dEPA
United States
Environmental Protection
Agency
Research and Development
Environmental Research
Laboratory
Corvallis OR 97330
EPA-600 3-79-041
April 1979
Transport of Oil
Under Smooth Ice
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EPA-600/3-79-041
April 1979
TRANSPORT OF OIL
UNDER SMOOTH ICE
M.S. Uzuner, F.B. Weiskopf, J.C. Cox
and L.A. Schultz
ARCTEC, Incorporated
9104 Red Branch Road
Columbia, Maryland 21045
Contract No. 68-03-2232
Project Officer
Merritt A. Mitchell
Arctic Environmental Research Station
Environmental Research Laboratory
College, Alaska 99701
CORVALLIS ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U. S. ENVIRONMENTAL PROTECTION AGENCY
CORVALLIS, OREGON 97330
-------
DISCLAIMER
This report has been reviewed by the Corvallis Environmental Research
Laboratory, U.S. Environmental Protection Agency, and approved for publication.
Approval does not signify that the contents necessarily reflect the views and
policies of the U.S. Environmental Protection Agency, nor does mention of trade
names or commercial products constitute endorsement or recommendation for use.
-------
FOREWORD
Effective regulatory and enforcement actions by the Environmental Protec-
tion Agency would be virtually impossible without sound scientific data on
pollutants and their impact on environmental stability and human health. Respon-
sibility for building this data base has been assigned to EPA's Office of Research
and Development and its 15 major field installations, one of which is the Corvallis
Environmental Research Laboratory (CERL).
The primary mission of the Corvallis Laboratory is research on the effects of
environmental pollutants on terrestrial, freshwater and marine ecosystems; the be-
havior, effects and control of pollutants in lake and stream systems; and the de-
velopment of predictive models on the movement of pollutants in the biosphere.
This report describes the results of a study to examine the current-driven
spread of oil under a smooth ice cover. As oil and gas exploration activities
increase in cold climate areas, the problems associated with oil spills become
increasingly important.
James C. McCarty
Acting Director, CERL
-------
ABSTRACT
Previous studies of oil-ice interaction have been limited to spreading
under quiescent conditions. The present study examines the current driven
spread of oil under a smooth ice cover. Generalized relations between current
speed and oil transport rate are developed and found to be strongly dependent
upon the orientation of the oil slick to the direction of current flow. Methods
for application are presented.
The laboratory experiments reported were performed during October and
November 1975. A draft final report was submitted to EPA for review in December
1975. This report was submitted in fulfillment of Contract 68-03-2232 under the
sponsorship of the U.S. Environmental Protection Agency and work was completed
in February 1979.
TV
-------
TABLE OF CONTENTS
Page
INTRODUCTION 1
SUMMARY 4
CONCLUSIONS 5
BACKGROUND 7
Spread of Oil on Ice 1
Spread of Oil on Water 12
Spread of Oil Under Ice 16
ANALYTICAL APPROACH 20
EXPERIMENTAL PROGRAM 24
Test Apparatus 24
Test Procedure 26
Test Results 30
Analysis of Test Results 41
APPLICATION OF RESULTS 46
REFERENCES 48
-------
LIST OF FIGURES
No. Title Page
1 Schematic Representation of Events which Could Result
in Oil Spilled Beneath Ice 2
2 Relative Duration of Spreading Regimes 8
3 Reverse Flow at the Leading Edge of a Slick 15
4 Spreading of Oil Over and Under Sea Ice as Reported by
Hoult 17
5 Schematic Representation of Oil Slick Transport Under
Ice Cover 21
6 Schematic Depiction of ARCTEC's Ice Flume 25
7 Oil Discharge Calibration Data for Pressurized Oil
Injection Chamber 27
8 Photo of Pressurized Oil Injection Chamber 28
9 Viscosity vs Temperature for Crude Oil 29
10 Photo of Oil Skimmer in Tail Tank 31
11 Photo of #2 Fuel Oil Plume Under an Ice Sheet 32
12 Photo of Cold Crude Oil Under an Ice Sheet at High
Water Velocity 34
13 Schematic Representation of the Folding Phenomena at
the Upstream End of a Crude Oil Slick 35
14 Slick Speed versus Current Speed for #2 Fuel Oil 39
15 Slick Speed versus Current Speed for Crude Oil 40
16 Generalized Slick Transport Relationship Based on No. 2
Fuel Oil Tests where the Slick is Oriented Parallel to
the Flow . 43
17 Generalized Slick Transport Relationship Based on Crude
Oil Tests Where the Slick is Oriented Transverse to
the Flow 44
-------
LIST OF TABLES
No. Title Page
1 Equations for Oil Spreading Rate under Quiescent
Conditions On or Beneath an Ice Cover 19
2 Summary of Test Data 37
vii
-------
LIST OF SYMBOLS
A - plan surface area (cm2)
B, B _, B = experimentally determined coefficients
C = coefficient
C-, = drag coefficient
Cf - friction coefficient
C - shear force coefficient
s
C = fixed wall shear coefficient
w
d - water depth (cm)
F-, = form drag (gm-cm/sec2)
Ff = friction force due to buoyancy (gm-cm/sec2)
F = gravity force (gm-cm/sec2)
F. = inertia force (gm-cm/sec2)
X-
F = force due to a pressure drop (gm-cm/sec2)
F = shear force at oil water interface (gm-cm/sec2)
S
F - surface tension force (gm-cm/sec2)
F = viscous force (gm-cm/sec2)
g = gravitational constant = 980 cm/sec2
h ~ thickness of oil slick (cm)
k, kl3 k2 - experimental constants
1 - oil slick length (cm)
L = characteristic slick dimension (cm)
m = mass (gm)
U
N = densimetric Froude number^- w
N = slick Reynolds number =
Pfl
f Ar) 1/2
N - characteristic Reynolds number = v^ ; L
X \)
P = hydrostatic pressure (gin/cm-sec2)
Q = volumetric flow rate of the oil (cc/sec)
R = radius of oil slick (cm)
t - time (sec)
v i i i
-------
T = temperature (°C)
u = velocity (cm/sec)
u - nondimensional velocity = s/ w
U = slick velocity (cm/sec)
S
U = water velocity (cm/sec)
w
V = volume of oil (cc)
w = siick width (cm)
a = contact angle included in the oil
6 = water boundary 1 ayer thickness = A^fr (cm)
p - p
7 1 n
A = relative density difference = —
n = height of roughness element (cm)
9 = circumference of slick (cm)
K = proportionality constant
y0 = viscosity of oil (gm/cm sec)
y = viscositv of water (gm/cm sec)
w
v = kinematic viscosity of water (cm2/sec)
P0 = density of oil (gm/cc)
p = density of water (gm/cc)
w
T = shear stress (gm/cm-sec2)
a
net surface tension coefficient (dynes/cm)
a0 = surface tension coefficient (dynes/cm)
-------
ACKNOWLEDGMENTS
The authors wish to express their appreciation to Mr. Merritt A. Mitchell
of the EPA Arctic Environmental Research Laboratory for his assistance and
cooperation throughout the project.
Appreciation is also extended to the ARCTEC test team for their dedi-
cation and enthusiasm under difficult conditions including low temperatures
and the handling and clean-up problems inherent in laboratory testing with
crude and fuel oils. The test team included engineers Francis B. Weiskopf
and Peter P. Kosterich, and technicians Rick Shelsby and Roy Schnebelen,
under the direction of Mehmet S. Uzuner. Jack C. Cox and Lawrence A. Schultz
contributed to the final analysis of the test results.
-------
INTRODUCTION
As more energy is consumed, it becomes increasingly more difficult
to find new energy sources and to cope with the problems associated with
their development. Increasing demands for energy and recent discoveries
of petroleum in the arctic have resulted in the intensification of oil and
gas exploration activities in the arctic. The drilling operations associated
with both the exploration and development of these resources and the event-
ual transportation of oil to commercial centers results in an increase in
the possibility of oil spills on or beneath ice.
