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symmetry and limits variations to two spatial coordinates,
however, optical measurements are difficult. Thus, the choice of
a tank configuration must be predicated on measurement system
selection and the device chosen to impart mixing energy.
Since hydrocarbon concentrations can be evaluated as
functions of space and time, sample volume and sampling frequency
are important factors determining the size of the tank. Sampling
with time reduces the liquid volume in the tank but must not
influence significantly the concentration gradients in the hori-
zontal and vertical dimensions. The volume of the laboratory
tank is critical for test results to be meaningful and relevant
to those in the field.
Several tank systems have been used in previous investiga-
tions of the effectiveness of dispersants. For example, Murphy
and McCarthy (1969) and McCarthy et al. (1973) have described the
Simulated Environmental Tank (SET) system. It is a cylindrical
tank, 24 inches in diameter and 28 inches high. The Mackay
apparatus consists of a cylindrical glass tank 29 cm in diameter
and 29 cm high (Mackay et al., 1978). Wall surface interactions
will be significant due to the small volumes of these tanks.
The tank used for dispersion studies is the same as that
used for spreading experiments. This tank has been described
previously, but it was modified slightly by inclusion of 3/8 inch
Plexiglass tubes at different locations in the tank. Sampling is
accomplished by gravity flow through tubes positioned at 15
locations in the tank.
The arrangement of the sampling tubes in the tank is as
follows: two adjacent vertical sides have three sampling loca-
tions each at various heights (2, 8, 14 inches) above the bottom
of the tank, while a third side has the remaining tubes. The
fourth side is used for visual observation. Sampling tubes are
located such that water samples can be withdrawn at three depths
and 6 inches from the walls of the tank. Three additional samples
were generally withdrawn at three different depths but at the
center of the tank.
Dispersant Application--
The effective use of dispersants requires not only an effi-
cient material but an efficient application technique. Improper
and inefficient application techniques result in unsatisfactory
performance of the dispersant. For dispersants to perform at
maximum efficiency, they must be applied with proper equipment.
The proper application method is to spread the chemical evenly on
the oil slick.
In the field, the most common methods of applying dispersants
onto oil slicks are hand-held spraying equipment, fire-hoses and
spray booms mounted on work boats or vessels of opportunity, e.g.
62
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helicopters and planes. Use of hand-held sprayers is limited to
small spills. For treatment of moderate and large oil spills,
fire-hose systems and spray booms are necessary because of the
large oil slick areas to be treated. Aerial spraying is attrac-
tive because of the possibility of application in remote areas,
high dispersant dosage rates and fast response. In general,
spraying equipment is designed to spray the dispersant neat
(particularly for hydrocarbon-solvent-based dispersants) or to
spray a dilute dispersant solution by using an eductor that feeds
the chemical into a stream of seawater. Several spraying systems,
including spray booms, are available commercially. Spray booms
feature different nozzle arrangements; spraying height, spray
size, swath area, etc. can be controlled.
At the laboratory scale, several methods have been used to
introduce dispersants to treat oil:
a) mixing chemical with water prior to introducing the oil
to be dispersed;
b) pouring dispersant from a container;
c) syringe injection or pipetting of dispersant into the
middle of the patch of oil on water;
d) mixing dispersant with oil before pouring the mixture
onto water; and,
e) spraying with hand-held spray cans.
Some of these methods, such as a) and d) are not practical in the
field. These two methods will also provide maximum contact
between the dispersant and oil and cause efficiencies in labora-
tory tests to be higher than those in the field.
The method for dispersant application in laboratory studies
must reflect techniques used in the field. The method must be
reproducible and characterizable. Therefore, use of hand-held
spray cans or an atomizer/nebulizer is suggested. Oda (1969)
described a method for applying dispersants in a fine spray on
oil slicks. Application of dispersant was achieved by means of a
spraying device fitted on an aerosol bomb containing a pressurized
propellant. Spray cans equipped with triggers may be suitable
for applying dispersants. The difficulty with using hand-held
sprayers in comparative tests is the variability in hand motions
and the applied pressure on the spray trigger during dispersant
application. The droplet size and swath of the spray are diffi-
cult to control, also. Therefore, an atomizing system is
preferred. Regardless of the method used, the dispersant must be
applied uniformly and directly to the floating oil, in the form
of small droplets, and not as a fog or mist.
In SET and Mackay systems, a ring is used to contain the oil
slick and the dispersant is poured into the ring. In general,
dispersants are used in field situations where oil slicks cannot
be contained by booms due to spreading forces. Thus, the tech-
63
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niques for applying dispersants in both SET and Mackay systems
are not valid.
Chemical dispersants were applied by an ad hoc atomizing
unit. This system for applying dispersants consists of an adjus-
table atomizing nozzle manufactured by D. B. Smith & Co. (Utica,
N.Y., Model #147). The nozzle has a general purpose setting that
controls the drop size of the spray and the swath width. This
type of nozzle produces a uniform flat v-shaped spray pattern
instead of a hollow cone and the setting varies the size of the
nozzle orifice such that "fine-to-coarse" sprays can be produced.
The nozzle is connected to a short piece of metal tubing equipped
with two inlets. Laboratory compressed air flows through Tygon
tubing to one of the inlets. The air flow rate is monitored by a
flow meter (Brooks Instrument, Hartfield, Pa., Model #1555-
04C1AZZ). Dispersant solution is delivered to the second inlet
by a variable-speed Masterflex peristaltic pump (Cole-Parmer,
Chicago, 111., Ser. #51526). The flow rate of dispersant solu-
tion is regulated by means of a Masterflex controller connected
to the pump.
To apply a sample dispersant, compressed air and the disper-
sant solution are forced through the nozzle. By using different
combinations of flow rates of air and dispersant, the atomizing
system can produce different spray sizes and swaths.
A carriage resembling a railroad car was mounted on top of
the tank to continuously reposition the atomizing nozzle. The
car is positioned on a track consisting of two aluminum rods.
The rods are connected to two laboratory stands so that the track
crosses the tank lengthwise. The car is pulled by a fishing line
attached to the rotating shaft of a low-speed gear motor (Merkle-
Korff Gear Co.). This setup permits the nozzle to travel from
one end of the tank to the other at a constant speed of 0.075 ft/
sec to simulate the transport of a sprayer attached to a boat or"
plane during dispersant application in the field.
The design of the dispersant application system allows
several methods of dispersant application to be evaluated. For
example, the swath and droplet size of the dispersant spray can
be varied by adjusting the orifice of the nozzle and varying the
flow rates of air and dispersant solution. The height of the
nozzle above the water level in the tank can be varied by changing
the height of the track above the tank. The effects of variations
in the impact velocity of dispersant sprays on oil slicks, spray
angle, single and multiple passes, and spraying time per pass can
be investigated with this system.
64
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Application of Mixing Energy--
Some form of mixing or agitation must be provided to
chemically treated oil slicks for complete dispersion. There is
a direct relationship between mixing energy and the performance
of chemical dispersants. In the field, natural wave action may
provide the agitation required to disperse the treated oil. But,
during calm conditions at sea, mixing energy has to be provided
to disperse oil slicks even when dispersants have been applied.
Smith and McCracken (1977) and Smith (1978) have described
the major methods of supplying mechanical energy to treated oil
during field conditions: agitation by high pressure fire hoses,
specially constructed wooden breaker-boards in tow by vessels,
and turbulence produced by the propeller action of ship wakes.
These methods were investigated at the OHMSETT test facility.
The results of these investigations show that the efficiency of
the dispersion varies according to the technique. The depth of
droplet migration, and the rates of coalescence of oil droplets
and slick reformation will vary for different methods. This
underscores the importance of investigating different methods of
supplying energy to disperse oil slicks.
When oil spills occur in remote regions, dispersants can be
applied from the air but there are no means of providing mixing
energy. In such cases, natural wave motions are relied upon to
provide effective dispersal of the oil.
In laboratory tests, the contents of the test tank are
agitated by mechanical devices, such as shakers, pumps, vortex
blowers, impellers, etc. For example, the 0111/water/dispersant
mixture in the SET test is mixed by the shearing action of a
pump. In the Mackay system, air is bubbled through the tank.
Mechanical devices can create zones of dissimilar intensities of
mixing, which influence the local droplet size distribution and k
the depth of oil droplet penetration. The stability of emulsions
is a function of mechanical energy input; unstable phases will
tend to remain dispersed in the presence of turbulence.
The intensity of mixing provided by laboratory devices cannot
be compared with field methods for dispersing chemically-treated
oil spills. The energy of agitation per unit volume of liquid in
laboratory tests is likely to be much greater than under actual
field conditions. Shackleton et al . (1960) studied the emulsify-
ing characteristics of several pumps used for deballasting opera-
tions and found that stable emulsions were formed as a result of
the shearing action of these pumps. It is questionable whether
the mixing caused by wave motion is as intense as that provided
by laboratory equipment. In the oceans, wave motions vary in a
random manner, and variations occur in both space and time.
Forrester (1971) measured the sizes of oil globules following a
spill by the tanker Arrow and found that oil globules formed in
natural wave motions were relatively large in size.
65
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The experimental tank must be provided with means to impart
mixing energy. Two devices that are well known and have been
used extensively in wave studies are submersible ultrasonic
transducers and wave generators of the paddle type. It is
preferred to control both frequency and amplitude of mixing
energy, while not physically disrupting the slick or the upper
water column. An ultrasonic transducer and a wave generator meet
these requirements and both have a minimum physical presence
inside the tank. Also, they permit close regulation of the
turbulent structure in the tank, with direct influence on inci-
pient slick breakup and droplet motions. With these devices, the
turbulence in the tank can be varied, characterized and reproduced
By using a large tank, interference from waves produced by reflec-
tion at the walls can be minimized and/or artificial wave
dampeners may be used.
To impart mixing energy to the tank contents, a wave genera-
tor was designed. It consists of a paddle, made from 18 mm thick
galvanized steel, that is 12 inches high and 35 inches wide. The
paddle is hinged to two flexible aluminum plates, such that it is
suspended vertically and dips 3 inches into the water in the tank.
