units with regard to most flu ids, so the more common cent isto
ke
(cSt)
and centipoise (cP) are used. The dynamic viscosity
an
d kinematic viscosity of
water at 20 C ha
ve
values close to unity when expressed, respectively, in
centipoise and centistokes. Because the dens
it
y of most o ils differs by less than
30% from water, their viscosity nu mbers for dynamic and kinematic viscosity
are
of
the same order of magnitude when reponed
us
ing these
un
its.
Unfortunately, other, less standard units are often selected . For example, one
common system of units for kinematic viscosity
is
Saybo
t
Universal Seconds
(SUS).
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Most oils
and
oil products are more viscous than wate
r.
Kerosene, for
example, has a dynamic viscosity of approxi
mat
ely 10 cP, whercas crude oi ls
can have viscosities
of
several hundred centipoise or more. Emulsified oils ean
have viscosities that are orders of magnitude larger then the corresponding fresh
oil Figure 3 .
Ccntistokes
25.000
20.000
15,
000
.000
/
10,000
o
o
24
HO
URS
/
48
Figure 3: Expected inc rease in viscosity due to evaporation and emulsification
for a hypothetical spi ll
of7000
bbl
of
Arabian medium crud e oil.
Typically, once an emulsified oil reaches s
uch
a high viscosity, its
shear stress is no longer a linear function of the fluid ve\ociry gradient, meaning
that the o
il
has become non-Newtonian , acting mo re like a plastic se
mi
-solid
than a liquid. Viscosiry me
as
urement becomes dependent u
po
n
th
e shear ra tc.
Cleanup
of
such emulsions prese
nt
s considerable difficulties, si nce many pumps
and skimmers are not designed to ha ndle such thick fluid
s.
Even before the o
il
h
as
weathered to this state,
it
may be 100 visco
us
to be dispersible with chemical
treatment. The past rule-of-thumb has been that an oil could not be effectively
dispersed
if it
s
kin
ematic viscosity exceeded 2000 c
St
. However, manufac
tu
re
rs
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now claim that the new class of dispersants can handle oils several times thi s
viscosity.
Viscosity is a strong function
of
temperature. Therefore, it is necessary when
usi ng a historical value
for
an oi l s viscosity to know the refere nce temperature at
which the viscosity was measu red. A commonly used laboratory reference
temperature is
lOO
°
F,
wh ich is not a oommon temperature fo
un
d at oil sp
ills.
Maekay el
af
[5]
recommend an exponential fonn for the temperature correction
functi on,
v
~ p
[e( . __ll.
,of ,.
r T
-
3)
Payne et a/. [10] suggest 9000 K-\ for
Cor
but the author (NOAA
[II])
proposes
a smaller value of5000 K-l , based on laboratory data.
As
o
il
evaporates,
th
e relat
ive
concentrations
of
the various components
change . A oommon rule (Perry [12]) is that the visoosity
of
a nonpolar mixture
can be derived from the viscosities
of
its components, but th
is is
difficu
lt
to
implement for crude oi
ls
becau
se of
the large number
of
oomponents.
As
an
alternat i
ve,
Buchanan a
nd
Hurford
[6J
suggest that it is necessary only to track
one of these components, the asphaltene oontent,
n oc f
(4)
However, most modelers prefer to es t imate t
he
change in viscosity based on the
fract ion
of
the sl ick that
has
evaporated. For example, Mackay t af [13] util ize
the fraction evaporated for
th
eir
oo
rrelation
of
weathered oil viscosity wit h fresh
oil viscosity,
(5)
There is no agreement on the method to detenni
nc c
Mackay
et
al. {
l ]
say that the tenn depe
nds
upon the type
of oi
l. For three different o
il
s that they
tested, the numbers ranged
from
1.6 to 10.5. Howlett [14] uses I for light
fuel
s
and 10 for heavy fuel oils. NOAA
[II]
uses a fractional power law fit based on
the statistics generated from thei r oil properties library, with the initial viscosity
as the independent va riable . Alternatively, they use laboratory results
for
a
particular oil that has been artifi cially weathered to curve fit eqn (5).
As
mentioned earlier, the emulsifying process increases visoosity
significantly. Alm os t all weathering models use the Mooney equation (Schramm
1 5]) 10 forecas t this increase
of
viscosity with the increase in water fraction Y
of
the emul
si
fied oi l,
v
. - c
•
Y
6)
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The choice of2 5 for C l and 0.65 for C,,2 by Mackay et al [1 3] is adopted
by
most models, although some try
to
fit
them based on laboratory data for the
oil of concern. In the latter case, the values for C l range between and 5. Cy l
ranges between -0.9 and 0.9 (Aamo [16]) or can be estimated, based on average
and minimum water droplet size (NOAA [17J .
2.4
Surface
tension
Some spreading and dispersion algorithms require knowledge of an oil s
surface tension. Surface tension is the force
of
attraction between the surface
molecules of a liquid. Chemicals which reduce surface tension can be used to
facilitate dispersion. Laboratory data exist for the interfacial surface tension
between oil and water and oil and air. Mackay el a/ [
13J
proposed the following
formul
as
to describe ehange in surface tension as the oil weathers:
7)
=ST
. I+ In ) .
(8)
Rasmussen
[18J
has recommended that surface tension changes be tracked
by
a
linear superposition of the su rface tensions of the pseudo-component relative
fract ions (see section 2.5).
2.S Pseudo-components
Petroleum hydrocarbons are grouped into four major categories. Alkanes, al
so
caJted paraffins, are char
ac
terized by single-bonded, branched, or unbranched
chains of carbon atoms with attached hydrogen atoms. Alkenes are simil
ar
to
alkanes, but will have at least one double bond. Aromatics are organics having a
ben
ze
ne ring (or
rin
gs)
as
part
of
their chemical structures.
Na
ph
thenes also form
rin
gs, but have single carbon bonds. A small percentage of the oil may consist
of non-hydrocarbon compounds Ihat may contain oxygen, nitrogen, sulfur and
various trace metals.
Th
ese constituent
s,
which include such compounds as
asphaltenes, can have a significant effect on the way the oil weathers.
Oil components are also commonly grouped on the basis
of
the boi ling
point of the hydrocarbon constituent. Hydrocarbons with similar molecular
weights typically have similar boiling points (Jones [l9J). Because much of the
information on crude oils is collected for refining purposes, distillation data
exist for many oil
s.
Typically,
th
ese are given
in
tabular form, where the oil is
broken down into fractions. each fraction reprcsenling a range
of
boiling point
c
uts.
Oil-spill modelers often take advantage of this information to simulate the
very compl
ex
hydrocarbon mixture of a crude oil or oil product with a simpler
fictitious oil made up
of
pseudo-components (Payne el . [lOn, where each
component corresponds to one
of
the distillation fractions. The boiling point
of
each pseudo-component is the average temperature between consecutive cuts.
Other properties of these fictitious components can be approximated
as
well. The
molar volume and molecular weight can
be co
rrelated to the boiling point by
treating the component as
if
it were a mixture of alkanes (Jones [20]),
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v ..... =
.1
C
.o r.
+
C
T;,
.