The problem of oil spills is being investigated in order to provide
information on the spreading rate of oil slicks, their transport by winds
and currents, and their effects on the environment. The results of such
studies will influence the selection of proper spill response techniques,
both in terms of timelines and effectiveness. Most of these investigations,
however, are limited to spill location prediction models, cleanup procedures,
and the mobility of oil slicks in temperate waters. The behavior of oil
spilled in the presence of an ice cover on quiescent waters has also been
investigated to a limited extent. Little is known, however, as to how oil
will behave when spilled beneath an ice cover in the presence of a current.
A fundamental knowledge is required to provide a technique for predicting
the movement of oil beneath an ice cover in the presence of a current, in
order that the oil slick can be located, and effective spill response
activities undertaken.
The following events could result in an oil spill beneath ice cover:
1. Rupture of an underwater pipeline
2. Oil well leakage or blowout
3. Natural oil seepage
4. Oil leak from a ruptured vessel.
These situations are shown schematically in Figure 1. Oil leaking from these
sources will spread due to gravity forces and its internal energy while being
dragged along by the flow. After the leakage is detected and stopped, the
slick formed beneath the ice cover could be transported by the flow. The
rate of oil transport will most likely depend upon oil properties such as
viscosity and density, ice conditions such as surface roughness and porosity,
and the magnitude of the water current.
The hypotheses concerning the damaging effects of oil spills to the
arctic environment vary considerably from one investigator to another.
Campbell and Martin [1] and Barber [2] predicted that spills in arctic
regions would spread over a wide area causing large portions of the arctic
ice to melt as a result of the change in the heat balance, finally affecting
the climate of the entire northern hemisphere. On the other hand, Glaeser
and Vance [3] and Golden [4] predicted that the spilled oil would be confined
to a small area, causing limited ecological damage.
1
-------
/. SCV£AAT/C REPRESENTATION Of EVENTS WMCtf COMD
/A/ 0/L SP/LLED 0£N£ATH /C£
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The objective of this study is to develop a model for predicting the
behavior of an oil slick in a straight stream or river of uniform depth,
covered with a consolidated ice cover of uniform thickness. The water is
assumed to be unidirectionally flowing at a uniform rate. It is recognized
that field conditions can deviate significantly from these conditions;
however, this approach allows an investigation of the physical phenomena
involved.
-------
SUMMARY
This is the final report of a test program designed to establish the
transport rates for No. 2 fuel oil and crude oil under smooth ice. The
oils were tested in water currents ranging from 0 to 36 cm/sec, at temper-
atures between -5 and 0°C.
The spill velocity of No. 2 fuel oil varied linearly with water
current velocity, ranging from 0 to 11 cm/sec. The relationship between
spill velocity and current velocity for crude oil follows a power curve
over most of the range tested. The crude oil slick velocity ranged from
0 to 24 cm/sec.
After a thorough literature review and theoretical analysis, an
analytical expression was derived in an effort to generalize the transport
relation to any type of oil. The experimental results indicate that the
slick movement depends on whether the slick aligns itself longitudinally or
transversely to the current.
The analytical treatments developed have not been successful in de-
fining the distinguishing characteristics for the two types of behavior,
however, the proper relationship can be selected for field application after
observing the orientation of the slick relative to the flow.
-------
CONCLUSIONS
The conclusions which can be drawn from the work reported herein are
as follows:
1. For an oil slick beneath a smooth uniform ice sheet, the slick
velocity is related to the current velocity as follows:
Oil
Type
No. 2 Fuel
Crude
Viscosity
cp
7
24,500
Threshold
Velocity
cm/sec
4
8
Relationship of Slick
Velocity, Us, to
Water Velocity, f/w
cm/sec
us = 0.38 uw - 1.26
us = 8.6 x 10"6 uw'2%
us = 1.10 uw - 16.60
Range of
Applicability
cm/sec
0 - 36
8 - 28
28 - 36
2. For current velocities significantly greater than the range of
applicability specified above, the tests indicate that the oil slick will be-
come entrained in and distributed throughout the water column. The oil will
then be transported in suspension with the water flow in this distributed
manner, rather than along the underside of the ice surface in well-behaved
slicks. Further investigation of this type of oil spill transport is beyond
the scope of this study.
3. For oils other than the No. 2 fuel oil and crude oil used in the
test program a theoretical analysis of the forces controlling slick transport
and a comparison with the data yields a first approximation for predicting
the relationship between slick velocity and water velocity for oil slicks
transported beneath smooth uniform ice cover as follows:
(1-f/)2 = 2.15
0.450
1.1 5
for slicks oriented parallel
to the flow direction.
for slicks oriented transverse
to the flow direction.
4. In applying the above relationships it is necessary to know or
estimate the physical properties of the spilled oil. For refined oils
reasonable estimates of physical properties can be made if the actual
properties are not known. For crude oils, the physical properties can vary
drastically from reservoir to reservoir, and any estimate of physical proper-
ties, if the actual properties are not known, incorporates a greater level
of uncertainty.
5. Significant differences were observed in the behavior of the
crude oil slicks and the No. 2 fuel oil slicks. Crude oil slicks typically
became shorter and wider as they moved downstream, with some thickening of
the upstream portion at higher velocities. The crude oil slicks appeared to
-------
slide along the undersurface of the ice. In contrast to this, the No. 2
fuel oil slicks typically became longer and narrower as they moved downstream
and appeared to roll along the undersurface of the ice. Additional analysis
beyond the scope of this study would be required to explain the reasons for
these differences in behavior.
6. A single test performed using plexiglass as a simulated ice sheet
revealed that the behavior of the oil slick beneath such a simulated ice
cover was completely different. The crude oil used in this test adhered to
the plexiglass, leaving a stationary 0.25 to 0.50 cm thick coating on the
plexiglass. Neither crude oil nor No. 2 fuel oil adhered to either fresh
water or salt water ice in these tests.
7. Any significant discontinuities in the ice cover, such as an open
water ice edge or a slot, provided a region of containment and retention for
the oil slick.
8. It should be noted that the results of these tests apply to un-
bounded underice oil slicks. Any contact between the slick and a boundary,
such as the shores of rivers or streams, would be expected to result in the
retardation of slick movement.
-------
BACKGROUND
In order to introduce the problem of the spreading of oil and to
develop a knowledge of some possible approaches to modeling oil spill
behavior, previous work relating to oil spills over ice, under ice, and
in open water was examined.
For the spread of an oil slick on open water, there are several
analogies that can be drawn with stratified flows and saline wedges, thus
the problem is fairly well formulated. However, studies of oil spreading
on or under ice are very limited. The first comprehensive study of oil
spreading was done by Fay [5] who defined various regimes of oil slick be-
havior. For systems not under any external influence, such as winds or
currents, the driving forces due to hydrostatic pressure and surface tension
are balanced by the retarding inertial and viscous forces.
Initially in a slick spreading on open water, the inertial forces
and hydrostatic (gravity) forces dominate. As time progresses, the viscous
forces become more significant than the inertial, and, finally, as the slick
becomes thin enough, the surface tension force becomes more significant
than the gravity force. This results in three behavioral regimes: gravity-
inertia!, gravity-viscous, and surface tension-viscous. In Figure 2, Fay
suggests regions of applicability for each regime based on the size of the
slick and the duration of spreading. As can be seen, inertial effects can
be ignored fairly quickly after a spill has occurred.