The paddle is capable of generating surface waves when driven by
a cyclic mechanical drive. The paddle is driven by a 3-inch
diameter Plexiglass disk mounted on the shaft of a high-torque,
brush-type electric motor (Bodine Electric Co., Chicago, 111.,
Ser. # 3424955). The disk is mounted off-center on the motor
shaft to produce an eccentric sweep each half-turn.
Since the paddle was installed at one end of the tank, the
system generates surface waves as the rotational force from the
motor shaft is transmitted to the eccentric disk. As the disc
turns, it displaces the paddle. The forward and backward move-
ments of the paddle displace the water surface and generate waves.
Contact between the paddle and the disk is maintained by two "
springs connected to the paddle and the tanks, one on each side
of the disk.
Torque transfer from the motor to the paddle is controlled
by varing the voltage to the motor using a Variac. Wave amplitude
and frequency are controlled by varying the speed of the motor
and the depth of paddle immersion in the water. The maximum
displacement of the paddle is 1.5 inches. By allowing the system
to operate for about 10 minutes, a constant wave pattern can be
established in the tank. The wave pattern is reproducible and
artificial devices were not used at the tank walls to dampen the
waves.
W
66
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PROCEDURES
Cleaning of Glassware and Test Tanks
The capacity of oils and hydrocarbons to adsorb on surfaces
is well known. In the absence of adequate cleaning procedures,
the results of laboratory experiments may be biased due to arti-
facts from contamination of experimental apparatus. Separatory
funnels for extracting hydrocarbons from thief samples, collec-
tion bottles, etc., are critical to realistic determination of
oil concentrations. Thus, glassware must be cleaned thoroughly
to minimize contamination of samples. Cleaning of glassware and
laboratory equipment is an energy-intensive and time-consuming
process in experimental studies of oil/water systems.
All glassware was washed in soap solution (Sparkleen) and
rinsed in running warm tap water. Then, the glassware was
extracted with acetone and carbon tetrachloride and dried in an
oven at a temperature exceeding 150C. Cleaned glass containers
were kept capped until used.
The plexiglass tank was cleaned by scrubbing the walls with
sponge and Sparkleen soap. The tank was then rinsed with hot
water from a hand-held hose. Test water was always examined for
visible oil sheen before each spreading experiment. If an oil
sheen was present, the cleaning procedure was repeated. For the
chemical dispersion studies, the sampling tubes were disengaged
and cleaned independently. At the beginning of each experiment,
test water was sampled and extracted with carbon tetrachloride.
If the infrared spectra of the sample indicated the presence of
residual oil, the cleaning process was repeated.
Hydrophilic Treatment of Glass Surface
The spurious development of multiple phases during sampling^
of hydrocarbon/water systems poses great difficulty and biases
determinations of oil concentrations in water samples. This
phenomenon may be due to surface/oil interactions during sampling
As glass surfaces are wetted preferentially by oil, adsorption
onto surfaces of sampling probes constitutes a sink for hydro-
carbons when test solutions containing low concentrations of oil
are sampled.
In order to minimize interactions between glass surfaces and
oil, and experimental artifacts via sampling devices, it was
decided to precondition the surfaces of collection bottles,
sampling tubes, and separatory funnels to make them hydrophilic.
Glass surfaces were treated with trimethoxysi1ane to render
them hydrophilic. The treatment procedure described in the manu-
facturer's brochure was used. It consists of a) washing the
glassware with a suitable detergent, b) dipping glassware in a
67
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solution of trimethoxysi 1 ane for a few minutes, and c) air- or
oven-drying the glassware.
The manufacturer claims that the wetting agent forms a
protective film on the glassware. This film is stable to clean-
ing with organic solvents and solutions that have a broad pH
range, for over three months.
Preparation of Seawater Solutions
Synthetic seawater solutions used in this study were prepared
in batches, as required. Instant ocean sea salt was dissolved in
50 gallons of tap water in a 55 gallon drum. Complete dissolution
of the salt in water was achieved by a high speed mixer. A 50 ml
sample was taken from each batch and evaporated to dryness in an
oven .
The salt content of these samples showed that the percent
salt varied slightly for different batches; the average was
approximately 3.51%. This value is in agreement with the salt
content of natural seawater.
Sample Collection
Water samples were collected for analysis during experimental
investigations of the dissolution and chemical dispersion of oils.
Sampling can be complicated by emulsion formation or contamina-
tion. The procedure for sample collection must assure that a
representative portion of the test system liquid is withdrawn.
For the dissolution studies, the first sample in each experi-
ment was collected by means of vacuum suction. Thereafter,
sampling occurred by gravity flow. The first few mis of solution
that were retrieved during sampling were always discarded. This
corresponds to the liquid holdup in the probe. Approximately
250 mis of sample were collected daily for analysis.
During chemical dispersion studies, samples were collected
by gravity flow through the probes. Preliminary investigations
showed small gradients in oil concentrations when samples from
different locations in the tank were analyzed. So, a three-
dimensional matrix of water samples was always collected. 50-ml
samples were collected from each of the 15 locations. The
samples were combined to give a sample that is representative of
the tank contents.
All water samples were collected directly into separatory
funnels. The funnels were stoppered immediately to prevent
volatilization and changes in sample composition. Usually,
samples were extracted and analyzed within 10 hours so that
preservation of samples was not necessary.
68
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v- Determination of Oil Concentrations in Water
Measurement of the concentrations of oil in water samples is
a necessary part of most investigations of oil/water systems.
The determination of hydrocarbon concentrations in water poses
several analytic problems because of the very low concentrations
expected for a wide range of hydrocarbons. A review of the major
analytical techniques shows great diversity, but as yet no single
method is a panacea for all types of problems associated with the
determination of total and hydrocarbon species concentrations in
water. The primary methods now available for measuring the
concentrations of oil in water are spectroscopic, gravimetric,
and chromatographic techniques.
Infrared spectrophotometry is the most commonly used method.
The use of infrared (IR) spectroscopy to quantify the oil content
of water samples is an established procedure. The method is
sensitive, accurate and efficient. This technique has become
popular, also, because of the short time required for analysis.
But, this method is primarily for the analyses of alkanes and to
a lesser extent of aromatic compounds with side chains. In this
method, the oil/water sample is extracted with carbon tetra-
chloride (CCl^) and the total oil content of the extract is
quantified by measuring the maximum absorption attributable to
methylene (-CH-) stretching frequencies at 2930 cm in 1, 5 or
«*,,, J
10 cm path-length quartz crystal cells. Routine determinations of
the total concentration of oil in water samples were made with
the IR method.
Determination of the concentration of oil in water samples
using the IR method has been described in detail by Gruenfeld
(1977).
w
The procedure involves:
1. extracting oil from water samples with an organic
sol vent;
2. analyzing extracts with an IR spectrophotometer; and,
3. referring the maximum absorbance of the extract to a
calibration curve to determine the oil content of the
extract.
Gruenfeld (1977) discussed the influence of salt and acid
addition to water samples, prior to extraction with the solvent,
and the detection limits of oil by IR. Salt and acid were not
used in the present assays.
69
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Extraction--
Oils are soluble in
carbon tetrachloride was
oil from water
in high purity,
is recommended
15 mis of CC1,
most organic solvents. Spectral grade
selected as the solvent for extracting
samples for several reasons:
with little or no spectral
by the EPA. To extract oil
are added to the separatory
The funnel is stoppered and
: it can be obtained
interference, and it
from a water sample,
funnel containing the
water sample. The funnel is stoppered and shaken vigorously by
wrist action for a period of 3 minutes in an inverted position.
The stoppered funnel is placed on a stand and allowed to remain
undisturbed for about 1 hour. By this time, the content of the
funnel has separated into two distinct phases. The bottom phase
containing CC1, + oil is drained into a clean, solvent-rinsed
bottle. The extraction is repeated on the water phase with
another 15-ml portion of solvent. The extracts are combined and
shaken with 2 gms of anhydrous, granular sodium sulfate (Na^SC,)
to absorb moisture and water droplets that may be entrained in
the extract. The volume of the oil-free water sample is measured
using a graduated cylinder.
Infrared Analysis--
Two matched IR cells (1, 5 or 10 cm path-length) are care-
fully rinsed with CCl* and one cell, i.e. the reference cell is
filled with CC1,. The sample cell is filled with extract. The
cells are placed in the IR spectrophotometer and the differential
spectrum is scanned from 3200 to 2700 cm" wave numbers. The
maximum absorbance of the extract is measured: it occurs at
about 2930 cm" . The concentration of oil in the sample can be
determined by referencing the maximum absorbance to a calibration
curve of absorbance versus concentration for the cell size used.
If the maximum absorbance is greater than 1.0, a smaller cell is
used or the extract is diluted with a known amount of solvent.
The concentration of oil-in-water is determined from the follow-
ing equation :
Cc-VCCl
Co -
(43)
where
C = concentration of oil-in-water, yg/ml
C =
concentration of oil in the extract determined from
the calibration curve, yg/ml CC1,
volume of CC14 used to extract the sample, ml
70
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f = dilution factor (if used, otherwise f = 1)
V = volume of water sample, ml
The instrument was checked for baseline drift regularly.
CC1, from the same bottle was used for the extractions and for
filling the reference cell. A segment from the spectra of an
oil/water sample is shown in Figure 9.
Calibration Curves--
A concentration vs. absorbance plot derived from IR scans of
several known concentrations of oil in CC1. (solvent) is used for
quantitating oil in water samples. A standard solution is
prepared by dissolving a weighted amount of oil into 100 ml of
CCK. Aliquots of the standard solution are diluted with CC1. to
obtain solutions at different concentrations. Infrared analysis
of at least four solutions provides absorbance versus concentra-
tion data which is used to prepare a calibration curve for the
specific oil and cell size.
The absorbance and concentration data were correlated by
linear regression analysis. The correlation coefficients range
from 0.98 to 1.0, indicating significant linearity. The inverse
equations of the regression expressions were used to determine
oil concentrations in water samples. Appendix A shows sample
calibration curves for one of the oils.
Efficiency of Extraction--
The efficiency of the method that was used to extract oil
from water samples depends on several factors, such as the quan-
tity of oil in the sample, the volume of CC1., oil type, and the
distribution of oil between CCl/and water phases.