9)
1
0)
The individual properties of the pseudo-components can also e reassembled to
estimate global properties of the o
ri
ginal oil. For example, for some evaporation
models il is
ne
cessary to estimate the ini tial oil boiling point. This ean be do
ne
by numerically solv
in
g the follow ing equation, using the pseudo-component
boiling points and the ir relative mole fractions:
11)
Here, the subscri
pt)
refers to the individua l pseudo-component, and the boiling
point tenn without the subscript is for the orig inal oil.
2.6 Flash
point
An occasionally important tem perature for oils is the flash point, which
is
a
measure of the flammability of
th
e oil. Mackay
et al
7] use a linear fit to
fract ion evaporated to estimate change of the flash point ove r t ime, s imi lar to
eqn 2 ) for pour point. More recently, Jones [21] has re-examined the effects of
weathering on flash point. He has found
th
at the changing composition of the oil
as it evaporates changes the flash point. Us ing
th
e co ncept of pseudo
components, Jo
ne
s suggests thai the flash point can e predicted using a
correlation es tablished by Butler el aJ [21] [22] for middle distillates, provided
that the pseudo-components contain infonnation about the low-boiling
constituents. Noting
th
at the vapor pressure o f each component is a function
of
temperature, the flash point is reached when
12)
Here ,
th
e vapor
pr
essure and molecular weig
ht
are expressed in MKS units and
th
e sum is over the number of pseudo-components . This corresponds to
requiring the sum
of
the partial pressu
re
o f the oil volatiles to be a
bo ut
I of an
atmosphe re. As the oil evaporates, the mole fractions of the less volatile
components increase while
th
ose of the more volatile constituents decrease. In
order to preserve the equality, the vapor pressures must be referenced to an
in
creas
in
g flash point tempera ture.
3 Environmental
actors
The most general environmental factors affecting oil spill weathering are wate r
temperature , sea state, and wind speed. Also importanl, depending upon the
circumstance
of the spill incident, are so lar radiation, air temperature , water
density and salinity, ice cover, and sediment loading in
th
e wate
r.
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3.1 Wind
Most oil weathering models are based on wind speeds at a 10m reference height
above the water surface. Win d data measured at a different elevation must be
adj usted 10 this reference height. Th is c
an
be done by
us in
g either a logarithmic
Brutsaert [23]) or a power
law
approximation. A common fonnula Brutsae
rt
and
Yeh [24]) that will provide reasonable answers provided the measured height
of
th
e wind is less than 20 m is
)
. ==V. ;
13)
where z refers to the wi nd measurement hei
gh
t
in
meters and the su
bsc
r
ip
ts on
the wind speed U specifY the height at which the wi nd speed is referenced.
Furthennore, corrections must also be made
if
the location
of
the wind
me
asu
rement is a considerable distance from t
he
spill
si
te, or there are
intervening topographical obstructions.
St
olzenbach et al [25] have proposed a
scheme for interpolating spatial wind measurements and severa l oil spill models
incorporate this capability . However,
for
most real spill incidents, a spatially
constant wind fi
el
d is usually em ployed.
3.2 Waves
Sea state is important
for es
timating spread, dispersion, and emulsificat
ion.
A
sk illed on-scene observer can es timate significant wave height and wave period.
However, spill forecas ters often have to estimate these tenus from other factors
such as wind spced, fetch, and wi nd duration. Some simple
fo
rmulas to petform
this task have been developed
fo
r tile US Army Corps
of
Engineers Coastal
Engineering Research Center [26]). Fo r the case of fully dev
el
oped seas, the
si
gn
ificant wave height can
be
com
puted
using MKS
un
its, as
H 0.0248 .V,l
14)
and the period of the peak of the wave spectrum is estimated by
t 0.83 · U.
IS)
where the wind-stress vectorV is calculated
by
the fonnula
V = = 7 1 · U 16)
The case fo r fetch or duration-lim ited winds is similar. although the fonnulas are
somewhat more comp licated.
The h
is
tory
of
pas t
sp
ills indicates th
at
dispersion or em
ul
sification
of
t
he
sl
i
ck
often depends upon t
he
presence
of
breaking waves. Typically, waves
wi
ll
start to break when wind speeds exceed 5 to 10
knolS
, but estimating the fraction
oft he sea surface that is covered with whitecaps is an inexact science at bes t Wu
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{27], Monohan and O'Muircheartaigh [28), Holthuijsen and Herbers [29], and
O M uircheartaigh and Monohan [30] provide some guidance but their data shows
wide scatter. The NOAA [1
1J
weathering model uses a cubic polynomial fit
0 5 /.. 5. 1
(17)
which cuts off whiteca p generation below
3
mis, acts almost as a linear equation
for wind speeds of 8-12 mls and increases whitecap fraction rapidly for high
wind speeds.
3.3 Solar
radiation
Ph
oto-oxidation
of
spilled oil depends upon solar radiation. Experiments
(Overton [31]; FaIT (32]) indicate that solar radiation may contribute to crusting
on the surface of the sl ick and impede other weathering processes. The flux
of
solar shortwave radiation at the top of the atmosphere is 1367 m
2
Approximately 17-20
of
it
is absorbed by the clear atmosphere, and clouds act
to reflect or absorb even more.
t
is possib le to estimate ground-level radiation
flux levels based upon time of day, date, latitude, and cloud cov
er
(NOAA [33]).
4 Spill release
Many weather ing models assume an instantaneous
re
lease of the oi
l
an
unrealistic condition for large spills. Weathering models that are connected to a
trajectory model (Appl ied Science Associates [34]) often will a llow the user to
vary the amount spilled over space and time but typica
ll
y give little guidance for
estimating these terms. There has been surprisingly little
re
search into oil release
behavior, although current research anicles (Simccek-Beatty t af [35]; Rye [36);
Yapa and Zheng [37]) indicate that this may be changing.
4.1
Subsurface
release
Of particular concern arc releases that are subsurface. Subsurface releases that are
low pressure , such as releases from sunken vessels and some ruptured pipelines,
typ ically fonn a • flower blossom ' pattern, where the oil spreads out thinner than
it would during a surface release of the same amount of oil. Leaks caused by
blowouts from offshore wells can produce an in it ial surface slick of already
emulsified oil.
As drilling has moved into ever dee per waters, a major quest ion remains as
to whether a surface slick wi
ll
appear at all from a release at the ocean floor. A
key factor in answer ing this question will be found in the transition 7.one where
the release ceases to be described
by
a jet of water, oi l and gas, and becomes a
cloud of buoyant oil droplets that may, or may not surface, depending upon the
droplet size distribution.
Model development of
deep-water releases
is
still
an
active research area and
discussion
of
the various proposals is outside the scope
of
this essay. The reader
is refelTed to Rye (36) and Yapa and Zheng (37].
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4.2 Leaking
tankers
S
im
ecek-Beany
t
[35] have modeled the release
ofa
holed tanker by treating
it as an idealized cylindrical tank. They
id
entify three different leak scenari os.
The most simple is a
rel
ease
of
oil from above the water line, where the tank
itself
is
open to the atmosphere. Then, the
fl
ow rate is determined strictly by
Bernou
lli
s equation,
( \8 )
If the hole is below
the
water line, there
may be
water ingestion as well as
outflow
of
o
il
. The detennining factor
is
the equilibrium height, defined
as
z - z
0:= PM. p ail
.,
p
..