Spread of Oil on Ice
Glaeser and Vance [3], McMinn [6], and Chen et al. [7], looked at
the spread of oil over ice. Following the concepts outlined by Fay, they
proposed a horizontal hydrostatic driving force given by
F = (~h P(2-nE}dh . (5)
9 \ o
an inertial force given by
Fi = m ~dt '
a viscous force given by
and a surface tension force given by
FT= oQ , (8)
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F/GURE 2. RELAT)\/£ DUftAT/ON OF SPREAD/MO
AFTER FAY
-------
Now if the slick is assumed to expand radially, the plan area of
the slick is given as
l-^ (9)
and the circumference of the slick is
8 = 27Tfl. (10)
The hydrostatic pressure in the slick equals
P = P0gh (11)
and therefore the driving force must equal
rh
F = p0gh(2vR)dh = f>0gnh2R . (12)
J o
Similarly the viscous retarding force becomes
Fv - yX % • 03)
The surface tension becomes simply
F. = 2i\Ro . (14)
Z-
The form of the inertia force is not so straight forward. As Hoult [8]
points out, continuity must hold. Therefore if a constant flow rate is
specified
•nR2h = Qt. (15)
The speed of advance of the front of the slick, dR/dt, can be taken as pro-
portional to R/t.
dR/dt ~ R/t (16)
Actually the slick speed is a function of both radius and change in thickness.
The inertial force then takes the form
F. - m(R/t2}. (17)
Is
A balance between inertia and gravity becomes
m(R/t2} - pgvh2R, (18)
-------
but
m =
and from Equation 15
Relation 18 then takes the form
(19)
(20)
(21)
or
which gives
1/4 1/4 3/4
(gQ) *
(22)
McMinn carried out field measurements on oil spreading over ice and observed
that for his data
R = 1.3
(23)
Glaeser and Vance also performed field tests and found for fixed volumes of
oil
R =
(24)
The balance between gravity and viscous forces can be developed from
Equations 12 and 13. Since oil is quite viscous, linear shear is assumed
to occur in the oil as it spreads (Couette flow). This is probably a very
reasonable assumption, particularly as the slick edge grows further away from
the source, reducing any pressure gradient, and slowing down.
Then
and since u ~ R/t
du
dh
u_
h J
_
dh
= K
rj
th
where K is a proportionality constant, so that
F - y
V 0
Then equating this to the gravity force:
__
th
(25)
(26)
(27)
th
(28)
10
-------
where to be consistent with the other investigators
h = V/T\R2,
gives
v
tv
R.
Solving for the spill radius gives
or
R =
1/8
1/8
tl/8 y3/8 8
Instead of using the horizontal gravity driving force per unit volume
(29)
(30)
(31)
(32)
(33)
as in Equation 12, both Glaeser and Vance, and Chen, et al., chose to develop
a relation for viscous spreading based on the vertical gravity force per unit
volume
A/V ,
(34)
which gives a different form to the expression for gravity-viscous spreading:
(35)
Chen, et al . experimentally solved for the constants and found kl = 0.24,
and k2 = 0.35.
Glaeser and Vance offer some limited data on viscous spreading which
best fits a curve given in the form R ~ t1/2 .
Chen, et al . ran their experiments over varying degrees of roughness
and oil temperature. They seemed to feel that their results were insensitive
to changes in either of these conditions.
McMinn balanced the surface tension and the gravity force to find a
critical thickness for the slick where surface tension would become important:
(36)
11
-------
Solving for h gives:
h = (2a/po^)1/2 (37)
with
a = afl (1 - cosa). (38)
For an oil surface tension of aQ = 30 dynes/cm, typical of crude oil, and an
estimated contact angle on ice of a = 135°, McMinn obtains a resultant surface
tension of 51 dynes/cm. Then the critical thickness becomes hc = 0.345 cm for
representative densities of oil. McMinn indicates that in field experiments
of spreading oil over ice, the spreading thickness never diminished to 1/3 cm.
He therefore argues that the surface tension regime does not occur for oil
over ice, possibly due to the ice roughness and subsequent pocketing of the
oil within the roughness matrix.
Spread of Oil on Water
The basic theory of the previous section can be extended to apply to
the spread of oil on water. The horizontal gravity driving-force can be
easily altered to apply to a two fluid system by the inclusion of a relative
density difference factor
A= (Pu- P0) /Pu - (39).
Then the gravity equation transforms into a buoyancy equation.
F = kpwgi\h2R. (40)
\J
The inertia force remains the same as before:
Fi ~ p0nhN3/t2. (41)
The viscous force requires deeper scrutiny. As the oil slides over
the surface of the water there is viscous drag exerted by the water on the
oil. The viscous stress is continuous at the oil-water interface. Since
the oil thickness is smaller than the water boundary layer, the velocity
gradient in the oil in the vertical direction can be considered negligible
compared to that in the water. There is slug flow in the oil. The Retarding
force due to viscous drag then becomes [8]
Fv ~ V*2 ^ , (42)
where
6 = Svt (43)
is the water boundary layer thickness and v is the kinematic viscosity of water
12
-------
The surface tension remains as before,
F = o (2-nR),
'44;
where now a is the net combination of the air-water interfacial tension, oil-
water interfacial tension, and oil-air interfacial tension. Now balancing
gravity and inertia forces,
it)
3 /j-2
or for a fixed volume
which gives
h R'/t
V,
H =
P.
w
TTpf
E>
Ap gnh2R ~ U TT R2 —
The balance of gravity and viscous forces becomes
R_
tS '
D ~ _J h) *-" ^ 1/6
TT2 VJ '
or simplifying,
(45)
(46)
(47)
(48)
(49)
Glaeser and Vance developed a similar relation for one directional flow
in a channel, using
F = Ap gh2w
g Hwy
and
where
Balancing these gives
1
/vt
V = Iwh.
(50)
(51)
(52)
(53)
Field data for surface tension spreading is probably the hardest to
acquire, however, a relation can still be developed by balancing the surface
tension force with the viscous force
13
-------
yy TT - , (54)
or
R2 - ^~ a^ t3/2, (55)
^w
and simplifying gives
2t3/p2v)lA. (56)
Hoult [8] looked at detailed properties of the slick motion and developed
similarity solutions to the governing equations of motion. In the inertia
regime he found the spill radius to be described as:
E = *
max Tmax
where for one directional flow n - Q3 and L = vlfc,
and for axi symmetric flow n = 1, and L = V1^ .
For one directional spreading tj>n,ax was theoretically calculated to be 1.57.
The experimental value was found to be 1.5. For axisymmetric flow cj>max was
calculated to be 1 .14.
In the viscous regime the similarity solution takes the form
R
max _
L max
L
(3-n)/16 l/(8+4n)
t Nx , (58)
where N is a characteristic Reynolds nu.nber:
N - L. (59)
x v v '
Because the boundary conditions are not uniquely defined for this case,
was determined from experimental results:
=1.5 for n = 0
max
4) = 1.12 for n = 1.
Tmax
It also appears that, based on this analysis, a regime exists downstream
from the leading edge of the slick where reverse flow occurs. This feature is
shown in Figure 3.
For the surface tension regime the similarity solution is the same for
both the one directional and axi symmetrical cases:
14
-------
3. REVERSE FLOW AT THE LEADING EDGE or SLICK.
-------
R =
max Tmax
In this case the theoretical values become
= 0.665 for n = 0,
(60)
max
=0.128 for n = 1.
max
The experimental value of for n = 0 was found to be 1.33. No reason for
this variation was given. max
Spread of Oil Under Ice
Hoult [9] approached the problem of oil spread both under and over ice
by arguing that the only important retarding force was due to energy dissi-
pation as the slick moved across a rough surface. This would be proportional
to a pressure drop or head loss in the fluid. The retarding force would also
have to be proportional to the frontal area of roughness seen by the approach-
ing oil. This force can then be given as
Fp = k 2-nRr] PO
dR
where -TT is given as in Equation 16 and r\
dt
(61
is the equivalent roughness height.