Two water samples containing 0.5 and 1.0 gms of oil were
prepared as follows. The oils were dissolved in 5 mis of acetone
and the acetone solutions were spiked into 1 liter of water. For
a control, 5 mis of acetone were spiked into 1 liter of water.
The three water samples were then extracted with CCl^, and the
absorbance of the extracts determined. By subtracting the
absorbance for the control from those for the samples, the quan-
tity of oil extracted in each sample was determined. Four oils
were used in this experiment: #2 fuel, #6 fuel, Nigerian crude,
and Iranian crude.
In all experiments, the percent recovery was greater than
90%. The good results may be attributable to the quantity of CC1.
used in all extractions and the hydrophilic treatment of glassware
surfaces which minimizes the adsorption of oil.
71
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CO
CC
o
«/>
03
3500
3000
WAVENUMBERCCiN/T1)
2500
Figure 9. A Segment from the Spectra of the CC1.
Extract of an Oil/Water Sample
72
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Protocol for Studying Spreading Rates of Oils on Calm Water
Experimental studies to determine the spreading rates of the
12 oils were conducted in the open, rectangular Plexiglass tank.
Because of the constraint imposed by the two horizontal dimensions
of the tank (5'x3'), the duration of experimental runs was limited
to the first 35 minutes after slick initiation. A run was dis-
continued after 35 minutes or when the spreading oil contacted the
sides of the tank. This was necessary to minimize wall-effects on
the spreading slick.
The temperature of the tap water flowing into the tank was
controlled by adjusting the flow rates of cold and hot water
such that water temperature was approximately 20±1C. It was not
necessary to control the temperature of the water during a run
because of the short duration of the experiments.
For each oil, four different volumes (25, 50, 75, 100 mis)
were spilled. Although the oils were spilled at different rates,
they were discharged completely within 10 minutes.
The spreading experiments were performed according to the
following procedural sequence.
1. Tank was cleaned and rinsed as described in the cleaning
procedure section.
2. Tank was filled with tap water at 20 ± 1C to a depth of
12 inches. Water was checked for surface films or irridescent
color. Cleaning procedure was repeated if a surface film was
observed.
3. Flood lights were turned on.
4. Camera was mounted on the Techno! copy stand such that "
the whole tank could be viewed through the view finder.
5. A circular piece of carbon paper (3.625 inches in
diameter) was floated on the water surface. The camera was
focused on the paper. Exposure level and shutter speed were
selected to secure good contrast between paper and background.
All required adjustments on camera, motor-drive, flood lights,
etc. were completed.
6. The carbon paper was photographed. This served as the
basis for determination of the exact magnification of photographic
images of the spreading oil.
7. The oil-feeding system was installed and the volume of
test oil plus an allowance for clingage was measured into the oil
holding flask. The flask was connected to the oil-feeding system.
73
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8. The peristaltic pump was turned on.
9. The stopwatch was started and the interval timer acti-
vated as soon as oil was discharged from the oil-delivery tube
and rose to the water surface. The interval timer was adjusted
to sequence photograph at 1 minute interval .
10. The stopwatch was stopped when the oil has been
discharged completely and pertinent data recorded.
In each run, ample time was allowed for the water in the tank
to become quiescent and the procedure above was standard for all
the oils tested except #2 fuel oil. Because of the poor contrast
of #2 fuel, a small quantity of red dye was dissolved into the oil
before it was measured into the holding tank.
Determination of Oil Slick Spreading Areas--
All photographic films were developed and printed into
8"xlO" prints in the dark-room facilities of the Rutgers Depart-
ment of Mechanics and Material Sciences (New Brunswick, N.J.).
Figure 10 shows sequence photographs of one of the spreading oils.
The areas of the photographic images in the photographs were
measured using a Compensating Polar Planimeter (Model #620010,
Ser. #85-203), manufactured by Keuffel and Esser Co. (Morristown,
N.J.).
The instrument differs slightly from a needle compass because
of the presence of a tracer point and a measuring wheel connected
to a vernier scale. To measure an area, the tracer point is run
around the periphery of the profile from a starting (and finish-
ing) point. As the figure is traced, the measuring wheel rotates.
After a complete circuit of the figure, the distance which the
wheel has revolved is determined from the difference of the
initial and final readings on the vernier scale.
For each series of photographs, the area of the image of the
reference carbon paper was first determined. Since the actual
area of the carbon paper is known, the areas of the images of the
spreading oils in the same sequence photographs could be deter-
mined. Each photograph was traced twice and the readings
averaged.
The planimeter was calibrated by measuring several areas of
rectangular, cylindrical and spherical geometries. From compari-
sons of the measured and actual areas, the precision of the
instrument was deemed greater than 99%. Thus, uncertainties in
measurement of actual spill areas are due largely to identifica-
tion of spill boundaries as a result of poor imagery.
Accuracy of the Spreading Areas--
It was observed during the spreading experiments that the oil
slicks did not spread uniformly. Regions with different thick-
74
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Figure 10. Sequence Photographs of Oil During Spreading
75
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nesses of oil were visible and appeared as different intensities
in the dark color of the images when photographs were printed.
Usually, darker regions were surrounded by lighter ones. Most of
the oil was present in the dark regions.
The spreading patterns of the oils showed great diversity,
also. Different configurations could be seen for different oil
types; however, spreading patterns were more round than rectangu-
lar. A few oils spread in a circular fashion. It was not known
whether the different configurations were caused by the molecular
motions of water and small advection currents or by the unequal
surface tension forces at the free surfaces of the oil slicks.
Situations were encountered in which the spreading oil
covered the water surface within a few minutes and impacted the
tank walls. Experiments were repeated in such cases. In other
cases, the determination of the area! extent of spreading oil was
impossible with a planimeter because spreading was not continuous.
These oils usually formed fingers that were disjointed and
separated by water streaks.
It was difficult to identify regions with similar contrast
in all the photographs because of different spreading behaviors.
Clearly, the accuracy of the spreading areas depends on the
configuration and spreading behavior of the slick. For two
identical experiments, the areas covered by the same oil could
vary by as much as 20%. This underscores the need for a more
accurate technique for determining the spreading areas of oil
slicks. A color densitometer may be better suited for measuring
spreading areas directly from photographic negatives.
Protocol for Studying the Dissolution Rates of Oils
The experiments to study dissolution rates of oils were
conducted in three phases. In the first phase experiments, the v
dissolution of oils in tap water was studied. All twelve crude
oils and derivatives were tested during this experimental phase.
In the initial stages of the experiment, two oils (Nigerian and
Iranian crudes) were equilibrated with water for three weeks.
The results of these experiments showed that equilibrium was
achieved in about two weeks. Therefore, the duration of subse-
quent dissolution experiments was reduced to two weeks.
During the second phase of experiments, the dissolution
rates of only six oils in salt water were studied. Five crude
oils and #2 fuel oil were tested. The crude oils are: Nigerian,
La Rosa (Venezuela), Brass River (Algeria), Iranian and North
Slope (Alaska). All oi1/salt-water systems were allowed to
equilibrate for two weeks.
Experiments using tap water and salt water were conducted in
the dissolution test tank described earlier. The procedure
76
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outlined below was used for the experiments during both phases.
1. Test tank was cleaned according to the established
cleaning procedure.
2. Cooling coils attached to the constant temperature
bath were installed in the tank. The sampling tube
was installed, also.
3. 30 liters of water (tap or 3.5% salt water) was
metered into the tank.
4. Water was sampled by vacuum suction and analyzed for
oil contamination. If there was contamination, the
procedural sequence 1) to 4) was repeated.
5. 300 mis of oil were layered on the water by gently
pouring the oil via the side of the tank.
6. The constant temperature bath was turned on.
7. The water was sampled daily for the duration of the
experiment.
Prior to each sample collection, the position of the sampling
probe was adjusted gently so that all samples are collected 6
inches below the oil/water interface, in the center of the
cylindrical tank. The volumes of water samples collected varied
from 250 to 500 mis. During sampling, precaution was taken so
that the surface slick was not disturbed.
In the third phase of the dissolution experiments, concen-
trations at saturation were determined for all twelve oils. The
procedure followed was different from that used in the first two
phases. In brief, 200 mis of each oil were poured into 1-liter
separatory funnels containing 500 mis of tap water. The funnels
were stoppered tightly and stored in the dark for three months.
After this time, 400 mis of the aqueous phase was withdrawn from
each separatory funnel. Samples were extracted with CC1. and
analyzed to determine their oil content.
It was assumed that the oil concentrations determined by
this procedure would be close to the "actual" saturation values
of the oils tested. The rationale in adopting this procedure
stems from the fact that oil/water systems can become mutually
saturated when the ratio of oil to water is close. Since oils
equilibrate slowly with water, prolonged equilibration and
"closed" experiments are necessary conditions for accurate deter-
mination of concentrations at saturation.
77
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Protocol for Chemical Dispersion Studies
Although several procedures have been used to determine the
effectiveness of oil spill dispersants, there is no meaningful
common ground regarding acceptable procedures for evaluating
dispersants.
The efficiencies of 5 dispersants were evaluated in this
study. The dispersants are referred to as products A, B, C, D,
and E. Three oils were treated with the dispersants. They are
#2 fuel oil, Iranian crude, and #6 fuel oil. The degree of diffi-
culty with which these oils can be dispersed varies from "easy"
to "tough".
Several variables influence the effectiveness of oil spill
dispersants, and it is cumbersome to evaluate all the factors,
even for one oil/dispersant pair. The effects of three oil-to-
dispersant dosage rates (1:1, 5:1 and 10:1 vol/vol) were studied
using #2 fuel oil. The chemical dispersion of the other two oils
was studied at a 5:1 oi1-to-dispersant ratio only. Thus, one
emphasis of this comparative study concerns the influence of
oil/dispersant ratio on the effectiveness of chemical dispersants,
These tests above were conducted with similar levels of agitation,
The effect of turbulence on the effectiveness of dispersants
is well known. The efficiency of oil spill dispersants increases
with the intensity of agitation. As some manufacturers have
claimed that it is not always necessary to provide mixing energy
for certain dispersants, tests were conducted with product B to
determine the efficiency of the dispersion with continuous agita-
tion and without agitation.