\9)
If the equ ilibr
iu
m height is above the hole height, on ly water will
fl
ow in
fanning a water bottom
in
the
tank. If
th
e
eq
uilibrium
he
ight is below
th
e hole
height, only oil
wi ll
be
rel
eased until the equilibrium height reaches the hole
height,
at
which
ti
me both water ingestion and o
il
out
fl
ow
wi ll
occur.
The third leak scenario is the situation where the tank
is
not open to the
atmosphere and a vacuum forms inside the tan k, slowing the release of the oil
and causing air ingestion to
eq
uali ze the pressure. Suc h a situation occurs if the
tank s
va
cuum reli
ef
valve is damaged or del iberately closed
by th
e c
rew to
slow
the release
of
the
oi l.
Whatever the mechanism that describes the oil
re
lease behavior, oil that
is
released over a time
pe ri
od compa rab
le
to the t
ime it
takes for
th
e o
il
to spread
over the water will have different area coverage than the same amount
of
oil that
is
spilled quickly. Th
is
can have consequences for those weathering processes
that are strong functions
of
s
li
ck are
a.
5
Weather
ing processes
Weathering processes can be divided into three categories. Rap idly occurr
in
g
processes have immediate consequences for the spill response. Such
pro
cesses
include spreading, evaporation di spe
rsi
on, dissolution , and emulsification .
Other weathering mechanisms operate more slowly
and
are importa
nt
usually
in
regard to studies
of
the lon g-tenn effects of the spill. Examples include photo
oxidation
and
biodegradation. Fin a
ll
y
th
ere are so
me
processes that arc
important only under pa rt
ic
ular envi
ro
nmental cond
iti
ons. Such processes
include sedimentation an d oil-ice int eraction.
5.1
Sp readin g
Th e rate
at
which
oi
l spreads on open water can affect other weathering processes
s
uch
as dispersion, evaporation and emulsificat
io
n. The cleanup itself needs
accurate information on expected
sp
ill size when planning su
ch
strategies as
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skimming operations or dispersant use. Unfortunately, spreading
is
an
immensely complicated phenomen on involving bo th the physical properties
of
the spilled product and the environmental state of the surface water on wh i
ch
it
is floating.
Oil begins to spread as soo n at it
is
spilled, but it does no t spread
uniform l
y.
Any shear in the surface current will cau
se
st
fCtchin
g,
an
d even a
slight wind wi
ll
cause a thickening of the slick
in
the downwind direction. Mo st
spills qu ickly fonn a comet shape where a small black region is trai l
ed
by a
mu
ch larger sh
een
that can
e of
varyi
ng
colors. Fig
ure
4 shows s
uch
a s
it
uation
for an experimental spill
of 50
bbl
of
Arabian crude oil. Measurements show that
most
of
the o
il
from a spill
is in
the
bl
ack, thick pa
rt
,
wi
th only a small
percentage of thc spi
lled
o
il
in the sheen. A typical
ru
le-of-thumb is to assume
that the sheen represents only abo ut 10 of the vo lume of the spilled oi
l.
This
is
unfortunate for estimat
ing the
s
pi ll
size by visual observation (Research
In
stitute [38]). Although various formulas exi
st
to estimate the thickness
of
the
sheen bas ed
up
on
its
color (Canadian Coast Guard [39]), no such formulas exist
fo
r the t
hi
ck part
of
the slic
k.
.
sheen
thick oil
Figure
4:
Processed image
of
50-bbl test spill showing separation into thick
part and sheen, plus the beginning
of st
reamers.
As
the slick ages further, it is not uncommon to have
it
split into separate
streamers due to wave action or Langmuir effec ts (Craik and Leibovich [401 .
The laner refers 10 a pattern of re pea
ti
ng Langmu ir cells (Fig. 5) below the
surface that create a system
of
ridges
an
d troughs on t
he
surface. The troughs
become natural collection areas
for fl
oating
oi l.
The end resu
lt
is lines
of
o
il
that
may be spread over a
la
rge geographical area but effectively covcr only a sma
ll
percentage ofthe water surface.
The fina l fate of float
in
g
oi
l is typically to fonn small la
rbaJl
s spread out
over a large arca. These tarball fields arc difficult to
ob
serve
from
sponing
aircraft as they arc oft
en
subject to overwash. Their dispersal is based upon the
general turbu
le
nce state of the water.
The earliest spreading models (Blokker [
41
];
Fay
[42); Fazal and M
il
gram
[4
3]) exam i
ned
the properties
of
the idealized spreading
of fl
oati
ng
, insoluble
chemical, such as oil,
on
calm waler. Siokker [4
1J
hypothesized that
gravitational spreading was the key factor and proposed the re lationship
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where
.6 P - P
• p.
(20)
Figure
5:
F
onn
alion
of
Langmuir cells and oil streamers.
Mackay and Leinonen [44J used the Blokkcr equation to describe the overall
spread
of
the s
li
ck but, in order to compare with observed sp
ill
behavior,
di
vided
the s
li
ck into a thick part and a thin sheen with the thick part always assigned
one-eighth of the total area.
Blokker s equations, however, did not compare well with field data
(Stolzcnbach el [25]; Research Institute [381), nor did they give infonnation
indicating when spreading would cease. As an alternative, many models adopted
the Fay equations [45] 10 forecast slick area.
Fay divided the spreading process into three separale phases, depending upon
the major driving and retarding force for spreading. When the s
li
ck
is
relatively
thick, gravity causes the oil to spread late
ra
lly; later, interfacial tension at the
periphery will e the dominant spreading force . The main retarding force is
initially inertia followed later
by
the viscous drag of the water. Fay therefore
labeled the three phases: gravi
ty i
nertial, gravity-v iscous, and surface tens ion
viscous. The gravity-inertial phase happens rapidly, on the order of a few
minutes, except for the largest sp ills. The area grows as a linear function of
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A= 0.57nJA..gV. (21)
unti l the time (Dodge et af [46]) when the relative thickness
is
sma
ll
enough
that the transition to gravity-viscous spreading occurs . Th is time is calculated by
th
e fonnula
(22)
The area at this transition time is often taken as the initial area for many
spread models .
t
is g iven by the formula
(23)
The area then continues to grow according to the gravity-viscous term
(24)
unti l it becomes so thin that sur ace tension becomes the driving fo rce. The area
for this phase is described by the a lgorithm
A=
2.
6Jt
·
where (25)
Other researchers (Waldman
ef
l [47]) have der
iv
ed slightly di
ffereOl
values for
the empirical coeffic ients used
in
the above equations, or have other small
varia
ti
ons in the form ulas for one o the phases (Buckmaster [48J). Mackay l
aJ
[49] have appl ied Mackay s concept of a thick-thin slick combination using the
Fay form ulas. Garcia-Martinez et aJ [50] proposed modi ying some o the
constants in the Mackay method to account better for the oil and water physical
propenies.