The driving gravity force is identical with that given in Equation 40
as
F = Ap
g '-'•
Equating these two forces gives
i /6
R =
R.
w
Pr
1/6
n
1/6
(62)
Experimental data for this case is plotted in Figure 4. Hoult
suggests that the value of L-^- 1//6 should be 0.25 based upon the data;
Y-T\lk\
however, a value of 0.55 seems to be more satisfactory. The expression
R = 0.55
2/3
(63)
is also plotted in Figure 4. For comparison, Equation 32 for viscous spreading
can be adjusted for oil under ice by again introducing the relative density
difference factor or A (Equation 39), giving
16
-------
IOOO6\
10
too
$P/?£AD/A/G OF OIL
/OOO
AND
l/4 ,0000
/C£ AS
/OOQO&
BY HOUIT [9]
-------
R =
1/8
1/8
,3/3
(64)
By inserting some typical values for A, p , g, y0,andn into both equations
36 and 65, it becomes apparent that thesewtwo relations differ significantly
only with respect to time over a broad range of values for the flow rate.
A prediction for the equilibrium thickness of a slick based upon the
balance of surface tension and hydrostatic forces can also be made by intro-
ducing A into Equation 38:
2a
Again a = a (1
- (65)
cosa), where a is the angle included in the oil, and
a0 is now the interfacial surface tension. MacKay et al. [10] indicate that
typical underice oil slick thicknesses will range from 0.9 to 1.2 cm.
The various theories for oil spreading are listed in Table 1. All of
the relations can only be approximate since the speed of advance of the slick
front is only known in a proportional sense. An exact relation for slick
radius as a function of time must follow a similarity solution, as carried
out by Hoult [9], which assumes that velocity is proportional to R/t.
In general, long term spreading of oil on water will probably be con-
trolled by surface tension so that
E
w
(66)
For oil spreading on or under ice the viscous regime will dominate so that
H
1/8
73/
(67)
If the ice is rough, the oil will spread according to
1/6
R = 0.55
Pnn
,2/3
(68)
-------
REGIME
Gravity-Inertia
Gravity-Viscous
TABLE 1. SUMMARY OF THEORETICAL OIL SPREADING UNDER QUIESCENT CONDITIONS
OIL ON
WATER
R ~
1/1
(Af7!/)'A
(radial spreading)
(radial flow)'
(one directional )
OIL ON
ICE
J] I
(radial spreading)
V*
(radial spreading)
OIL UNDER
ICE
l/B
V8
(radial spreading)
INVESTIGATION
McMinn
Glaeser & Vance
Hoult 72
Fay
Chen et al. (Corrected)
Glaeser & Vance
Hoult 72
Fay
Glaeser & Vance
Chen et al. (Adjusted)
Surface Tension-
Viscous
Head Losses
tf- /Z(cr fVpyVr''
(radial spreading)
K = 0.55
Hoult 72
Fay
Hoult 74 (Corrected)
-------
ANALYTICAL APPROACH
When oil is released into a stream beneath an ice cover, the slick will
take several different forms depending upon the flow conditions, oil properties
and roughness of the ice cover. A theory universally applicable to oil slicks
in general, describing the behavior of different types of oil on or beneath
various types of ice covers, would be unyielding and impractical. The following
analysis is therefore only applicable within the framework of the cases con-
sidered in this study. The goal of the analysis is to derive the most compre-
hensive analytical relation for the motion of crude oil and No. 2 fuel oil
beneath a smooth ice cover. In the analytic model, a complete force balance
equation for an element of rectangular planform taken from an oil slick be-
neath uniform ice cover and subject to a current would include a liquid-solid
shear drag at the ice-oil interface, a liquid-liquid shear drag at the oil-
water interface, a negative surface tension spreading coefficient at the oil-
ice-water interface, and gravity forces. Preliminary tests indicated that
the gravity forces and surface tension forces could be eliminated from the
model since they either cancelled each other or were overpowered by the other
forces. The modified analysis presented, which is of a more simplified nature,
examines the force balance in the streamwise direction for the patch of oil.
As such, it considers only the frictional force at the ice-oil interface, the
shear force at the oil-water interface, and a form drag due to the shape of
the slick. The oil injected under the ice cover is assumed to be at the same
temperature as the ice, so that the ice does not melt as a result of heat flux
from the oil to the ice and thereby affect oil movement. Moreover, the
analysis is valid only after the oil forms a slick beneath the ice cover. The
analysis does not account for the transient conditions associated with the in-
jection of the oil, the behavior of the oil plume as it surfaces to the bottom
of the ice, and the initial spreading of the oil at the ice surface. The
analysis is concerned only with the subsequent transport of the oil slick be-
neath the ice due to the water current.
Consider that a known amount of oil is injected into the stream beneath
a continuous ice sheet as depicted schematically in Figure 5. After the oil
is released, it will rise to the bottom of the ice cover as a result of buoy-
ancy forces, and it will either collect in an inverted mound, as was the case
with crude oil or will form a uniform layer, as was the case with No. 2 fuel
oil. Depending upon the type and orientation of the slick, different forces
govern the force balance on the slick. The driving forces acting on the slick
are the form drag, which results from the pressure difference between*the up-
stream and downstream ends of the slick, and the shear force at the oil-water
interface, which is due to the water current. The retarding force is the
sliding or rolling friction between the ice surface and the oil, treating the
oil as a solid.
The slick geometry in this analysis can be represented by a mean height,
20
-------
OIL INJECTION CHAMBER
ICE COVER
/^/ / / /—r /—/-/ / -^+—/- 7 )/
/
flu
W
7
F/GUtfE 5. SCHEMATIC REPRESENTATION OF O/L SLICK TRANSPORT UND£R
A A/ ICE
-------
h, width, w, and length £. The volume of the oil slick, v, is then:
V = h £ w . (69)
Form Drag: The drag is caused by the difference in pressure exerted on the
upstream and downstream ends of the slick, and is expressed as:
Fd = ?Cd<>» (UW-Us]2wh (70)
where Q is a drag coefficient, pw is the water density, uw is the mean
water velocity, and us is the mean slick velocity. Note that this force
becomes more important as the slick formed beneath the ice cover thickens.
Shear Force at Oil -Water Interface: This is a driving force due to the shear
applied to the oil at the oil -water interface by the moving current. Assume
an averaged shear stress based upon the relative velocity between the two
fluids:
F = C p (U
s 2 s Kw ^
w
- U )2
s'
w £
(71)
The shear stress coefficient, Cs is not the same as a drag
coefficient over
a flat plate. Jeffreys [11] defined this coefficient as a sheltering coef-
ficient, usually applied to cases of wind and waves. By considering the pressure
normal to a wavy
at flow near the
surface he estimates Cs to be 0.3.
Jirka et al [12], looking
Cs - 0.64
interface of two fluids give a relation for Cs as
cw, where Cw - 16/N0> N0 being the oil Reynolds number. The range of
Cs for a moving slick using this approach would typically be 0.01 to 0.1. The
most significant point is that values of cs for this case are at least one to
two orders of magnitude larger than those for a rigid flat plate.
Ice-Oil Interfacial Friction Force: The retarding force on the slick as it
a "rigid" body can be estimated from the normal buoyant
exerts on the ice cover and a kinetic friction factor.
F = C (pw - p0) 9V
slides downstream as
force that the slick
(72)
The coefficient Cf is a solid-solid type of friction factor.
Force Balance: For equilibrium, the retarding forces must balance ttfe driving
forces.