The effect of salt water on the dispersion of oil slicks
with dispersants was also investigated with product B. Tests to
determine the effects of salt water and turbulence on chemical
dispersion were conducted at an oil-to-dispersant ratio of 5:1.
Iranian crude and #2 fuel oil were used.
Before actual comparative tests were begun, standard proce-
dures for dispersant application and wave generation were
developed in preliminary tests.
All dispersants were atomized by pumping the dispersant
solution at 2cc/sec and flowing compressed air at 375 cc/min to
the nozzle. The nozzle tip was adjusted to produce a fine spray
with a 9 inch swath at the water line. The railroad car (and
nozzle) travels at a constant height of 18 inches above the water
level. The dispersant solution is sprayed vertically downwards
at a constant angle onto the oil layer and hits the water surface
with a constant impact velocity. The direction of travel of the
buggy is always from the downstream end of the tank (where wave
breaking occurs) to the upstream end (where waves are generated).
78
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Usually dispersants were applied in 1 pass as the nozzle travelled
across the tank at a constant speed of 0.075 ft/sec. The buggy
was stopped, at selected points along the tank, during application
of 300 mis of dispersant in order to discharge the chemical in 1
pass.
The standard waves in all tests were generated by adjusting
Variac output to 65 volts. At this setting, the eccentric disc
of the wave generator makes 50 revolutions per minute. At the
beginning of wave generation, waves can be seen breaking at the
downstream end of the tank. After about 10 minutes of continuous
wave generation, a quasi-equi1ibrium is established. Surface
waves are random and have a characteristic amplitude of approxi-
mately 3 inches and a wave length of about 15 inches.
The procedural sequence for chemical dispersion studies
follows.
1. The tank was cleaned according to the established
procedure and filled with tap water to a depth of
18 inches. The temperature of the tap water was
maintained at 25 ± 1C by controlling the flow
rates of hot and cold water.
2. The water was sampled and the sample analyzed to
determine whether residual oil was present. If
necessary, the tank was cleaned again.
3. The wave generator was turned on and the setting
on the Variac checked. Waves were generated for
up to 10 minutes to establish a steady-state wave
and current pattern in the tank.
4. 300 mis of oil were poured on the water in the
tank. The oil was allowed to spread for approximately
5 minutes.
5. The volume of dispersant to be tested was measured
into the dispersant holding vessel.
6. Application of the dispersant onto the oil was commenced.
7. Wave generation was stopped after 15 minutes.
8. As soon as the wave generator was stopped, approximately
50 ml samples were collected from each of the 15
sampling probes, using gravity flow. Samples were trans-
ferred into 1-liter separatory funnels for extraction
and analysis.
W
79
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9. Samples were collected every fifteen minutes for the
first hour, and at thirty minute intervals during the
next hour. Later, samples were collected twice at
hourly i ntervals.
PRESENTATION OF EXPERIMENTAL DATA
Experimental data are presented in Appendices B to E.
Appendices B and C include data for oil solubility studies in tap
and salt water, respectively. All of the oils were equilibrated
in tap water; only six oils were equilibrated in salt water. The
experimental data for runs in tap and salt water show similar
trends. The concentration of oil in water rises during the first
few days; after it dropped gradually. Generally, concentration
for runs in salt water were approximately an order-of-magnitude
(or more) lower than runs in tap water.
Appendix D contains data for areas covered by spreading oils.
Four different volumes were spilled for each oil. The experi-
mental data shows a steady increase in area covered by any oil
during the first few minutes; later, the area increased at a
slower rate.
Appendix E shows the data for the chemical dispersion studies
The dispersion data for #2 fuel oil and the 5 dispersants
(Products A to E) at 1:1, 5:1, and 10:1 oil-to-dispersant (0/D)
ratios are given in Tables El, E2 , and E3, respectively. It can
be seen that oil concentration declined throughout the sampling
period, that is after the wave generator had been turned off.
Also, oil concentrations are higher for high dispersant dosage
rates. Tables E4 and E5 present the data for the dispersion of
Iranian crude oil and #6 fuel oil, respectively. Table E6
summarizes the data for the dispersion of #2 fuel oil and Iranian
crude in salt water. When this data is compared with those in
Tables E2 and E4, for the same oil/dispersant pair, two conclu-
sions can be made concerning the effect of salts. First, there
were no significant differences between the data for the disper-
sion of #2 fuel oil in tap and salt water. In contrast, Iranian
crude behaved differently in dispersion studies in tap and salt
water. Table E7 compares the dispersion behavior of #2 fuel oil
and Iranian crude under calm conditions and continuous agitation.
The low oil concentrations in tests without agitation suggest the
necessity for additional mixing energy for efficient dispersion
of chemically-treated oil spills. When mixing energy is supplied
continuously to disperse oil slicks, almost complete dispersion
can be achieved.
80
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SECTION 8
MODELING OF OIL SLICK DISPERSAL MECHANICS
Mathematical models are important for advance quantitative
and qualitative assessment of contamination of marine environ-
ments by oil spills. It is impossible to derive models that are
valid for all oil spill situations because the rates of oil
dispersal processes are site dependent. Also, the hydrodynamics
of the water column under an oil slick and numerous environmental
factors control the rates of oil slick dispersal processes.
Since a majority of factors affecting oil dispersion cannot be
quantified accurately, there is little merit in sophisticated
models when accurate input data are unavailable.
In this section, simplistic models for the rates of
(i) dissolution and (ii) spreading on calm water of crude oils
and petroleum products are developed. A major feature of each
model is the ability to fit experimental data closely. These
models should provide reasonable estimates of these dispersal
processes under the environmental conditions for which the models
are valid. Also, the models will require as input only physical
properties of the oil and water phases and other properties of
the system which can be determined easily.
Finally, the mechanisms of chemical dispersion and rate
expressions for some of the mechanisms will be presented.
Because of the complexity of chemical dispersion processes, an
overall rate expression is difficult to derive.
THE MECHANISMS OF DISSOLUTION
Discharges of oil on water masses can occur instantaneously,
continuously or in a combination of both rates. In the models to
be derived, it is assumed that the oil has been discharged
completely before commencement of the dissolution process. Thus,
the oil/water system considered here is an unlikely worst case of
an oil spill, such as an oil pool which covers the entire surface
of a lake or pond. This situation is different from other oil/
water systems, e.g. those formed from natural seeps, as infusion
and dissolution of oil occur simultaneously.
81
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Figure 11 shows an oil/water system in dynamic equilibrium.
The system consists of three phases: air, oil and water. The
thickness of the oil layer is much less than the other two phases.
Regions of major interest are the air/oil and oil/water inter-
faces. The system may be visualized as the worst possible oil
spill in a marine environment, as the oil is assumed to cover the
entire water surface.
The following mass transfer processes occur when the system
is allowed to equilibrate:
a) volatile hydrocarbon evaporate at the air/oil interface;
b) hydrocarbon species diffuse from the bulk oil layer to
both the air/oil and oil/water interfaces; and
c) hydrocarbon species diffuse into and dissolve in the
bulk water phase.
These processes occur simultaneously and the individual rates
are dependent on each other. The rates of evaporation and disso-
lution depend on the supply of volatile and soluble hydrocarbon
species from the bulk oil. The relative rates of both processes
depend on the extent to which the species partition into gas and
water phases.
Before deriving the equation for the rate of dissolution of
crude oils and petroleum products in water, it is useful to
consider the trend of the experimental data presented in Appendix
B. The data for all experimental runs show the following trends.
AIR
air/oil interface
OIL
UATCD oil/water interface
Figure 11. The Three Phases of an Oil/Water System
82
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At the beginning of the equilibration processes, oil concentra-
tions in water are low but increase gradually to maximum values,
within a few days. All oils did not reach maximum concentrations
in water on the same day. In general, oils reached maximum solu-
bility levels in water after approximately eight days. Oil
concentrations declined gradually, during the later stages of the
equilibration period.
The trend in the experimental data suggests that diffusion
of hydrocarbon from the saturated oil/water interface into the
bulk liquid column occurs during the early stages of the equili-
bration process, until the concentration of oil in water reaches
a maximum. During this period, the driving force for the diffu-
sion process is the concentration gradient, i.e. the differential
concentration between the oil/water interface which is assumed to
be saturated with oil and the concentration of oil in the bulk of
the water column. The water column is assumed to have a uniform
concentration of oil.
Movement of hydrocarbons to the oil/water interface occurs
by molecular diffusion from the bulk oil layer. This transfer of
soluble/volatile hydrocarbon species is necessary to "saturate"
the interface but causes depletion of these materials in the bulk
oil layer. Molecular diffusion of similar materials occurs from
the bulk oil layer to the air/oil interface where they are lost
to the atmosphere by evaporation. Thus, evaporation and dissolu-
tion processes are occurring simultaneously, but these processes
may not necessarily be in equilibrium.
After maximum oil concentrations have been reached, the
steady decline in concentration of oil in the water phase is
caused by evaporation. Volatile hydrocarbons escape and deplete
the top layers of the oil. If evaporation of hydrocarbons is to
proceed, the transfer of volatile hydrocarbons from the bulk oi'K
layer must be maintained. When the bulk oil layer is depleted of
volatile hydrocarbons, diffusion of hydrocarbon to the air/oil
interface continues with transfer of oil already dissolved in the
water column. This is due to the greater partition coefficients
of hydrocarbons with air than water. Thus, some of the hydro-
carbon that evaporates at the air/oil interface is derived from
the oil in aqueous solution, even though the oil may be present
at a concentration which is less than saturation. The final
concentration of oil during the later stages of equilibration
depends on the hydrocarbon species present in each oil. Some
soluble hydrocarbon species are not volatile and are retained in
solution.
Formulation of the Kinetics of Dissolution
Crude oils and petroleum-based products contain organic
materials that are soluble in water. Typically, these water-
soluble species include hydrocarbon compounds that contain from 1
83
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to 20 carbon atoms (C-i-Cog). as we^ as hydrocarbon compounds
with nitrogen, sulfur, and oxygen molecules, and organo-metal1ic
compounds. The complete range of soluble and volatile compounds
cannot be identified for any oil type.