Although the Fay fonnul
as
are theoretically sound, they have perfonned
poorly in actual spi lls. In most repo ned cases, they have underestimated sp ill
area (Murray [51]; Conomos [52]; Lehr et
f
[5 3
}
, whereas in at least one case,
they significantly overeslimated the area (Ross and
Oi
ckins [54]). Also, Jeffery
[55 ] no
ti
ced no transition betwecn the d ifferent spreading phases. Lehr et f [56]
have pointed out that only the grav ity-viscous phase happens in the time frame
when sp ill response is typically occurring.
There have been numerous suggestions on how to improve the Fay spreading
fonnulas. Plutchak and Kolpak [57) cla
im
ed that the change in surface tension
a
nd density due to wea
th
ering needed to be determined to use Fay spreading
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optimally. In order to account for wind spreading effects, Lehr
et al. [56]
proposed altering the shape of the sp ill from a circle to an ellipse with the long
axis being parallel to the wind. Considering only r v i t y v i s o u s spreading to
be
important, they proposed the area to be estimated by (MKS units)
.
A= 2.27 A. V
); .
, +O
04(A
.vu')., .
(26)
Curious ly . the Fay equations do not depend upon the viscosity of the sp illed
oil, while common
se
nse says that a heavy fuel oil would spread more slowly
than a light refined product like gasoline. Ross and Energetex Engineering [58]
modified the Fay equation by inserting a correction facto r that is equal to the
oil-to-water viscosity ratio raised to the 0.15 power. El -Tahan and Venkatesh
[59] introduced the concept of 'velocity gradient' which
is
inversely related to
the oil viscosity and represents vert ical shear resistance
in
the o il slick .
However, it is doubtful that any mere patches to the Fay formulas will allow
accurate prediction
of
slick area over any extended time period because
of
the
neglect
of
outside environmental factors and details
of
the initial release. As an
alterna
ti
ve,
re
searchers have attempled to model sl
ick
spreading as strictly a
wa
ter turbulence phenomenon with the oil acting as a neutral tracer (Murray
[51]). When a neulrally buoyant dye
is
dropped onto the ocean surface, the dye
begins to disperse due
1
water turbulen ce . The area of sea surface covered by the
dye wi
ll
grow as a function of time and a suitab
ly
defin ed eddy diffusion
coefficient,
(27)
Presuming that this same phenomena affects
th
e dis persion of positively
buoyant spilled oi l, Ahlstrom (60] has recommended simu lating this process by
dividi ng th e o il inlo a suitable number of separate elements, often referred to as
Lagrangian elements, and then randomly displacing these elements over time
using a properly chosen eddy diffusion coefficient. Elliot
et
al. [61] conclude
that such a process
is
non-Fickian. and that a time-depend ent diffusion parameter
be
tter represents empirical results. Their diffusion parameter is (MKS units)
D..
= 0 .033 " . (28)
t
is possible to incorporate Fay spreading with diffusive spreading by
treat ing the fo
rm
er as a pseudo-diffusion process and matching
rw
ice the standard
deviation of
the distribution
of
o
il
element locations with the radius
of
th e o
il
slick as predicted
by
the standard Fay formula. This yields a Fay pseudo
diffusion coefficient of
JA V ) l
I
D ..
= 1
\ 7
i
(29)
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Another approach
is
to allow the individual elements
to
spread according to
Fay spreading rules, treating these elements as ' minispills '(ASA [34]). The
minispills are then dispersed and moved by water turbulence and other forces.
Care must
e
taken not to bias the results by the number
of
elements seleeted
and to handle interaction between the e lements properly.
Evell including water turbulence. Fay spreading is still incomplete, however
(Lehr [62]). Probably the most important cause of long term oil spreading is
wind stress on the slick and surface water. Unfortunately, this is a complicated
phenomenon that
is
ollly partly understood. Observations at past spills have
resulted
in
a rule-of-thumb that the o
il
slick moves
at
approximately 3
of
the
wind speed measured at 10 m above the water surface. Roughly two-thirds
of
this movement represents Stokes drift
of
the surface waves. The remaining one
third repre
se nt
s the movement
of
the slick along the water surface. Also, o
il is
driven into the water column by breaking waves and broken into droplets
of
different size (Dclvigne and Sweeney [63]). The larger droplets quickly resurface
while the smaller droplets
re
main subsurface for longer time periods and trail the
mov
in
g main slick.
Elli
ot
et a/. 6
1
hypothesize that this
is
the cause
fo
r the
'comer shape
of
many slicks where a thicker pan of the
oi
l at the upwind pan
is
encompassed in a larger sheen wh ich trails out behind the thick part. The
smallest droplets never resurface and are thus permanently removed from the
surface slic
k
Proper modeling of such phenomena requires a numerical
simulation
of
the lIear surface water flow
lborpe
[64]). However,
an
often
adequate a
lt
ernative
is to
use a boundary layer approach (E
lli
ot
[6
5]) where the
horizontal current velocity follows a logarithmic pro
fil
c and the vertical velocity
is calculated by using a suitably modified fonn (Kolluru et al. [66])
of
Stokes
L,w
w _ (drop) ' g6.
18v.
(30)
As
mentioned earlier, oil slicks often break
inlO
wind rows due to the effects
of
Langmuir circulation.
t is
generally believed that Langmuir circulation
is
produced by the illleraction of surface currents and Stokes drift due to waves
(Csanady [67]). Thorpe [68] and Farmer and i [69] have sketched
an
outline of
how to include Langmuir
eff
ects in weathering models but, at present, none of
the widely used models includes this feature.
There are other
fac
tors which can easily affect the area
of
a slick. Mosl
spreading algorithms assume ins tantaneous release
of
the spi
ll
ed o
il
and open
water conditions. However, r
eal
spill incidents may be causcd by leaks which
continue
al a varying ra te fo r hours or days and occur near a shoreline or other
impediments to spreading Changing currents from tides or other forces will aher
spreading patterns. Human interference through skimming and booming will
modify slick area. The importance
of
any of these factors will depend on the
spill incident.
Even
tu
ally, all slicks stop spreading. They may even shrink due to wave
stress. They also break into increas ingly smaller patches. The Fay fonnulas
theoretica
ll
y allow a mechanism
fo
r spread ing to stop (Mattson and Grose [70]).
If the net radial surface tcnsion is negative, the oil should stop surface tension
viscosity sp reading and, instead, contract into a lens with its thickness
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controlled by gravity. In practice, a lternative stopping mechanisms based on
sp
ill
volume or thickness are used instead
by
most models. Fay (45) himself
recommended that the
final
area
be
est
ima
t
ed from
the initial volume,
A
,'
V
(31)
Dodgc l a/.[46J state that the
sl
ick effectively stops spreading w
hcn
the thick
pan of the slick reaches a thickness of 0.1 mm. Many models use this value for
crude oils and a smaller number
for li
ght refined products (Reed [71 . There is
little accurate empirical
inf
ormation on final spill thickness from real
spi
lls
because techniques to perfonn the measurements are crude and unreliable, and are
seldom perfonned in any casc.