Ff = Fd
F
<73>
By substituting the expressions for Ff, Fj, and Fs from Equations 70, 71
and 72, the expression for the force balance becomes:
22
-------
J
(p - p ) ghwti = i C, p (U - U )2 wh + i C1 p (t/ - £/ )
x Kw 'o' y 2 d tj v w s' 2 s ^w w s
This can be nondimensionalized through the introduction of the densimetric
Froude number:
The general form for the force balance then becomes:
(1 - U)
2 _
2C
l_
h + c
I+ °SJ
N
F
(74)
(75)
(76)
Provided that the coefficients can be estimated, the spread of any slick could
be expected to follow a relation of the form:
(1 - u}2 =
(77)
The presence of the term h/l in Equation 76 should be noted. The affect of
this term is to make form drag important if the shape of a slick becomes narrow
in the direction of the current, i.e., orients itself transverse to the flow.
If the slick becomes very long, shear stress becomes the more important driving
force.
23
-------
EXPERIMENTAL PROGRAM
The analytical model of oil slick movement beneath smooth ice cover
contains coefficients which must be determined experimentally. To quantify
these coefficients and verify the theory, experiments were conducted in
ARCTEC's Ice Flume. The apparatus and the test procedure used in these tests
are described below.
Test Apparatus
The facility and the main apparatus used in the tests consist of the
flume and the pressurized oil injection chamber. The instruments used in
determining the oil properties are described in the Test Procedures section.
Flume. The experiments for this investigation were conducted in ARCTEC's
insulated, glass walled Ice Flume which is depicted schematically in Figure
6. The test section of the flume is 13.7 m long, 0.94 m wide, and 0.61 m
deep. The flume is located in ARCTEC's insulated low temperature test
facility. Ice is made in the flow section by a patented cryogenic system.
The glass walls, channel bottom, return pipe, and the drive unit are insulated
to prevent ice formation inside the system during the freezing process. In-
sulation panels for the glass walls are removable in sections along the flume
where under-ice observations are made. There are two glass windows, 6 m
apart, along the channel floor for under-ice photography.
Flume capacity is about 170 liters per second with 15 cms of water
achieved by a ten horsepower variable speed motor and a 25 cm diameter axial
flow pump. The maximum allowable water depth is 46 cms with 18 cms of free-
board. The discharge of the flume is measured by a conventional precalibrat-
ed orifice-meter mounted between two flanges of the return line. The piezo-
meters of the orifice-meter are connected to a differential manometer located
near the flume inside a specially built, heated container.
Pressurized Oil Injection Chamber. The pressurized oil injection chamber
(hereinafter referred to as a box) was designed to inject oil at a point just
below the bottom surface of the ice sheet thru a 2.0 cm hole drilled in the
middle of the box. The volume of the box is 26.5 liters. This unit is
turned on or off by pneumatically raising or lowering a two way piston that
has a plug mounted on the end of it. A system of three way valves which con-
trols the piston is manipulated so that one side of the two way piston is
being bled to atmosphere while the other side is being pressurized. After
the plug has been lifted from the hole, the pressure inside the box is in-
creased by adjusting a throttle valve to a point such that the oil plume is
penetrating about 2 to 4 cms into the flow. The volume of oil in the box is
monitored with a surface-following float attached to a lever arm and con-
nected to a 10 turn potentiometer. By reading the resistance change of the
24
-------
CARRIAGE
no
en
•HEAO TANK
I—ORIFICE METER
-RETURN LINE
/C£
-------
potentiometer on a 5 place digital multimeter, the volume of oil remaining in
the chamber can be established. The oil is turned off after a predetermined
volume of oil has been injected into the flow. The calibration data for the
box is presented in Figure 7 and a photograph of the box is shown on Figure 8.
Test Procedure
The first step for each test was to freeze an ice sheet in the flume
using ARCTEC's cryogenic freezing system. The freezing procedure can be re-
motely controlled from the control room. While the ice sheet was being frozen,
the properties of the oil to be used in the tests were determined. This was
done before each test to monitor any property variations due to temperature
changes or nonuniformity of oil samples. The properties measured were vis-
cosity, surface tension, and specific gravity. All measurements were made
inside the small cold room located near the refrigerated test facility using
instruments and procedures meeting ASTM specifications.
The instruments used to measure the specific gravity were ASTM approved
hydrometers meeting specification E 100-66. The appropriate hydrometer was
lowered into the sample and allowed to settle. After equilibrium temperature
is reached, the hydrometer scale and the temperature of the sample were
recorded.
A Brookfield Viscometer, Model LVT, was used to measure apparent vis-
cosity. The viscometer operates by rotating a cylinder or disc in the fluid
and measuring the torque necessary to overcome the viscous resistance to the
induced movement. This is accomplished by driving the immersed element, which
is called a spindle, through a beryllium copper spring. The degree to which
the spring is wound, indicated by the position of a red pointer on the visco-
meter's dial, is proportional to the viscosity of the fluid for any given speed
and spindle. The viscometer is able to measure over a number of ranges, since
for a given drag or spring deflection, the actual viscosity is proportional to
the spindle speed, and is also related to the spindle's size and shape. For
a material of given viscosity, the drag will be greater as the spindle size
and/or rotational speed increase. The minimum range of any viscometer model
is obtained by using the largest spindle at the highest speed, the maximum
range by using the smallest spindle at the slowest speed. These procedures
are in accordance with ASTM specification D 2983-72. The results obtained
for crude oil are shown in Figure 9.
A Fisher Surface Tensiometer Model 20 was calibrated and used to
measure the oil/water surface tension. The Model 20 is a torsion-type
balance instrument, the kind currently specified by ASTM in Methods D-971
and D-1331. In this instrument, a platinum-irridium ring of precisely known
dimensions is suspended from a counter-balanced lever arm. The arm is held
horizontal by torsion applied to a taut stainless steel wire, to which it is
clamped. Increasing the torsion in the wire raises the arm and the ring,
26
-------
24
22
20
18
16
_ 14
12
O 10
u.
1
O
N
A
O
O
a
A
Q
AD
O
a «
KEY
Test #1 O No. 2 fuel
Test #2 A No 2 fuei
Test #3 a No. 2 fuel
Test #4 « crude
O 2O 4O 6O 8O 1OO 12O 14O 16O 18O 2OO 3OO
fi (OHMS)
F/GURE 7 OIL DISCHARGE CALIBRAT/OM DATA FOR PRESSURIZED
OIL INJECTION CHAMBER
27
-------
ORIFICE PLUG
.ACTUATOR
Co
INTERNAL PRESSURE
GAGE
MAIN AIR SUPPLY
FITTING
OIL LEVEL GAGE
OIL INPUT PORT
ADJUSTABLE
RAIL SUPPORT
FIGURE 8 PHOTO OF PRESSURIZED OIL INJECTION CHAMBER
-------
5 -
4-
r\i
_ 1,000
-------
which carries with it a film of the liquid in which it is immersed. The force
necessary to pull the test ring free from this surface film is measured. The
surface tensiometer shows this "apparent" surface tension on a calibrated dial.
The dial readings are then converted to "true" values by using the correction
factors provided with the instrument.
Initally, the oil/water surface tension was measured in the cold room
using oil at about 0°C. At this temperature the crude oil was too viscous to
establish a sharp interface with the water; thus the surface tension tests
could not be conducted in a reasonable amount of time (note that ASTM standards
put a time limitation on the existence of the oil/water interface before the
test is conducted, i.e., after the oil/water interface is formed the test must
be conducted within a certain time period). However, it is generally correct
that interfacial surface tension is a strong function of the materials in-
volved, and weak function of the temperatures of the materials.
Thermometers used in this program were accurate to 0.1°C. Temperatures
were recorded when measuring viscosity, surface tension and specific gravity
in both the pre- and post-test series.