In order to derive an expression for the rate of dissolution
of oils in water, it is important to comment briefly on the
transport of materials through systems consisting of multiple
phases. Several processes which involve transport of materials
between layers of different phases are important in nature. For
example, the exchanges of gas across air/water interfaces (Liss,
1973; Liss and Slater, 1974; Broecker and Peng, 1974), and evap-
oration of hydrocarbons (Mackay and Matsugu, 1973; Mackay and
Wolkoff, 1973; Butler, 1975; and Cohen et al ., 1978) have been
investigated.
The rate of transfer of materials across interfaces can be
calculated by several methods depending on the physical system
and the given set of conditions. Danckwerts (1951) described
several models which have been proposed to explain transport
across multiple phases. The concept of stagnant films at inter-
faces is well entrenched in engineering literature. Also, the
film theory is useful for visualizing processes at interfaces.
This concept is applied here.
The air/oil and oil/water interfaces in Figure 11 are each
assumed to consist of two films. For example, for the air/oil
interface, it is assumed that there is a thin film of gas on the
air side and a thin oil film on the oil side. Similarly, oil and
water films exist on either side of the oil/water interface.
Since the thickness of the oil layer formed by a majority of
spills is negligible, it is convenient to visualize an oil/water
system as consisting of only two films: gas and liquid films on
the air and water sides, respectively. Thus, the oil layer is
considered to be an extended interface separating air and water
phases. The regions of an oil/water system and theoretical
profiles of the oil concentrations are shown in Figure 12.
The two-film theory assumes that transport of a material
from one phase to the other occurs by molecular diffusion through
both films. If the transfer is a steady-state process, there is
no concentration build-up in the interface and resistance to
transport is due to the gas and liquid films. Gas and liquid
film resistances may be considered to be in series and the rate
of transfer of material is controlled by the film which offers
the greatest resistance to diffusion. This theory has been used
with great success to explain rates of gas transfer between air
and water and evaporation of liquids. In some situations, only
one of the two resistances is significant. For instance, there
is no liquid film resistance during the evaporation of pure
liquids because of the absence of a concentration gradient in pure
1 iquids .
84
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BULK AIR
GAS FILM
LIQUID FILM
AIR/OIL
INTERFACE
OIL/WATER
INTERFACE
Figure 12. The Regions and Concentration Profiles
of an Oil/Water System
For the most general case of non-steady-state transfer of a
compound between two phases, the basic equation for the one-
dimensional case has the form:
dC n
d2C
(44}
where
3
C = concentration, mg/cm
2
D = diffusivity, cm /day
z = direction normal to the plane across which transfer
occurs, cm
t = time, days
If the transfer process occurs by molecular diffusion and steady-
state conditions apply, Pick's first law is used to determine the
diffusional flux in the direction of transport:
85
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F = D (45)
where
2
F = the flux of the compounds through the layer, mg/daycm
2
D = diffusivity, cm /day
C = concentration, mg/cm
z = distance in the direction of transport, cm
Equation (45) is usually written as
F = kAC (46)
where
k = mass transfer coefficient or velocity of the transfer
process, cm/day
AC = the concentration difference between the boundary
surface and the average bulk concentration, mg/cm3
Thus, the flux of a material across a layer is proportional
to the concentration driving force. The magnitude of k is deter-
mined by the geometry and the flow characteristics of the system.
The experimental data suggests that the dissolution process
could be divided into two parts with separate rate expressions
for the solution and evaporation phases. The combined equations
yield the rate of dissolution for the duration of the equilibra-
tion period.
K.
During the early stages of equilibration when oil is
dissolving in the aqueous phase, a material balance on oil in the
bulk water phase is
Accumulation = Input by diffusion from the liquid film
i = k .(r _r"\ (47 \
dt L V^ L ' ( '
where
j P
-nr = rate of change of oil concentration in the bulk liquid
3
phase, mg/cm -day
k. = diffusivity of soluble species in the liquid, cm/day
86
-------
2
A = interfacial area, cm
o
V = volume of liquid, cm
3
C, = concentration of oil in the liquid film, mg/cm
C = average concentration of oil in the liquid phase,
mg/cm
The interfacial area and the initial volume of liquid are known
from the experimental system, but V is not constant because of
loss of liquid from sample withdrawals. If it is assumed that
the liquid film is saturated with oil, the rate of accumulation
of oil in solution at any time is given by
=MCs-C) t < tm (48)
TT(0) = 0 (Initial Condition)
where
K. = the mass transfer coefficient (k, A/V) ,day~
C = oil concentration at "saturation" at the liquid film,
5 mg/1
Cf = average oil concentration in the liquid, mg/1
Equation (48) is valid for the solution phase, that is up to some
time (tm) at which the concentration of oil in the aqueous phase
is maximum. Also, it is assumed that the system is well mixed.
Actually, oil concentration will vary with distance from the oil/
water interface. In this study, preliminary experimental runs
showed that the concentration of the sample taken 6-inches below^
the interface was the closest to the average value of the oil
concentrations from all the locations.
During the latter part of the equilibration period, the
concentration of oil in the aqueous phase decreases as a result
of evaporation of hydrocarbons from solution in which the oil
concentration is less than saturation. A material balance on oil
in the water phase gives the rate of oil loss:
Depletion = Diffusion across the liquid film
- -KL(C-C*) t > tm (49)
where C* is the oil concentration at the oil/water interface and
K^ is the average mass transfer coefficient of the volatile
fraction of the dissolved species. The derivation of the equa-
87
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tion relating C* to C follows.
The rate of evaporation of oil from solution is controlled
by three resistances due to the liquid film, the oil layer, and a
gas film. The resistance to diffusion due to the oil layer is
negligible because of the small distance the volatile species
travel. If there is no accumulation in the oil layer, the rate
of diffusion of volatile species from solution is in equilibrium
with the rate of evaporation at the air/oil interface. Under
steady-state conditions, Pick's first law is applied to the liquid
and gas phases to determine the diffusional flux in the direction
of transport
KL(C-C*) - Kg(cg-cj
where
(50)
"
K,,K = liquid and gas mass transfer coefficients, day" ,
9 resectively
C\C*,C
,
9
= concentrations of volatile/soluble species
in liquid bulk, in the liquid at the inter-
face, in the gas at the interface, and in
bulk air, mg/1 , respectively
The interfacial concentrations can be related by an empirical
equation of the form
Cg = KHC* (51 )
Equation (51 ) is similar to Henry's Law, where KH is the Henry's
Law constant or the partition coefficient of the volatile species
in gas and liquid phases.
The concentration of these materials in air, C^, is negligi-
ble. Substituting for C in Equation (50) and eliminating C^
gives 9
K[(C-C*) =
(52)
Solving for C* in Equation (52) and substituting the result into
Equation (49), gives
dt
t > t
m
(53)
where
(Initial Condition)
88
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-L = J_ + _1_ (54)
v " v \f *3 '
KE KL Kg H
and C = maximum concentration attained at time equal t , mg/1.
The duration of the equilibration period determines which of
the two processes, i.e. solution or evaporation, is operative.
Equations (48) and (53) jointly give the rate of dissolution.
The lag period between the transfer of oil into water and the
beginning of evaporation from solution is accounted for by using
different integration limits for the two equations.
Actually, these equations are for individual hydrocarbon
species that are volatile and soluble. Thus, the final
expressions should be summations over all volatile and soluble
species. Crude oils and petroleum products contain numerous
compounds with varying solubilities and volatilities. It is an
impossible task to identify completely all the compounds in any
given oil that dissolve into water and later evaporate from solu-
tion. The analytical method used in this study measures only the
total concentration of extractable organics.
If the mass transfer coefficients are assumed constant,
integration of Equations (48) and (53) and substitution of the
initial conditions gives
C = Cs(l-e~ L ) (t < tm) (55)
and
C = CmexPC-KE(t-tm)] (t > tm) (56)
where
-K, t
Cm - Cs(l-e L m) (57)
The dissolution equations can be considered as a segmented model
with a joint point at t . If the equilibration period is less
than t , Equation (55) gives the variation of oil concentration
as a function of time of equilibration. If the oil/water system
is allowed to equilibrate beyond tm, the concentration of oil in
the liquid phase varies with time according to Equation (56).
89
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THE RATE OF OIL SPREADING ON CALM WATER
It is impossible to predict accurately the rate of spreading
of an oil slick. Spreading rates are site dependent and are
influenced by the hydrodynamics of the underlying water and
surface air columns.
A few theoretical studies which have improved the knowledge
of oil slick transport have been reviewed. More recent experi-
mental investigations have involved actual field studies in which
large volumes of oil have been spilled intentionally at sea. The
costs associated with such studies are exorbitant and the infor-
mation derived from actual field tests may be relevant only to
specific spill situations.
Usually, the spreading of oils on water is considered to
consist of two independent mechanisms (Hoult, 1972). The first
mechanism is the tendency of the oil to spread as a gravity wave
on calm water; the second mechanism comprises the gross transport
of oil masses in the presence of external forces, i.e. the
convective forces of winds, currents, tides and waves. The total
area covered by an oil spill is a combination of the areas
covered by both spreading mechanisms. Knowledge of oil transport
by convective forces at sea is improving because of increasing
observations of actual spills.
Two approaches have emerged from previous work for dealing
with the spreading of oils on calm water. A most significant
contribution was made by Fay (1969, 1971), who proposed three
stages during the spreading history of oil slicks on calm water
for oils discharged instantaneously. Each stage is a balance
between a retarding and a spreading force.
Using a different approach, Murray (1972) derived an
expression for the area covered by an oil slick from the solution
of the one-dimensional Fickian diffusion equation. Fannelop and
Waldman (1971), Hoult (1972) and Buckmaster (1973) showed that
expressions similar to Fay's can be derived by solving the basic
equations for describing movement and mixing of a contaminant,
i.e., continuity and momentum equations, with specific boundary
conditions.
The approach used by Fay is better from the standpoint of
ease of estimation of the areal extents of oil slicks on calm
water. This method is adopted here. The goal is to develop
expression(s) that permit prediction of areal increase with time,
for an oil slick spreading from a stationary source, using as
input data only the limited information available at a spill
site. This information includes an estimate of the total volume
of oil spilled, duration or rate of spill, and the physical
properties of the oil and water, i.e. viscosity, density, surface
and interfacial tension.