Consideration must be given to the numerical techniques used in simulating
spreadin
g. As
spreading algorithms incorporate more features, an ana
lyti
c
solution becomes increasingly impractical. A numerical solution, us
in
g the
Lagrangian element method, is the normal choice
for
many models. While
th
e
minispill approach mentioned earlier is computationa
lly
attractive, it has some
inherent drawbacks. Such
an
approach neglects thc
fact
that the forces acting on
the slick are interconnected and non- linear in oil volume. More imponantly,
it
ignores the fact that
all
the above-described processes are acting simultaneously
on all the sp illed o
il.
Separation
of
the slick into distinct patches is a naturally
occurring mechanism
and
should, ideally, be the end result of the modc1ing
process rather than pre-defined as to shape and number by the modeler. An
alternative technique is leave the Lagrangian elements as distinct points that are
equa lly subject to
all
the physical forces described. Oa[t[72] describes a method
fo
r translating a set
of
distinct points into a continuous distribution for area
calculations by utilizing Thiessen polygons.
5.2 Evaporation
Probably
no
area
of
oil weathering has been more studied and tested than
evaporation. It is therefore surprising that there is still considerable controversy
on the exact mechanism controlling evaporation rale.
It
is , however,
not
at all
surprising that the reason
for
any disagreement can be traced
10
the fact that the
oil is a mixture and not a pure chemical.
Certain points are agreed upon
by
experts in the field.
It
is recognized that,
for
most spills. evaporation is the major mechanism
for
mass removal from the
surface slick. This includes both natural processes and cleanup attempts.
t
is
quite
po
ssible to lose half
of
a light crude spill ju
st
due
10
evaporation. Small,
light refined produ
ct
spills will typically disappear in less than a
day
due to
evaporation unless high sea states drive the oi l
int
o the water column.
Also, evaporation changes the chem i
cal
mixture of the slick as the lighter
components evaporate more qu ickly than the heavier hydrocarbons. The structure
of
thc molecule is
of
some importance. Aromatic
s
for example, lag behind
para
ffin s.
However, the major factor is molecular weight. The vapor pressures
of
hydrocarbons with a carbon number of
10
or above are orders of magnitude
sma
ll
er than the vapor pressures of hydrocarbons with carbon number of 6 or
below. If the only infonnation needed for cleanup is, say, how much oil will
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reach a beach after a week at sea,
t
may not be necessary to calculate a time
dependent evaporation rate for the slick. Instead, it may be suffi cient to simply
determine which fractions wi
ll
, or will not, evaporate. Smith and Macintyre [73]
found that very linle
of
any d
is
tillation cut with a boiling point above 270°C
will evaporate. This corresponds to a cutoff for non-evaporation
of
all
hydrocarbons with 15 carbon atoms or more.
Most spill weathering models base thei r evaporation algorithms on the
assumpt ion that the oil slick can be treated as a ven ica
ll
y homogeneo
us
mixture .
This
w
ell-mixed assumption a
ll
ows, with suitab
le
modification, the
us
e
of
evaporation estimation techniques developed for homogeneous liqu ids (Brutsaen
(2 3]). The driving factor for evaporation will be t
he
effective vapor pressure
of
the oil and the limiting factor
will
be the ability
of
the wi
nd
to remove the oil
vapor from the surface boundary layer.
Given the well-mixed assumption, there are two general approaches to
calculating evaporation rates. The
fi
rst approach is the pseudo-component
method (Payne el al. [10]; Jones [20)),
wh
ere, as mentioned earlier, the oil is
pos
tu
lated to consist
of
a
li
mit
ed
number
of
components, with each component
corresponding to one of the cuts from the distillation data for the o
il of
concern .
Each component is characterized by a mole fraction and a vapor press ure. The
evaporative
flu
x of each component is assumed to be a fun ction of the vapor
pressure of the liquid phase
of
the component
(32)
where the j subscript refers to the individual pseudo-component. Assuming
Ra oult
s
Law for an ideal mixture, the total evaporati on rate is given by the sum
of the individual rates. Note that whi Ie the overall evaporation rate fo r the slick
decreases with time,
it
is poss
ib
le
fo
r t
he
evaporative flux
of
a particu lar
component to increase
if
the mole fraction
of
that component increases.
Different researchers ha
ve
different expressions for the mass transfer
coefficient
K .
Mackay an d Matsugu (74] suggest a mass transfer coefficient
re lated to the Schmidt number. which
is
defined as the ratio
of
the kinematic
viscos
it
y to the molecular di
ffu
sivity.
J
K _
o) (3 3)
Si
nce there arc different Schm idt numbers for each
of
the pseudo-components,
there
wo ul
d theoretica
ll
y be different mass transfer coefficients for each
component as
weI .
In practice, howeve
r,
an average value, related to 7/9 of th e
wind speed, is usually used (Mackay and Leinonen [44]). Typical ranges for K
are between a 0.5 and 2 cm /s. Williams el
al
. (7 5] proposed an exponential
function
of
the wind speed for the
li
ghter hydrocarbons and a constant value for
the heavier ones. Others use a
ma
ss transfer coefficient thaI is linear in wind
speed.
The oil temperature in the denominator of eqn (32) is usually set to the
ambient water temperature, although some models have used th e ai r temperature
instead. Because of oil s insulating capabilities, and the effects
of
solar radiation
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on
th
e dark slick, oil sl icks which are contained and thick may, in fact, have a
surface temperature that
is
much warmer than the surrounding water or air
temperature (Mackay and Matsugu [74); lon es el
aJ
[76] .
In real ity, the mixture of hydrocarbons that makes up an oil s
li
ck is not an
ideal mixture and Raoult s Law is not stric
ll
y true. There is the heat
of
solution
caused
by the mixing,
in
addi tion to the heat
of
vaporiza
ti
on, that mu st
e
ovcrcome for evaporation to occur. One
wa
y to correct for this is to reduce the
pseudo--component vapor pressure by multiplying it by an activity coefficient
which
is
slightly less than one (Stolzenbach et al. [ 5] .
Rather than deal with the complexities
of
the pseud
o--co
mponent model,
Mackay et al 7 J suggestcd treating the slick as
if
it were a single-component
fluid with changing properties due to weathering. They introduced the idea of a
dimensionl ess variable e called evaporative exposure,
K t
0 = -
v
(34)
which was proportional to time but had a linear relat ionship to fract ion
evaporated
(35)
II is
important to note that the above equation uses the liquid-pha
se
boiling
point temperatu re rather than the more common vapor·phase temperature. t also
assumes that the liquid di stillation curve can be adequately characterized by a
straight line, which ma y not e correct in some cases.
The mass transfer constant
in
this model, often referred to as the Stiver
Mackay model, has a sim ilar form to the one used for the pseudo·component
mode\. S
ti
ver and Mackay [77] recommend
K
o.o02u . 36)
The dimension less constants a and b
in
eqn (35) arc empirica
ll
y
fit
, Mackay f
af [7] suggest
a = 6.3 b=10
.3
,
(37)
whereas Bobra [7S] and Belore and Buist [79] determine a and b values fo r
specific oils through laboratory measurements and a curve-fitting process.
Unfortunately, a and b are not independent, and small experimental and curve
fitting errors can generate widely varying values for them. Also, Overstreet
er
al.
[SO] showed that model results were, in some cases, highly sensitive
to ,
wh
ich it
sclfmust
be estimated through laboratory measurements .