After the ice sheet was frozen, the flume was prepared for the test
and the test apparatus was installed. The flume was then turned on to the
desired flow rate and oil was injected using the pressurized oil injection
chamber. As the oil entered the flow and started to move downstream, the
position of the oil slick was recorded as a function of time, and still photo-
graphs and movies of the oil slick motion were taken. After the oil was turned
off, the length of the slick was measured (when appropriate) as the slick
traveled down the flume. When the downstream edge of the slick reached the
tail tank, the test was terminated. At this point the flume was turned off and
cleanup procedures were started. The cleanup consisted of mounting an oil
skimmer, as shown in Figure 10, in the tail tank and pumping off the top
layer of the oil/water system. This was then pumped through an oily water
separator, or directly into waste oil containers. Absorbent rags and cloths
were used to clean up the remaining oil.
Test Results
After an ice sheet of desired thickness was frozen and the apparatus
was installed in the flume, each experiment was started by turning on the flume
to a predetermined flow rate. The discharge was adjusted by varying the speed
of the drive motor and by checking the differential manometer attached to the
piezometers of the orifice-meter located along the return line of the flume.
After a steady state condition was achieved, approximately 18.9 liters of oil
was injected into the stream through a 2 cm diameter hole on the bottom of the
pressurized oil injection chamber. The oil was forced through the hole at a
slight pressure so that the flow rate was approximately 0.12 liters/sec. After
leaving the box, the plume formed by the oil was bent because of the flow, and
rose to the underside of the ice sheet due to buoyancy as shown in Figure 11.
Depending upon the jet Reynolds Number, the oil plume either broke up into
large drops as in the case of No. 2 fuel oil, or formed a continuous plume
30
-------
FIGURE 10 PHOTO OF THE OIL SKIMMER IN THE TAIL TANK
31
-------
FLOW
FIGURE 11 PHOTO OF NO. 2 FUEL OIL PLUME
UNDERNEATH AN ICE SHEET
32
-------
before rising to the underside of the ice sheet as in the case of the crude
oil.
Another difference between the No,
that the gravity forces acting on the No.
crude oil because of its lower density.
suited in different trajectories for the
two plumes to come into contact with the
the flume.
2 fuel oil and the crude oil was
2 fuel oil were larger than for the
The difference in vertical forces re-
plume which consequently caused the
ice sheet at different locations along
As portions of the slick left the box region, the crude oil and No. 2
fuel oil exhibited distinct behavior patterns. Typically, the slick formed by
the crude oil was short and wide, oriented transversely to the flow, and moved
downstream like a solid body. At low water velocities the crude oil rose to
the underside of the ice cover in the region of the pressurized oil injection
chamber, and spread both laterally and streamwise. In this case, the slick
remained attached to the box for a long time before being swept downstream with
the flow. The slick deformed very slightly, and there were no oil/water inter-
facial waves. At high water velocities, the plume moved further downstream
before it came into contact with the ice sheet. Because of the high viscosity,
the crude oil did not spread transversely; instead, it initially kept its rope-
like shape as it was carried downstream by the flow as shown in Figure 12. Sub-
sequently, the rope broke and formed small elongated patches of oil. The oil
slicks compacted into a mass whose transverse dimensions were greater than
their streamwise dimensions. As the slick formed and moved downstream, its up-
stream edge thickened as a result of the water accelerating around the edge of
the slick as shown in Figure 13. Some patches of crude, torn from the sides of
the major slick would move downstream at a higher velocity than the main, but
again would orient transverse to the flow.
The appearance of a fuel oil slick was considerably different than that
of the crude oil slick. The slick formed by the fuel oil had a uniform thick-
ness of about 0.5 cm and a very smooth oil/water interface, the only roughness
being the interfacial waves observed at the higher velocities. It was observed
that the fuel oil slick "rolled" along the underside of the ice sheet. At
high water velocities, small patches of oil would separate from the main slick
as it traveled down the flume. Some of the patches would recombine with the
main slick, whereas others would move downstream independently. These small
patches would travel at a higher speed than the parent.
After the first few tests had been run with No. 2 fuel oil it was noted
that the oil slick thickness quickly reached a limiting value, determined by
a balance between the negative surface tension spreading coefficient and the
buoyant forces. This same limiting thickness condition also seemed to be
apparent in the static water cases that were run with the cold crude oil. In
these cases the oil slick was allowed to sit overnight after it had been con-
firmed that the slick had a constant thickness. Also, for one flume test
where the crude oil was significantly warmer than 0°C, the spread rate was very
33
-------
FIGURE 12 PHOTO OF COLD CRUDE OIL UNDER AN ICE
SHEET AT HIGH WATER VELOCITY
34
-------
FLOW
F/GURE J3. SCHEMATIC REPRESE/VTAT/OM OF THE FOLDING
PHE/VOMF.A/A AT THE UPSTREAM £NP OF A
CRUDE: OIL SLICK
35
-------
rapid and the crude seemed to reach a limiting thickness. However, for the
cases where the crude oil was very cold, i.e., below 0°C, the oil collected
where the plume came into contact with the bottom of the ice sheet for low
water velocities, or was swept away as soon as it arrived at the bottom of
the ice sheet for the high water velocities. For those cases where the slick
did not move, it was noted that during the course of the experiment the slick
did not become appreciably thinner. Because the oil is so viscous, it cannot
flow on a time period comparable to that of the No. 2 fuel oil, or within a
time period comparable to the length of the experiment.
Tests conducted with salt water did not show any significant differences
in the behavior of the oil. However, it was observed that oil droplets en-
trained in the water later became enmeshed in the pores of the ice upon rising
to the ice/water interface. This "trapped oil" gave the underside of the ice
sheet a dirty appearance. It can be concluded from this that additional clean-
up after melting may be necessary for oil spills beneath salt water ice covers
if emulsification occurs at the time of the spill.
In order to investigate the feasibility of using plexiglass as a simu-
lated ice cover, a test was conducted with plexiglass in the same manner as the
other tests. A plexiglass sheet, 0.83 cm thick and 180.0 cm long, was placed
in the flume approximately 300 cm downstream from where the oil was injected.
The ice was cut out and removed, and the plexiglass fitted into its place. The
plexiglass sheet was placed in the flume approximately 45 minutes before the
initiation of the test in order to allow it to come to thermal equilibrium.
As the oil passed under the simulated cover, the slick was slowed down and was
finally stopped. After the oil slick had stopped moving, the test was allowed
to continue for approximately 15 minutes before the pumps were turned off in
order to be certain that the slick had completely stopped. When the sheet was
lifted from the surface of the water at the completion of the test, a uniform
coating of oil remained adhered to the sheet. The oil beneath a plexiglass
sheet therefore showed a totally different behavior than oil under an actual
ice cover.
A test to simulate the dynamics of a hot oil slick beneath an ice cover
was also performed. In this test, approximately 11 liters of hot crude oil at
50°C was injected into the stream from a simulated point source located approx-
imately 5 cms below the ice/water interface.
Qualitatively, the hot crude oil behaved in a manner analogous to the low
viscosity No. 2 fuel oil. The high water velocity broke up the jet,*and the
large patches were carried downstream before they rose to the surface at an open
water region; consequently, no interaction between the hot oil and the ice was
observed.
The physical parameters measured during each test in order to quantify
and verify the analytical model are listed in Table 2. Figure 14 and 15 are
plots of the mean slick velocity versus current velocity for No. 2 fuel oil and
crude oil. Data points from tests 20 and 21 have been deleted from these plots.