90
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Assumptions are that:
a) physical properties of oil and water phases do not vary
with time;
b) the thickness of the oil layer is always smaller than
the horizontal dimensions of the slick; and
c) oil is discharged onto water at a relatively constant
rate.
The first assumption is only valid during the initial stages
of spreading. Since the experimental spreading studies lasted
only 35 minutes, changes in the physical and chemical properties
of oil and water phases were not considered significant. In
general, weathering processes operate on oil slicks and cause
changes in oil composition. Evaporation causes volatile compo-
nents of the oil to be lost to the atmosphere and dissolution
causes soluble components to leach into water. The effects of
other weathering processes, e.g. microbial degradation, photo-
oxidation, etc., may be significant also, depending on the
duration of oil exposure. Density and viscosity of oil increase
with time but the net value of the surface tension balance may be
positive or negative at any instant. The second assumption is
necessary if the oil is to be in hydrostatic equilibrium in the
vertical dimension.
Formulation of Spreading Equations
Figure 13 is a schematic diagram showing an oil slick on
water. The thickness (h) of the slick varies with time, t. The
oil floats a height Ah above the mean water surface. If the
flowrate of oil onto water, Q, is assumed to be fairly constant
then
V = Qt t < tD (5B)
V = Vt t > tD (59)
where
V = volume of oil, cm
V. = total volume spilled, cm
Q = volumetric oil flowrate, cm /sec
t = time, sec
tp = duration of oil spill, sec
If exchanges of oil at the free surface boundaries of the slick
due to evaporation and dissolution are negligible, conservation
91
-------
w
WATER
Figure 13.
Schematic Diagram of an Oil Slick
on Calm Water Showing Spreading
and Retarding Forces
of mass requires that
where
V = Ah
(60)
A = areal extent of the slick, cm
w
h = mean thickness of slick, cm
The forces which cause oil slicks to spread and/or shrink
are identified and considered next.
Surface Tension--
Surface tension forces at the leading edges of oil slicks
influence the spreading rate of oils on calm water. Figure 13
shows the direction of surface tension forces acting on a slick.
The net value of the balance of the surface tension forces, at
any time, determines the contribution of surface tension to the
overall spreading rate of the oil. The resultant surface tension
(a) is
a =
cos eraow
cos a,
(61)
92
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where
a ,a ,a = surface tensions of water, oil and interfacial
tension between oil and water, dynes/cm,
respectively
9,,92 = instantaneous contact angles formed by the oil
phase at the air and water boundaries, degrees,
respectively
Oil slick thickness is smallest along the periphery of slicks;
the effect of surface tension is significant here because the
contact angles are nearly zero. Actually, the contact angles
decrease with time as the oil spreads outwards. Since the value
of cos 9 approaches 1 as 9 approaches zero degrees, Equation (61)
can be written as
Depending on the value of a, surface tension forces may accelerate
or retard spreading.
A positive value for a speeds spreading, while a negative
value has the opposite effect. The net surface tension divided
by the area of the slick gives the surface tension force per unit
volume of oil (F )
Fa = k^/A (63)
where
a = net surface tension, dynes/cm
2
A = area of the slick, cm
k, = proportionality factor
The factor k-j was introduced to account for the variations of the
contact angles and the surface and interfacial tensions with time.
The spreading force due to surface tension may not be uniform
along the free surfaces of the oil slick. Variation of surface
tension along the periphery of oil slicks are partially responsi-
ble for unsymmetric spreading patterns.
Gravity--
The effect of gravity on an oil slick can be evaluated by
considering the two components of the gravity vector, g (in the
X
direction of spreading) and g (normal to the spreading), as
93
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shown in Figure 13. The component g of the gravity force acts
vertically downward and produces only hydrostatic pressure. This
pressure increases with distance measured downward from the free
surface of the oil slick. Since the oil slick is in hydrostatic
equilibrium, a hydrostatic balance on the oil is
37 -Vo (64)
where
2
P = the hydrostatic pressure on the oil, gm/cm»sec
vertic
cm/sec
g = vertical component of acceleration due to gravity
j
p = density of oil, gm/cm
y = vertical coordinate axis, cm
Integrating Equation (64) over the thickness of the oil layer
above the water surface yields the magnitude of the hydrostatic
pressure difference (AP).
P = 9yP0Ah = k2gpoAh (65)
where
k2 = constant of proportionality
Ah = thickness of the oil layer above the mean water surface,
cm
To eliminate Ah from Equation (65), a buoyancy equation is used.v
Since the oil floats on water, the equation of buoyancy is
gpw(h-Ah) = gP()h (66)
where
Ah = thickness of the oil above mean water level, cm
h = mean oil slick thickness, cm
p ,p = densities of water and oil, gm/cm , respectively
W 0
2
g = gravitational acceleration, cm/sec
Solving for Ah gives
94
-------
Ah = (1 - )h (67)
Substituting Equation (67) in Equation (65) yields
P = k29P00-P0/Pw)h (68)
The gravity force per unit volume of oil which corresponds to the
pressure force is
Fg ' "Z9P0<1-P0/P,,>T- <69'
Eliminating h in Equation (69), using Equation (60), gives
% "2gp0
This pressure force is caused by the downward-acting force of
gravity, tending to decrease the height of the oil.
The component g of the acceleration due to gravity generates
A
flow in the x-direction, also. The magnitude of this force is
Fg = gxPQh(x)6x (71)
/\
where
g = the x-direction component of the acceleration due to
x 2
gravity, cm/sec
h(x) = variation of oil slick thickness along the x-direction,
cm
<5x = unit width along the x-axis, cm
Since g is much smaller than g the influence of F on the
/\
spreading oil is negligible.
Viscous--
At the water surface, the dynamics of the spreading process
depends on the magnitude of the viscous forces at the air and
water interfaces. The air at the top and the water layer in
close proximity to the oil, i.e. the water-boundary layer, exert
viscous drags on the oil. In the absence of turbulent wind, the
95
-------
viscous drag at the air interface is insignificant. The shear
stress acting on the oil slick at the oil/water interface is the
viscous force which impedes oil spreading. The magnitude of this
viscous force per unit volume of oil, F , is
Fv = TA/V (72)
where
T = shear stress exerted by the water column on the oil
2
slick, gm/cm»sec
For Newtonian fluids, there is a linear relation between shear
stress and strain rate or gradient in velocity
T - y0 & (73)
where
y = viscosity of oil, gm/cm«sec
-rr- = velocity gradient in the oil in the direction of oil
an _,
thickness, sec
If the velocity profile in the oil is assumed to be linear in the
vertical direction, then
*J»' \/ \i ,
'l-^l <">
v - 4 (75)
and
W
where
k3 = proportionality constant
v = spreading velocity, cm/sec
I - characteristic length in the direction of spreading
(A = t2), cm
t = time of spreading, sec
h = mean oil slick thickness, cm
96
-------
Equation (74) is substituted into (73) to give
k3P0A"2
Substituting Equation (76) into (72) yields
W1/2 A
Fv = ^Ih -- T <77>
When h is eliminated in Equation (77) by using Equation (60), the
viscous force becomes
(78)
Inertia--
During the early stages, i.e. the initiation of spreading,
the force of inertia is important. As a slick accelerates from
rest, the motion is retarded by force of inertia. The magnitude
of this force, F.. , can be approximately determined by a momentum
balance in the direction of motion of the slick
FT = K4P0a (79)
where
PQ = mass density of the oil, gm/cm
o
a = acceleration of the oil, cm/sec
k^ = proportionality constant
The acceleration of the oil can be written as
a = -4 (80)
*
where
I = characteristic length of the oil slick, equals (A)1/2,
cm
t = time of spreading, sec
97
-------
The inertia force becomes
Fi = k4P0Al/2/t2 (81)
Equations of Spreading
The equation of spreading is derived by equating the forces
which cause and oppose spreading. These equations are (63), (70),
(78), and (81). Thus, the spreading equation is
F +F = F +F. (82)
a g vi v '
R/? 1 17
2 k u A k p A
(7 i / . \ V 3 o 4 o / n *\ \
1 A + k29Po^" p)~3 = 2 + 2 ^ '
where
Ap = Pn/P » ratio of oil to water densities
0 W
Algebraic manipulation of Equation (83) to solve for A as a func-
tion of the other terms is not practical. Following the method
of Fay (1969,1971), each of the spreading forces can be equated
to the retarding forces and the expression is solved for A to
give several spreading regimes.
For F = F (surface-tension/viscous spreading)
kl
a 3o
*" )
A = k5
/2t
yo
2/7 (85,
kl 2/7
where k =
Fo
r F = F. (surface-tension/inertia spreading)
1
g . ,86)
-- - - (86)
98
-------
A = k,
at'
2/3
(87)
where k,. = (-r-i-)
b k4
For F = FV (gravity/viscous spreading)
5/2
kgp
(88)
A = k.
gp
2/11
(89)
where k? = (^-)
2/11
For F = F.. (gravity/inertia spreading)
2 k.p A
1/2
(90)
A = k<
g(l-Ap)V2t2
2/7
(91)
where k
2/7
8
Equations (85), (87), (89) and (91) are functions of only
the physical properties of oil and water, volume of oil and
elapsed time. These equations relate the area! extent of oil
slicks spreading on calm water to elapsed time. It is interesting
to find that the equation for the surface-tension/inertia stage
is independent of the volume of oil spilled. As such, this equa-
tion is not expected to be a good predictor of the area of a
slick. The volume of oil spilled is related to the duration of
the spill and the time of spreading via Equations (58) and (59).
MECHANISMS OF CHEMICAL DISPERSION OF OIL SLICKS
The importance of dealing with oil spills by diversion^
containment and collection of floating oil cannot be underempha-
sized. These methods are not practical in all spill situations,
99
-------
for several reasons cited earlier. For example, there is a sea-
state threshold beyond which containment and recovery of oil
slicks are impossible. Dispersion of oil slicks by chemical
treatment may be the only option available to reduce adverse
impacts on the environment. The economics of this oil spill
cleanup method are favorable when aerial spraying can be used and
when mixing energy can be provided by winds, waves, tides and
currents.
Previous investigations of chemical dispersion of oil slicks
were limited to laboratory tests of the effectiveness of disper-
sants and toxicity to marine life forms. Thus, no phenomenologi-
cal theories are available to explain the mechanisms of dispersant
action on oil slicks during cleanup operations.