Jones [
20}
found that the Stiver-Mackay model generally predicted larger
evaporation amounts than hi s version of a psuedo-component model. Recently,
Reed el 01. [SI] have questioned the linearity assumption implicit
in
the
exponent
in
eqn (35) for some oils .
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A conceptually different approach than the well-mixed model has been
proposed by Fingas [82J, based on laboratory experiments at Environment
Canada. Fingas proposes that evaporation is not boundary layer limited and can
be described by equations that are functions of temperature and time alone.
Except for a
few refi ned products, Fingas fi
ts
most oils to a logarithmic curve.
For example, the fraction evaporated for Prudhoe Bay crude is given by the
fonnula
= [0
.0169 +0.0045· (1
-
2 7 3 ) J . l n 6 ~ l
(38)
Fi
gure 6 shows a compari
so
n of the expected evaporat ion from a Prudhoe Bay
crude spill according to the Fingas model and the Stiver-Mackay evaporat ive
exposure model, assuming a
10
knot wind, I mm. thick sl
ick
and water
temperature of 15°C.
1
•
•
S
]
j
g
0
.4 ------ --------
0.3 I-
0 2 I
-
i ~
0.1 f
--
_.--_
..
---
-
O ~ ~ I ~
o
S M
Ping
SO
ho
100
Figure 6: Comparison of evaporation estimates using the Stiver-M ackay model
and the Fingas model for a
Prudhoe Bay crude spill
One could argue from theoretical principles that the Fingas model wou
ld
be
consistent with a model proposed by Payne et al [10] and Hanna and Drivas
(8 3] for removal
of
the lighter slick components. According to Hanna and Drivas
[83] , for high volatility componenls, diffusion through the sl ick itself is the
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mechanism limiting their evaporation rate. The presumption is that, shortly after
the spill happens, the volatiles close to the surface are preferentially removed,
leaving behind the larger molecules with lower vapor pressure. The volatile
compounds deeper into the slick then migrate to the surface, creating a
concentration gradient within the slick. This diffusive process, and not
boundary-layer effects, is the limiting factor controlling evaporation of these
lighter molecules. Hanna and Drivas [83] develop an inequality to detennine
whether a
component j is diffusion limited.
In
slightly modified form, it is
(39)
Provided this time-dependent inequality holds, the process is diffusion-limited.
If
so, the governing equation is the one-dimensional diffusion equation for the
concentration
of
the particular volatile component being modeled
(40)
major difficulty is to estimate the appropriate value for the diffusivity D
Hanna and Drivas [83] use a correlation for organic/organic liquid diffusivity
from Perry [12]
41 )
Typically, the volatile component selected
is
benzene since it is the lightest
of
the aromatic compounds and is a known human carcinogen. The benzene
content
of crude oil averages about 0.2 and is higher for certain refined
products. Holliday and Park [84] review some of the work on modeling benzene
and other oil vapors.
third possibility for evaporation was proposed by Payne l al to] and by
Lehr [85]. Both suggest that, under cenain conditions, while most
of
the slick is
well-mixed, a thin crust may form and impede evaporation. Photo-oxidation
could playa role in the fonnation
of
such a crust.
5.3 Dissolution
The old saying that oil and water do not mix is scientifically accurate when it
relates to molecular dissolution of oil into the surrounding water. Dissolution is
unimportant for estimating the mass balance
of
the slick. Removal by this
process
is
orders
of
magnitude smaller than evaporation. Furthennore,
components that do dissolve may later evaporate from the water surface.
Unfortunately, the more soluble hydrocarbons are likely to be the more toxic, so
that even small concentrations may have adverse biological consequences .
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Few models exist for dissolution. Mackay and Shiu [86] have measured the
aqueous solubility of fresh and weathered crude oil. Payne
el
al
[101
and
Mackay and Leinonen [44J have constructed pseudo-component models similar
to the ones used for evaporation . or example, Mackay and Leinonen [44J
ca
lculate the dissolution flux for pseudo-componentj according
to
the fonnula
(42)
The key factor
in
properly estimating dissolution is estimating the surface area
of
any dispersed oil, since dissolution is apt to be much faster from the dispersed
droplets than from the surface slick. Based on mass transfer rate measurements,
Mackay and Leinonen [44J suggest a Sherwood number (the ratio
of
the droplet
diameter times the mass transfer constant to the diffusivity in the water) of about
2. They conclude that, for droplets
le ss
than
0 1
mm in diameter, dissolution is
very rapid for any component that will dissolve at all. Any remaining material in
the drop
le
t will consist
of
relatively inso
lu
ble hydrocarbons, i.e. hydrocarbons
with a carbon number greate r than about 10.
5.4 Dispersion
While oil may not dissolve in water to any great extent,
it
can certainly disperse
as a cloud of droplets when subject to turbulent wave energy . These droplets will
e
in
various sizes, and will be subject to the conflicting forces of buoyancy and
turbulence. For th e smallest oi l droplets, as for the smallest dust particles in the
air, turbulence will win the battle and the droplet will not refloat to rejoin the
slick. For slicks of
low viscosity oil under high sea state conditions, dispersion
becomes the dominant mechanism for removing spilled
oi
l and can easily
displace 90 or more of the surface slick.
The early models (Blaike ly el al.[87] of dispersion simply assumed a
constant dispersion rate as percentage of th e oi l slick per day, based on the sea
state . These numbers tended to
be
quite large, from
10
to 60 per day. This was
an
overestimate for large, weathered oil slicks.
Mackay
t
af. [49] also constructed a fonnu
la
that computed a fractional rate
of removal of the slick by dispersion. Rather than using a simple look-up table
based on sea state, their model was a product of two factors. The first factor
calcu lated the fraction of the sea surface subject to dispersion and the second
factor estimated the fraction that would not rejoin the slick, staying pennanentiy
dispersed in stead.
About the same time, Aravamudan
et al.[88J
developed a somewhat
inappropriately named simpli fied model to calculate dispersion. While too
complex to gain wide acceptance, it laid the foundation for othe r models that
followed. t not only calculated th e rale of dispersed oil droplet fonnation based
o n the fraction of breaking waves, but also predicted the distribution
in
droplet
sIzes.
Most weathering programs now use some version of
the dispersion model
developed by Delvigne and Sweeney [63]. For this model, the entrainment of oil
is estimated as
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(43)
where the dissipation ofwave energy per unit area is given
by
2\ = O.OOI7·gp H:
(44)
and the fraction of breaking waves per wave period
j ,
is estimated to be
(45)
f
is
obtained (to within a constant) by integrat
in
g the product of the droplet
volume and the frequency distribution of droplets over the volume of oil. In
practice, thc integration
is
performed between the minimum droplet size and
maximum droplet size, determined from cxperimenlal data. This yields
(46)
where a maximum droplet size 6
max
is usually set equal to the maximum
droplet size that would not
e
expected to refloat, based on Stokes Law or
experimental observation. Typically. this is about 50 to 70 microns. Larger
droplets than this will
re fl
oat faster than the su rface slick can traverse
th
e area
covered by the dispersed oil and hence will rejoin the surface slick. Drops 70
microns or smaller arc effectively held in suspension as shown by examin ing the
steady-state tail of the droplet diameter ve rsus refloat time curve as measured by
Delvigne et al. [89). Reed et al. [81J have objected to usi ng a fixed droplet size
as a criterion for refloating, pointing out that the lim
it
for pennanent dispersion
should
e
related to droplet rise velocity and sea state. A commonly used,
although no t necessari
ly
correct, minimum droplet size is 5 microns.