36
-------
TABLE 2. SUMMARY OF TEST DATA
Test
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Water
Velocity,
(crn/s)
5.0
14.0
5.4
9.9
15.1
?0.1
20.1
9.8
20.0
20.0
14.9
14.3
19.7
24.2
15.8
24.8
30.1
36.1
19.4
Oil
Type
#2Fuel
#2Fuel
#2Fuel
#2Fuel
#2Fuel
#2Fuel
Crude
Crude
Crude
Crude
Crude
Crude
Crude
Crude
Crude
Crude
Crude
Crude
Crude
Slick
Velocity*,
£/„
(cm?s)
0.4
3.5
0.6
2.0
4.1
6.6
2.3
0.0
3.7
4.4
O.E
0.5
3.4
10.6
1.9
12.3
15.7
24.6
4.4
Oil
Viscosity,
^0
(centipoise)
7
7
7
7
8
7
25000
15000
15000
15000
25500
25500
36500
36500
36500
25500
25500
25500
25500
Slick
Thickness,
h
(cm)
0.5
0.5
0.5
0.5
0.5
0.5
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
Oil
Density,
PO
(gm/cm3)
0.86
0.86
0.86
0.86
0.86
0.86
0.91
0.91
0.91
0.91
0.91
0.91
0.91
0.91
0.91
0.90
0.90
0.91
0.91
Water
Depth,
d
(cm)
27.8
27.4
25.6
23.5
23.6
22.7
23.0
21.7
21.7
21.7
23.4
23.4
16.1
16.1
16.1
13.4
13.4
13.4
13.4
Oil
Temperature,*
T*
(°c)
_
1.5
-2.6
1.0
-1.4
-0.4
-0.8
-0.8
-0.8
-
1.8
1.8
-0.3
-
-
2.0
2.9
5.5
1.5
Interfacial
Surface
Tension,
a
(dyn/cm)
_
-
16.6
12.8
14.8
19.3
69.0
38.0
38.0
38.0
15.8
15.8
17.0
17.0
17.0
15.8
15.8
15.8
15.8
Froude Nondimensional
Number, Velocity,
NF V
0.60
1.69
0.65
1.20
1.82
2.43
1.88
0.92
1.87
1.39
1.33
1.84
2.26
1.48
2.19
2.67
2.67
3.37
1.81
0.08
0.25
0.11
0.21
0.27
0.33
0.12
0.00
0.18
0.22
0.03
0.04
0.17
0.44
0.12
0.50
0.52
0.68
0.23
-------
TABLE 2. SUMMARY OF TEST DATA (CONTINUED)
Test
No.
20
21
22
23
24
25
26
27
28
29
30
31
Water
Velocity,
As)
21 .3
24.5
19.5
27.2
32.3
25.0
9.1
14.9
21.0
14.5
19.4
25.8
Oil
Type
#2Fuel
#2Fuel
#2Fuel
#2Fuel
#2Fuel
#2Fuel
#2Fuel
#2Fuel
#2Fuel
Crude
Crude
Crude
Slick
Velocity*,
us
(cm/s)
9.3
16.7
5.8
9.7
10.7
7.8
2.4
4.7
7.0
1.0
4.8
10.6
Oil
Viscosity,
^0
(centipoise)
7
7
7
7
7
7
7
7
7
25500
25500
25500
Slick
Thickness,
h
(cm)
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
1.3
1.3
1.3
Oil
Density,
PO
(gm/cm3)
0.86
0.86
0.86
0.86
0.86
0.86
0.86
0.86
0.86
0.91
0.91
0.91
Water Oil
Depth, Temperature, +
d TO
(cm) (°C)
10.5
10.5
13.9
13.9
13.9
13.9
14.9
14.9
14.9
15.2
15.2
15.2
2.4
2.2
-0.1
0.0
0.0
0.1
-0.4
-1.0
-1.0
-1.5
0.7
-2.3
Interfacial
Surface
Tension,
a
(dyn/cm)
13.4
13.4
10.1
10.1
10.1
10.1
9.3
9.3
9.3
16.4
16.4
16.4
Froude Nondimensional
Number, Velocity,
N U
2.57
2.95
2.35
3.28
3.90
3.02
1.10
1.80
2.54
1.35
1.81
2.41
0.^6
0.68
0.30'
0.36
0.33
0.31
0.27
0.32
0.33
0.07
0.25
0.41
* Computed as the change in downstream position of the slick edge divided by the change
in time and average overall readings.
+ Temperature of oil prior to being injected into the stream.
-------
12
-* IO
I
o
= O.38 Uw - /.26
of
Determination - O.966
O
024-68
10 12 14 16 18 20 22 24 26 28 3O
Cur-re fit \/e/oc/fy, Uw > cm / sec
32
36
PLOT OF SLICK VELOCITY vs. CURRENT VELOCITY FOR No.2 FUEL OIL
-------
26
20
16
14
n
* 10
Us=8.& x /O'6 U
Indejc of
Determination O.9/3
O.952
Indet of
Deter m/nat'i
2468/0/2/4/6/8 20 22 24 26 28 30 32 34 36 38
Current Vf/ocity } Uyy
/5. PLOT OF SLICK VELOCITY vs. CUtfAfA/T VfLOC/TY /=~O# Cftl/D£ OIL
-------
Movies of tests 20 and 21 show the No.. 2 fuel oil slick to be highly broken up.
The test results are therefore suspect, particularly in view of the fact that
smaller slicks seem to move at much higher velocities than larger slicks for
the same current speed.
The No. 2 fuel oil slick speed exhibits a very strong linear relation
with the current speed. The threshold velocity for smooth ice is seen to be
approximately 4 cm/sec. The slick velocity follows the relation:
U = 0.38 U
s w
- 1.26, for 0 < U < 36.
—. w —
(78)
The slick speed for crude oil also appears to follow a linear relation-
ship for high current speeds; however, this best fit line is seen to predict a
threshold velocity which the data shows to be too high. A power curve has
therefore also been fit through the data. The result is a more reasonable
threshold velocity with the slope of the curve approximately that of a straight
line for intermediate velocities. By this method the threshold velocity is
estimated to be 8 cm/sec, and the crude oil slick velocity relation becomes:
U = 8.6 x 10"
s
U
4.29
W
for 8 < u < 28.
w
(79)
This curve should really not be extended above a current speed of 28
cm/sec, however. As seen in Figure 15, above this value the linear expression
is judged to be more representative:
U = 1.10 U
s w
- 16.60, for 28 < u < 36.
w
(CO)
Analysis of Test Results
In order to generalize the test results for oils of any type, it is
necessary to test the theoretical equation derived earlier. Recall that the
force balance equates the friction force to the sum of the forces due to form
drag and interfacial shear:
(73)
From observations of the shape of the crude oil slicks and the No. 2 fuel oil
slicks, it is apparent that a different force dominates in each case. The No. 2
oil slick always remained long and narrow. The dominant driving force here is .
the shear applied to the interface. The force balance could then be approximated
by:
F n =
f
(81)
41
-------
Conversely, crude oil slicks always oriented themselves to the flow, becoming
very short in length measured with the flow direction. Form drag must there-
fore dominate for crude slicks, and the force balance can be approximated by:
Ff - Fd . (82)
For the No. 2 fuel oil, Equation 76 reduces to:
(1 -
(83)
where
2C
(84)
This form of relation is plotted with the data in Figure 16.
stants are then determined from a best fit of the data as:
The con-
(1 - U)2 =
+ 0.450.
(85)
The presence of the constant term may at first appear unsettling, however there
could be momentum losses due to wave formation at the oil water interface. This
loss would be solely a function of the current speed, and would be of the form
pu ufj. The force balance would then become of the form:
F „ = F + C p
/ s K
U
w
(86)
^ '
For large enough Froude numbers, this wave motion would tend to dominate,
eventually causing breakup of the slick.
For crude oil Equation 76 reduces to:
(1 - U}2 =|^-
F
(87)
where
(88)
This form of relation is plotted with the data in Figure 17.
constants are then determined from a best fit of the data as:
The
(1 - U}2 = 2.15 ()
1'15
"F
(89)
42
-------
00
1.0
0.9
0.8
0.1
0.6
0.5
OA
0.2
O.I
0
O.4SO
_i I i I J I
0 0.2 Q.+ 0.6 0.8 1.0 1.2 /.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.O 3-2
/6. GENERALIZED SUCK TRANSPORT RELATIONSHIP BASED
O/V A/o. 2 FUEL OIL TESTS WHERE TH£ SLICK /5
ORIENTED PARALLEL TO THE FLOW.