In this section, the mass transfer processes that lead to
dispersion of oil slicks in water are identified. Primary
mechanistic steps are distinguished from those that are ancillary.
Mathematical equations are presented to quantify the key
mechanisms. The effect of introducing mixing energy into oil/
water dispersant systems by using mechanical devices or the action
of turbulence generated during high sea states will be discussed
in qualitative terms. The limitations of the model will be
apparent as consequences of the assumptions made as the model is
developed.
Mechanistic Steps
The mechanisms of chemical dispersion are poorly understood.
An attempt to explain dispersion of oil slicks with chemical
agents was made by Canevari (1969a,b). He proposed three mechan-
istic steps:
a) diffusion of dispersant molecules through the oil layer;
b) incorporation of oil globules into micelles; and
c) diffusion of micelles into the underlying column of
water where they become stranded.
Although these mechanisms are useful in providing a general
description of dispersion processes, they do not include all the
mass transfer processes that contribute to chemical dispersion.
Also, it may be that none of the mechanisms cited is the rate-
determining step. Canevari (1969b) described the mode of action
of the self-mix dispersants by an analogy to the "diffusion and
stranding" mechanism that occurs in spontaneous emulsification
processes (Davies and Rideal, 1963).
Chan et al. (1976) used detergency theory to explain the
mechanism of solubilization in a detergent-saturated solution.
Similarly, Prudich and Henry (1978) discussed their experimental
data for the transfer of hydrophilic-coated-mineral-matter parti-
cles from a hydrocarbon phase to an aqueous phase using concepts of
100
-------
partial detergency. Drawing from the efforts of these investiga-
tors, concepts in colloid chemistry and homogeneous catalysis, an
attempt will be made to create a general description of oil slick
dispersion using chemical dispersants.
Dispersion practice varies and depends on several factors,
e.g. size of oil slick, accessibility of the oil spill site, etc.
The case considered here is as follows. Dispersant is applied
aerially in a fine mist, such that the droplets settle gently on
the oil layer. The impact velocity of the spray is negligible
and the dispersant does not penetrate the oil; it forms a uniform
film at the surface of the oil slick.
In the absence of body forces in the water column (i.e.,
prior to mixing of the dispersant/oiI/water system) and with
sufficient contact between dispersant and oil, the processes that
cause transfer of oily material from the oil layer to the aqueous
phase are:
a) diffusion of dispersant molecules (and micelles) from
dispersant solution to dispersant/oil (d/o) interfaces;
b) distribution of molecules at d/o interfaces;
c) saturation of d/o interfaces;
d) diffusion of molecules through the oil layer to oil/water
(o/w) interfaces;
e) distribution of molecules at o/w interfaces;
f) adsorption of micelles at o/w interfaces;
g) formation of mixed micelles and interfacial complexes at
o/w interfaces;
h) desorption of mixed micelles from o/w interfaces;
i) diffusion of mixed micelles into the bulk aqueous phase;
j) dissolution/accommodation/solubilization of oil particles
in aqueous phase; and
k) diffusion of free molecules back to o/w interfaces or
away from the zone of contamination.
These mechanisms give a comprehensive picture of chemical disper-
sion processes. The fundamental dispersion processes are (f),
(g), (h), (i) and (j); these steps are important for anionic,
cationic and nonionic dispersants. The other steps are
auxilliary. Steps (a) to (e) can be lumped together and consider-
ed as a diffusional step across the oil layer. Figure 14 shows
the mass transfer processes that are important in dispersion
processes.
The relative importance of each of these steps varies,
depending on the situation. In some situations, some of the
secondary processes can become important. The importance of
individual steps or processes depends on the structure of the
surface-active agent, the oil, the solvent base used to formulate
the dispersant, and the concentration and dosage of the surfac-
"**""" tant. For instance, hydrocarbons are generally miscible with
%**>
101
-------
a>
102
-------
other hydrocarbons, because of the near zero Gibbs free energy of
mixing. Thus, dispersants formulated in hydrocarbon solvents
will diffuse through oil slicks faster than those that are
aqueous-based.
Formulation of Model Equations
Before mathematical equations are derived for the fundamen-
tal processes, a brief discussion of micellization is necessary
to an understanding of chemical dispersion of oil slicks.
The behavior of a surface-active agent depends on its state
of solution. Generally, dispersion processes are favored if the
surfactant is present in the solvent solution as micelles rather
than as single ions or molecules. When sufficiently concentrated,
dispersant solutions contain micelles. These aggregates are
considered to be thermodynamically stable and contain from 10 to
more than 100 surfactant molecules. For example, sodium lauryl
sulfate (CH3(CH2)1-|-NaS04) forms micelles consisting of 62 mole-
cules (Elworthy et al., 1968).
The size of a micelle is determined by the structure; micelle
o
diameters range from 40 to 100 A. The concentration of surfactant
at which micelles become significant, i.e. the critical micelle
concentration (CMC), is related to the number of carbon atoms in
a straight chain dispersant molecule by
where
log CMC = a-bm
m = the number of carbon atoms
(92)
a,b = constants
Nonionic surfactants form micelles at lower concentrations than
ionic types, at the same hydrocarbon chain length. Since
commercially available dispersant formulations may consist of
more than one type of surfactant molecules, the CMC of a mixture
will lie between the values of the components.
The law of mass action is usually applied to the association
of single molecules to form aggregates and complex molecules. A
basic assumption is that equilibrium exists between single mole-
cules and micellar aggregates. For non-ionic surfactants, the
reversible process is
mC.
r
103
m
(93)
-------
If the activities are equated to concentrations, the equilibrium
constant, K , for the micellization of non- ionic dispersants is
k* Cm
Kn = r = :£ (»«)
r C.
where
k,r,k = rate constants for the forward and reverse reactions,
-1
sec , respectively
3
C = mass concentration of aggregates or micelles, gm/cm
C. = mass concentration of single surfactant molecules,
3
gm/cm
m = the association number for the surfactant
For ionic surfactants, the reversible process is
kf
mC.+(m-p)Cc b Cm (95)
and
k* Cm
- m
_ .
i k rmr(m-p)
r LiLc
where
C = mass concentration of counter-ions, gm/cm
p = number of counter-ions not attached to the micelle
The degree of ionization of the ionic surfactant is p divided by
m.
If the structure of a dispersant is known, it is possible
to determine m. For dispersants with a linear hydrocarbon
compound, m equals the number of -CH^- groups. Unfortunately,
information on the structure and types of surface active agents
in commercial dispersant formulations is proprietary, and m is
unknown for commercial dispersants.
Since micelles in solutions of ionic surface-active agents
are charged, they repel each other. According to Hartley (1976),
104
-------
the distance between charged micelles is
d3 = _8l_ (j)r3 (97)
3/2
where
d = distance between the centers of the micelles, A°
<(> = weight fraction of the total volume occupied by
micelles
r = micelle radius (assumed spherical), A°
The formation of micelles in dispersant solutions influences the
rate of chemical dispersion. The diffusion of surface-active
materials to various interfaces and transport of oil droplets
into bulk aqueous phase are affected by the degree of micelliza-
tion. The total quantity of surfactant available for dispersion
is increased when surface-active agents are present in crude
oils, petroleum products and surface layers of seawater prior to
the application of dispersants to oil slicks.
Diffusion of Micelles to Interfaces--
Micelles must diffuse through the dispersant solution and
the oil layer to reach oil/water interfaces. A high concentra-
tion of surface-active material in the dispersant solution is
favorable to high diffusive flux. Dispersants formulated in
hydrocarbon solvents approach molecular solution and diffuse
rapidly through the oil layer. Dispersants formulated in water
must undergo two diffusion steps; through both aqueous solvent
and oil layers. Because of these two diffusion steps, the former
dispersants may be slightly more efficient than those of the
latter type.
Since micelles and unaggregated molecules are in equilibrium
in dispersant solutions, both species diffuse but the flux of
micelles will be less than for single molecules. The rate of a
diffusion process may be expressed by Fick's First Law. For
simple diffusion, Fick's Law can be written for micelles and
sing!e molecu!es .
m m 3x
F - D ^1
where
105
-------
2
F ,F. = mass fluxes of micelles and single molecules, gm/cm -sec,
respectively
Dm»D,- = diffusion coefficients of micelles and dispersant mole-
IT] 1 e*
cules, cm /sec, respectively
ar a r
m i
-T , -r = local concentration gradients in the direction of
a X a X «
diffusion, gm/cm
The combined diffusive flux (F.) for both species is
Fd = Fm+Fi (100)
The actual Fd will be smaller than the sum of the individual
fluxes because of interactions between the diffusing species and
the effect of other intermolecular forces.
Diffusion coefficients of micelles and single molecules can
be estimated from the simple Stokes-Einstein Equation
NDT
where
2
D = diffusion coefficient, cm /sec
Ng = Boltzmann's constant, dynes cm/°K
T = absolute temperature, °K
2
y = viscosity of solvent, dynes-sec/cm
r = mean hydrodynamic radius of the micelle or molecule, cm
The diffusion coefficient for single molecules will be greater
than that for a micelle.
Ward and Tordai (1946) derived an expression for the rate of
diffusion of molecules to interfaces. They applied the penetra-
tion theory of mass transfer across a liquid-liquid interface and
derived the following equation for the rate of diffusion
dji _ /_D_J/2 / A > o ,., nn\
dt " Wt'
where
106
-------
n = the number of molecules arriving at a unit cross section-
2
al area of the interface, molecules/cm
D = diffusion coefficient of the molecule through the medium,
2
cm /sec
t = time, sec
23
N, = Avogadro's number, 6x10 molecu!es/gm-moles
C = concentration of surface-active molecules diffusing from
the surface, gm-moles/£
Equation (102) assumes
a) molecules diffuse at a uniform velocity;
b) there is no back-diffusion; and
c) there is no energy barrier, mechanical mixing or thermal
convention in the medium
When an energy barrier opposes the process, a lower rate of
diffusion will result. This equation is applicable to the diffu-
sion of single molecules, micelles, and mixed micelles.