N( J), the number
of
oil droplets per unit volume
of
water per unit droplet
diameter, is a
fun
ction
of
droplet size
_i
{b ocb
(47)
The experimentally determined parameter c
is
highly sensitive to the viscosity
of
the oil F igure 7).
As
the slick becomes more viscous, the energy required to
tear
it
into sma
ll
droplets increases and its dispersibility decreases. Laboratory
model studies (Delvigne {90D showed that droplet entrainment is difficult when
the slick s kinematic viscosity exceeds 3000 cSt.
The dispersed oil droplets are presumed to e initially distributed
unifonn ly throughout the water column to a depth
of
1.5
wave heights. The
larger droplets retum 1 the sl ick
wh
i
le
the smaller droplets diffuse th rough the
water column. Mackay et
al
.[91] have proposed a constant vertical diffusion
coefficient of over 100 square centimeters per second for use
in
estimating this
dispersion. Others have suggested using a diffusion coefficient scaled to the
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existing wind speed and current in the area
o
the slic
k
Farmer and Li [69] argue
that the effects
o
Langmu ir circu lation must be taken into account when
estimating subsurface oil concentration. While wave energy dominates the
mixing process in the first
few
meters, Langmuir cells are more important for
greater depths. Therefore, diffusion coefficien ts may have to be properly
determined based upon the appropriate depth scale
2 0 0 0 ------
----
------
--
-----
1500
1000
500
centistokes
Figure 7: Plot o empirical dispersion constant versus viscosity.
5.5 SWimentation
Sedimentation is defined as adhesion
o
oil to solid particles
in
the water
column.The significance
o
sedimentation as an important removal process
depends critically on the sediment load o thc surrounding water. For muddy
rivers, where the sediment load can bemore than 0 5 kglm
3
, the removal
by
sedimenta
ti
on
is
considerable and exceeds the loss due to normal dispersion. For
open ocean condi tions, where sediment load
is
less than 1 o this amount,
removal by sedimentation is trivial.
The actual physical process
o
sedimentation is quite complicated and has
been o
nly
fragmentarily researched. Studies
by
Poirier and Thiel [92]
and by
Hartung and Klinger [93] indicated that the process
is
affected by type and size
o
the suspended material, salin ity o the water, and sulfur content o the oil
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Others have suggested that oil drop let size,
wh
ich is directly
re
lated to oil
viscos ity and wave energy, plays a signifi cant ro le. One fonnula proposed by
Science App
li
cations Interna tion
al
(Payne et .[94] computes the mass of oil
los t per unit water volume per unit time as
q k/fC C
48)
The sl
ickin
g parameter
k de
pends on the type and si
ze of
the particl
e.
Typical
values would
be
on the order of
1
00 cm
3
/
kg
of material.
Th
e energy dissipation
r
ateE
can
be
estimated by the breaking wave energy calculations described
previously. In fact, the assu
mp
tions that are included in the Oelvigne dispersion
model can
be
combined with this model to yie ld a fonn u
la
for the total
sedimentation rate pe r
un
it area o f the slick. Th is involves integrating over the
water depth th at the breaking waves drive the oi l droplets,
l .l
lI
Q :
(4
9)
•
The combin ed oil-sediment particle will typically have a different buoyancy than
either alone. Us ually, th e buoyancy wi ll be negative. and turbulence will be
req
ui re
d to
ke
ep the oil-sediment particle from
se
ttling to
th
e bo
tt
om.
5.6 Emulsification
Emulsi
fi
cation is t
he
rever
se
of dispers ion. Rather than oil droplets dispersing
into the water column, water is entrained
in
th e oil. This causes significant
changes
in
the volume, density, and , especia
ll
y, viscosity of the slick.
It
is not
uncommon for the viscosity
of
an emulsified oil to e two or three orders of
magnitude larger than the viscosity
of
the fresh oi l. Thi s has importa
nt
imp
li
cations fo r cleanup policy, as many common cleanup tools may be rendered
ineffective when the oil becomes too visco
us.
Not all oils will emulsify and so
me
oils w
ill
e
mul
sify only after they have
weathered to a certain extent. Caneveri and Fiocco [95] con
cl
uded th at trace
metal content may playa factor
in
the emu
ls
ification
of
fresh crude oils. They
asse rt that o
il
s with vanad ium and nickel content above 15 ppm readily emu ls ify
whereas those with less do not. However, for mo st oi ls, it appears that wax and,
most
imp
ortantly, asp haltene content play the d
om
inant role in detennining
wheth er emulsification will occur. Waxes and asphaltenes may be conside
re
d as
so lutes in a sol
ven
t consisting
of
the lighter hydrocarbon components of the o
il.
As
the oil weathers and loses the light ends, these large molec ules may
precipitate out, fonn
in
g crystals th at stabilize small water droplets in the oi l
(Bridie el al [96 J . Resin level may playa role as well, since resi ns he lp to
maintain asphaltencs
in
solution
S
peight [97]) bu t al
so
can act alone
as
effective
emulsifiers (80bra [98]). A common, but not ne cessarily reliable, ru le-of-thumb,
is that crude oil will emuls ifY when the wax and asphaltene content reach 5
of
the mass
of
the oil.
Li ght refined products generally w ill not emulsify s
in
ce they do not contain
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the right hydrocarbon compo nents to stabi lize the water droplets. In rare cases,
old diesel spills appear to emu
ls
i
fy,
pe rh aps due to the creation
o
emulsifYing
molecules by photo-oxidatio n. Bunker fuel s may fonn weak emulsions with
relatively low water content.
Fingas and Fieldhouse (99) have reccntly divi
ded
oils into three categoric
s,
ba
sc
d on the
ir
abil ity
to
fonn stable
em ul
sions. They c
la
ssi
fy
stable emulsions
as those that retain their water content over time and show very large increases
in
viscos it
y.
Stable emulsions have su fficient as
ph
altene conte
nt
, typical1y greater
than 5 , to stabilize the water droplets in the oil. Mesostable emu ls ions have
insufficient asphaJtenes to make them completely stable. They will lose some of
their water content i left und
is
turbed and will show viscosity increases an order
o
magnitude less than stable emul sions. The third category
is un
stable
emulsions,
wh
ich w
ill los
e practically
all
their water content
i
left at rest.
As mentioned ea
rli
er, the onset o
em
ulsification
is
important for cleanup
decisions and it is therefore use
fu
l fo r a weathering mod
el
to have the capabi l
ity
to forecast
thi
s event. Unfortunately, the best way to do this is to u
se
observational data from actual spills. Since this is not avai lable except for a
handful o oil s, results from small test slicks or laboratory data from artificially
weathered oil must e used in stead (Oaling et al. 1 00
1).
Sometimes, estimates
ean be made on new oils by compar ing them wi th tested oils o similar
composition.