-------
5.0
2.0
l.o
.50
.20
.10
.01
1.15
.01
• 10
.20
.50
/.O
2.0
17. GENERALIZED SLICK TRANSPORT RELATIONSHIP
BASED ON CRUDE OIL TESTS WHERE THE SLICK
IS ORIENTED TRANSVERSE TO THE. FLOW.
44
-------
The exponent on the term (~\/Ng2) is close to unity, indicating the
approximate validity of the force balance. This relationship compares favor-
ably with the linear relation found for larger values of uw as plotted in
Figure 15, but again, the use of the linear relationship is not reasonable
when trying to predict threshold velocity. Also recognize that Bi is not a
pure constant, but rather contains the factor (a/h). Generally, as the crude
oil slick orients itself transversely to the flow, the £ dimension narrows to
the point when it is comparable with h so that the ratio may approach a con-
stant. However, this cannot always be assumed to be true and, as such the
range of validity for this value of B2 is limited.
45
-------
APPLICATION OF RESULTS
Equations 78 and 79 or 80 may be used directly to calculate the speed
of advance for No'. 2 fuel oil slicks and crude oil slicks, respectively, under
a smooth ice sheet. In order to apply the more generalized predictive re-
lationship of Equations 85 and 89, the oil properties must be known. In addi-
tion, it is important to know whether a slick will tend to orient itself longi-
tudinally with the flow, or tend to allign itself transverse to the flow. This
behavior is probably viscosity dependent; however, tests with only two types
of oil are insufficient for the establishment of a single relation which takes
this factor into account. This complication does not necessarily detract
from the ability of field personnel to use the generalized predictive relation-
ship however, since in many river spills it will be relatively easy to observe
the slick orientation through the ice cover. The selection of the proper
predictive relationship is then based on the slick orientation, and with a
knowledge of the>oil properties and the current velocity, the slick velocity
can be predicted as shown in the following sample calculations.
Slick Oriented Parallel to Flow
Consider a No. 2 fuel
of the oil is 0.86 grams/cm3
oil is typically 10 dynes/cm
velocity is 20 cm/sec. Then from Equation 66,
can be calculated as follows:
oil spill beneath smooth river ice. The density
The interfacial surface tension for the No. 2
and the contact angle is 135°. The mean current
the equilibrium slick thickness
, _ 2a0 (1 - cosa) _ (2) (10) (1.71) _ n ,
h ~ ~~~ (0.14) (1) (980) ~ U"
rm
Cm '
Calculating the densimetric Froude number gives:
N
2 _
F
. (20)f f
(0.14) (980) (0.5)
Then, since No. 2 fuel oil will remain aligned with the mean flow, Equation
85 is used to determine the slick velocity as follows:
u
or
w
U
20
2 _
0.146
+ 0.450
0.145
5.83
+ 0.450 = 0.475
Solving for the slick speed, us, we find the oil slick velocity to be about
6.2 cm/sec.
46
-------
Slick Oriented Transverse to the Flow
Consider a crude oil spill beneath smooth river ice. The density of the
oil is 0.91 grams/cm3. The interfacial surface tension for the crude oil is
typically 38 dynes/cm and the contact angle is 160°. The mean current velocity
is 20 cm/sec. Then from Equation 66, the equilibrium thickness is found to be:
, _ 2a0 (1 - cosa)
2(38) (1.94)
(0.089) (1) (980)
= 1.3 cm
The densimetric Froude number becomes:
U 2
_ w _
(20):
(0.089) (980) (1.3)
= 3.53
Crude oil slicks orient themselves transversely to the mean flow, therefore
Equation 89 applies:
2
J \ 1.15
U
1 - -i
U
w
= 2-15
or
1 -
U
s
20
- 2.15
= °-50
Solving for the slick speed us, we find that the oil will move at about
5.8 cm/sec.
47
-------
REFERENCES
1. Campbell, W.J., and S. Martin, "Oil and Ice in the Arctic Ocean:
Possible Large-Scale Interactions," Science, July, 1973, pp. 56-58.
2. Barber, F.G., "Report of the Task Force-Operation Oil (Clean-up of
the Arrow Oil Spill in Chedabucto Bay)," Ministry of Transport,
Canada, 1971.
3. Glaeser, LTJG J.L., USCGR, LCDR G.P. Vance, USCG, "A Study of
the Behavior of Oil Spills in the Arctic," Final Report, U.S. Coast
Guard, Washington, D.C., February, 1971.
4. Golden, P.C., "Oil Removal Techniques in Our Arctic Environment,"
Marine Technology Society Journal, Vol. 8, No. 8, January,1974,
pp. 38-43.
5. Fay, J.A., "In Oil on the Sea," ed. D.P. Hoult, 5-13, New York:
Plenum, 1969.
6. McMinn, T.J., "Oil Spill Behavior in a Winter Arctic Environment,"
Offshore Technology Conference, Paper Number OTC 1747, 1973.
7. Chen, E.C., J.C.K. Overall, and C.R. Phillips, "Spreading of Crude
Oil on an Ice Surface," Canadian Journal of Chemical Engineering,
Vol. 52, February, 1974.
8. Hoult, D.P., "Oil Spreading on the Sea," Annual Review of Fluid
Mechanics, Vol. 4, 1972, pp. 341-368.
9. Hoult, D.P., "Oil in the Arctic," Report No. CG-D-96-75, USCG, Office
of Research and Development, Washington, D.C., February, 1974.
10. Mackay, D., M. Medir, D. Thornton, "Interfacial Behavior of Oil Under
Ice," Canadian Chemical Engineer, Vol. 54, February/April, 1976.
11. Jeffreys, "On the Formation of Water Waves by Wind," Royal Society
Proceedings A, Vol. 107, 1925.
12. Jirka, G., G. Abraham, D. Harleman, "An Assessment of Techniques for
Hydrothermal Prediction," Ralph M. Parsons Laboratory for Water
Resources and Hydrodynamics, Report No. 205, July, 1975.
48
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/3-79-Q41
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
Transport of Oil Under Smooth Ice
5. REPORT DATE
April 1979 issuing date
6. PERFORMING ORGANIZATION CODE
220C
7. AUTHOR(S)
M.S. Uzuner, F.B. Weiskopf, J.C. Cox, L.A. Schultz
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
ARCTEC, Incorporated
9104 Red Branch Road
Columbia, Maryland 21045
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
68-03-2232
12. SPONSORING AGENCY NAME AND ADDRESS
13. TYPE OF RE PORT AND PERIOD COVERED
Environmental Research Laboratory--Corvallis
Office of Research and Development
U.S. Environmental Protection Agency
Corvallis, Oregon 97330
Final
14. SPONSORING AGENCY CODE
EPA/600/02
15. SUPPLEMENTARY NOTES
Contact: Barry Reid, Corvallis, OR 97330 503/757-4607 (FTS 420-4607)
16. ABSTRACT
Previous studies of oil-ice interaction have been limited to spreading under
quiescent conditions. The present study examines the current driven spread
of oil under a smooth ice cover. Generalized relations between current speed
and oil transport rate are developed and found to be strongly dependent upon
the orientation of the oil slick to the direction of current flow. Methods
for application are presented.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
Oil spill
Arctic pollution
Oil-ice-current interaction
Crude
No. 2
oil
fuel
oil
18. DISTRIBUTION STATEMENT
Release to public
19. SECURITY CLASS (This Report)
Unclassified
21. NO. OF PAGES
20. SECURITY CLASS (This page)
Unclassified
22. PRICE
EPA Form 2220-1 (Rev. 4-77)
49
ft U S. Government Printing Office- 1979—698-323/140
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