Once an
oi
l begins to emuls
ifY
, the process typically proceeds at a rapid rate.
Most models use the simple
fi
rst-order rale law proposed by Mackay
et
aJ [49]
d
,
y )
= k U - .
dl ' y_
(50)
A typic
al
va
lu
e lor
k_
is I to 2 ms/m
2
o
s lick. Daling and Brandv
ik
[101]
concluded that the specific va lue depends upon the type o oil and its state o
w
ea
thering. However, the range
o
values appears to be small for most crudes.
Also, the trans
iti
on time
from
non-emuls ified oil to emulsified
oi
l is usually
smaller than the expected error in estimating the onset
o
emulsion fonnation.
Consider
th
e example
o an
oil wit h a water up take parameter
o
1.5 ms/m
2
and
a
ma.ximum
water content fraction of 0.75 expo
se
d to 10 m/s wind. The time for
the oil to reach 95 of complete emulsification according to eqn (50) is about 4.
t
is very un likely that the onset
o
emulsi
fi
ca
ti
on co uld be de tennined to this
accuracy in a real sp
ill
situation .
t
is questionable that a formula such as eqn (50), whi ch tracks only water
co
nt
en t, provides an adequate representat ion o emulsification.
As
Fingas and
Fieldhouse [99] have pointed o
ut
, it does not d
is
tinguish betwt:cn mesostable
and stable emulsions. Stability and viscosity may be re lated not only to to water
content but also to thc distribution of water drop let size in the emulsion (Barnes
[1021). Figu re 8 shows two oil-water em ulsions with the same water content but
different water drop
le
t distributions. The emulsion on the
ri
g
ht
w
ith
the greater
o
il
-water interfacial area would
be ex
pect
ed
to have higher viscosity and be mo
re
stable than th e emulsion on the left.
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o
l
Figure 8: Two different possible wa ter droplet distributions
in
emulsified o
il
Eley
el
[103] have suggested using a first-order equation in
interfacial area
d
dl S,..,
lI)
where
th
e intcrfacial parametcr k is sensitive 10 wave energy (NOAA [17])
k,
C ;
U .
52)
Other
processes
The two long term mechanisms
fo
r the breakdown of hydrocarbons in the
environment are photo-oxidation and biodegradatio
n.
For spills in a cold
environment, oil-ice interactions may be important.
6.1 Photo-oxidation
The combination
of
hydrocarbons with oxygen is called oxidation. The newly
fonn ed oxidized compounds ma y affect the oi l slick by increasing dissolutio
n,
dispersion or emul sification. While trace metals in the oil may influence the
oxidation process, ultraviolet light sig nificantly increases oxidation. Virtually all
of
the mo lecules that evaporate from t
he
slick undergo photochemical oxidation
in
hours or days (Altshuler and Bufalini [104); Heicklen [105]). Also, beach
ed
oil w ill show the effects of exposure to sunlight. Ev
en fl
oating oi l can show
chemical changes due to this
pr
ocess. Overton [
31}
exposed IXTOC I crude o
il
to sunlight and discovered the formation
of
tarry flakes, showing the
involvement
of
photolysis . Observers at the Mega Borg sp ill in the Gulf
of
Mexico noticed the formation of crusIs on floating tarmats and tar ba
ll
s, with the
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c
Co
~
~
c ,
Cyl
,e
1.
".
J.
f••
g
h
N,
' final slick area (m
2
)
' hole area (m2)
= initial area for gravity-viscous spreading (m
2
)
= empirical constant in Mackay-Stiver evaporation model
'" component concentration in slick (kg/m
3
)
=
drag coefficient
= empirica l dispersion constant (- kg 112lm3)
= psuedo-com ponent solubility (kg m
3
)
=
psuedo-component bulk water phase concentration (kg m
3
)
= 1.0538
)
10 -
4
m
3
/mol
=-3 .5589
)
10-
4
m
3
/ mol
K)
=
.2449
)
10
-
9
m
3
/
(mol.K
2
)
=4 .132x 10 -
2
kg /mol
=
1.985 x 10-
4
kg/(rnol · K)
= .494 x 10-
7
kg/(rnol· K2)
= o il droplet mass concentration in water (kg/m 3)
=
sediment mass load in water (kg/m
J)
=
constant relating viscosity to fraction evaporated
,.
constant relating viscosity to slick temperature
, -
0.2
= 0.015 (slm)
= I S
x
10-
5
s
m' )
=
parameters relating viscosity change to emulsion water content
= dissipation of wave energy per unit area 1
1
m2)
= eddy diffusion coefficient (r02/s)
:::
Fay pseudo diffusion coefficient
m
2
/s)
=
vertical diffusivity of volatile component through slick
(m2
/
s)
=
droplet diameter (m)
' volume fraction evaporated
:::
asphaltene fraction
' fraction of breaking waves per wave period
(5
.
1
)
= volume of o
il
entrained per unit water volume
=
fraction
of
sea sur face covered by whitecaps
=
gravitational acce lera tion
=
9.8
(m/
s
2
)
=
o
il
slick thickness (m)
=
significant wave height (m)
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K
=
mass transfer coefficient
m /s)
=
mass transfer coefficient for dissolution (mls)
K
im
=
Hanna-Drivas mass transfer coefficient (moVm
2
Pa sec)
k,
=
sedi mentation sticking para
me
ter
k_
=
water uptake parameter (slm
2
)
k, =
interfacial parameter (m
2
/s)
MW
=
mo
lecular weight
kg I
mol)
N O) =
oil droplet number per
un
it volume
of wa
t
er
per unit dro ple t
diameter
p.
=
vapor pressure
N /m
2
)
PP
=
pour point K)
PPo
=
pour poi nt of fresh oi l K
)
Q..,
=
o il entrainment rate (kgl(m
2
s )]
Q.
=
oil leak rate
m
3
/s)
q...
=
o
il
sed imentation rate per unit water volume (kgl(m
2
s)]
Q
...
=
o il sedimentation rate per unit slick surface area (kgf(m
2
s»)
r
=
radius
of
slick
(m)
R
=
gas constant
(J/K)
S
=
oil -water interfacial area
m
2
)
S , =
maximum oil-water interfacial area (m
2
)
S,
=
Schmidt
number
ST
oil-water interfacial tension N /m)
ST
,
initial o il -water interfacial tens ion
N /m)
air-water
internc
i
alle
nsion
N/m )
Sf ,
=
initial air-water interfacial tension
N/m)
l
=
oi l temperature
K)
T r
= reference temperature
K)
r. = boiling point
K)
r =
slope of liquid bo iling point versus fraction evaporated graph
K)
=
t ime (s)
I , =
period
ofthe
peak of the wave spectrum (s)
U, =
wind speed at z elevation (m/
s)
U,
=
wind stress fact
or
(m/s)
V
=
oil vo lume (m
3
)
Vo =: initial o il volume (m
3
)
w
dr
. = vertical droplet rise veloc ity (m /s)
Y = water fraction in the emulsion
Y
.. =
maximum water frac
ti
on
Z,q =
equil ibrium level (m)
Z_ ' hole level in tank
m)
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Proc. of the Nineteenth Arctic and Marine Oil Spill Program Technical
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19
96.
[
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il
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ll
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