Equation (102) can be integrated to give
i/o N
g/Dt J/2/ _A N r Mm^
The diffusion of surface-active agents from the bulk oil layer to
o/w interfaces will be rapid because it involves molecular diffu-
sion and small oil slick thicknesses.
At the interface, micelles dissociate into single molecules
prior to adsorption and when sufficient molecules have been
adsorbed, some molecules "react" with oil particles to form mixed
micelles that desorb. The proposed reaction between m molecules
and oil to form a mixed micelle is
mC.j+0 CmO
The assumed sequence of reversible steps is
k.
(1) Cn.+S = (CjS) (Adsorption)
107
-------
k2
(2) m(C.S)+0 = (CmOSm) (Reaction)
I |x m Ml
k
3
(3) (Cm°Sm) == cm°+mS (Desorption)
k-3
where
C. = concentration of single molecules
CmO = concentration of mixed micelles
S = an adsorption site
m = number of adsorption sites
(C.jS) = adsorbed single molecule
(C OS ) = adsorbed mixed micelles
0 = concentration of oil
The individual steps are next considered in greater detail.
Adsorption of Dispersant Molecules--
The rate of adsorption of surface-active molecules at o/w
interfaces is governed by the rate of diffusion from the oil
layer. Since single molecules and micelles diffuse together,
they arrive jointly at o/w interfaces where they adsorb as single
molecules.
From step 1, the rate of adsorption is
r* = C.S-kCC.S) (104)
where
C. = concentration of surfactant molecules
S = an adsorption site
(C.S) = concentration of adsorbed molecules
k-, , k -, = adsorption coefficients for the forward and reverse
reactions
108
-------
All concentration terms refer to concentrations at the interface.
"***** The adsorption coefficients follow Arrhenius' Law
k = kQ exp(-E/RT) (105)
where
k = frequency of adsorption, sec"
E = energy of adsorption, cal/gm-mole
R = gas constant, cal/gm-mole»K
T = absolute temperature, K
At equilibrium, the rates of the forward and reverse reactions
are equal
SklC1 = k.^C.S) (106)
and
k, (C.S)
Kl = TT7=-rc (107)
where K-j is the equilibrium adsorption constant.
Surfactant molecules are held at the interface by molecular
forces. They are oriented with hydrophobic groups anchored to
the oil phase and hydrophilic groups immersed in the aqueous
phase.
Formation of Mixed Micelles and Interfacial Complexes--
When a sufficient number of dispersant molecules have been
adsorbed at the interface, a "reaction" occurs between a number
"m" of absorbed molecules which are close neighbors and micro oil
particles to form mixed micelles and/or interfacial complexes.
The stoichiometry of this "reaction" is not known. The reaction
may be a simple coexistence of oil and dispersant molecules as
the oil particles are merely incorporated into the hydrophobic
core of the micelles. The formation of mixed micelles is an
important mechanism in the chemical dispersion of oil. If the
reaction is assumed to be bimolecular, then the rate of the
reaction can be written as
r2 = k20(CiS)m-k_2(CmOSm) (108)
where
1 09
-------
0 = amount of oil particle incorporated into the micellar
core
(C OS ) = surface concentration of adsorbed mixed micelles
k2'k-2 = coefficients of the forward and reverse reactions
Free oil is always in excess at the interface and Equation
(108) can be simplified to
r2 = k2^CiS^m"k-2^Cm°Sm^ 009)
*
where k~ = k20
The equilibrium constant for the reaction is
K = £L_ . ^m^mj (11Q)
2 k-2 (C.S)m
This reaction will not occur if the number of molecules adsorbed
on adjacent sites is less than the association number of the
surface-active compound.
Desorption of Mixed Micelles--
The desorption of mixed micelles from the interface exposes
additional surfaces for adsorption of molecules arriving at the
interface by diffusion from the oil layer. In this process, m
adsorption sites become available. The rate of desorption
according to step 3 is
v = \t (r rK \-\( <;mr n M11 ^
r3 k3(Cm°V k-3S Cm° U'V
where
(CmOSm) = concentration of adsorbed mixed micelles
CmO = concentration of mixed micelles at the interface
Sm = "m" number of adsorption sites which is equal to mS
k3,k_3 = desorption coefficients
At equilibrium, the desorption constant K, is
k SmCO
no
-, i 7 \
'
-------
As the mixed micelles desorb from the interface, they take with
them oil particles that are occluded in their core regions.
The coefficients of the reaction and desorption steps follow
Arrhenius1 Law, also. Davies and Rideal (1963) present equations
for estimating the desorption energies (E) of some nonionic and
ionic surfactants for a few interfaces in which the bottom phase
is water. For nonionic and ionic surfactants, the equations are
E = A +mw (113)
and
E = Ap+mw-z^^ (114)
where
A = energy of polarization of the unionized polar group,
p cal/g-mole
m
= the number of -CH2- groups
w = van der Waals adsorption energy associated with each
-CHg- group, cal/gm-mole
z-| = valency of the surface-active ion
e = electron charge
^ = electrical potential of the surface
Comparison of Equations (113) and (114) shows that the desorption
energies of nonionic surfactants are usually greater than those *
of ionic agents of the same chain length. Davies and Rideal
(1963) give values for ImM of sodium laurly sulfate for a para-
ffinic oil/water interface, with no salt added, as
Ap = +160 (20C), +1800 (50C)
w = +810
z-|£^0 = -5000
In the presence of salt, the value of z-|e^0 increases.
Diffusion of Mixed Micelles into the Aqueous Phase--
As mixed micelles desorb from the interfaces, the layer
directly below the interface becomes saturated with mixed
micelles. The concentration gradient that builds up between this
layer and the bulk aqueous phase provides the driving force that
111
-------
causes mixed micelles to diffuse away from the
This diffusion step is similar to the diffusion
sant molecules and micelles. Equation (102) is
this mass transfer.
surface layer.
of single disper-
applicable to
Dissolution/Accommodation/Solubilization of Oil in the Aqueous
Phase--
The transfer of oil into the underlying column of water is
the ultimate goal of chemical dispersion. During the initial
stages of the dispersion process, the concentration of oil in the
aqueous phase is nearly zero. Then, as the mixed micelles diffuse
into water, dissolution of the oil in water occurs. The first
micelles release their oil particles into water, where the oil
goes into molecular solution. The mixed micelles become unaggre-
gate molecules and, if the oil/water system is static, these
molecules diffuse back to the interface. In this case, there is
no net loss of dispersant; but, in flow systems, the dispersant
molecules may be flushed away from the zone of contamination.
As the diffusion of mixed micelles into the water layer
continues, the concentration of oil increases. In time, oil in
water will be present as molecularly dissolved, accommodated and
solubilized species. These forms coexist in water until the
system reaches "supersaturation." At this point, microemulsions
are formed. These coalesce into larger particles -that can become
buoyant, rise and recoalesce with the surface slick. These
processes occur only in chemically treated and static oil/water
systems when the dosage of dispersant is large enough
accommodation/solubilization/microemu 1 si on phenomena.
heavily contaminated waters, these phenomena will not
in flow systems as dilution of oil in solution occurs
by inflowing fresh water.
to lead to
Except in
take place
continuously
The combined rate of these processes is derived from a
material balance on the oil in solution. The rate of change of
oil concentration in the aqueous phase is equal to the rate of
molecular diffusion of mixed micelles from the interface which is
assumed to be saturated. It follows that
R =
KL(CmO-C)
(115)
where
K, = overall liquid mass transfer coefficient
V
concentration of mixed micelles at the o/w interfaces
on the water side
= average concentration of oil in the aqueous phase
112
-------
The concentration of oil in water consists of oily material from
the slick as well as hydrophobic portions of mixed micelles in
solution. Under field conditions, some oil may sediment after
adsorbing onto solid particles in suspension.
The Rate-Determining Step
The concept of a rate-limiting step is useful when consider-
ing a sequence of several steps. If a step is assumed to be the
slowest step,then its rate controls the rate of the overall
reaction. All steps except the limiting step are assumed to be
at steady-state or in equilibrium and the overall rate is derived
in terms of the slowest step and relevant parameters.
The diffusion steps are probably not rate-limiting as some
mixing is usually available to chemically treated oil/water
systems. The effect of mixing on oil/water/dispersant systems
will be discussed later. Thus, the rate-determining steps are
most likely adsorption, reaction or desorption.
Adsorption Control Model--
Adsorption is a surface phenomenon and is important in homo-
geneous and heterogeneous catalysis. Several models have been
proposed in the literature for the kinetics of adsorption. The
model used here is based on the treatment by Langmuir-Hinshelwood-
Hougen-Watson (Carberry, 1976). This treatment assumes
i) monolayer coverage, ii) no interactions between adsorbed
molecules, and iii) homogeneous surfaces and uniformly energetic
adsorption sites. By mass-action, the rate of adsorption is
proportional to the concentration of the adsorbent and the
fraction of the surface that is unoccupied (0)
rA = k^.d-6) (116)
where k, is the adsorption coefficient.
The total concentration of adsorption sites includes those
either vacant or containing adsorbed species. It follows that
SQ = s+(CiS)+(cm°Sm) (117)
where S = total concentration of adsorption sites
S = adsorption sites that are vacant.
The equilibrium constants are used to eliminate the adsorbed
species in Equation (117). From Equation (107), (C.S) is equal
to ^
(C.S) = SK]Ci (118)
113
-------
Since all sites are identical and if all surfactant molecules are
similar, Equation (118) can be written as
(C.S)m = mK.C^.S (119)
and
(C.S)m
mKl = C.S (120)
The product of Equations (110) and (118) is solved for (C OS ) to
give m m
(CmOSm) = mSK1K2Ci (121)
If Equations (118) and (121) are substituted into (117), the
result is
,K2Ci (122)
Equation (122) can be written as
^~ = TT r~~^ T (123)
Since Equation (123) is equal to (1-e), i.e. the fraction of the
interface that is unoccupied, the expression for the adsorption-
control model, Equation (116), becomes
k,C.
rA = (i+K C.+mK K C.) (124)
The interfacial concentration term C. cannot be measured directly.
The procedure to relate C.. to CmO is as follows. First, Equations
(110), (112) and (120) are multiplied; the result is
SmCmO (125)
Using the relation mS = Sm and solving for C. gives
Cm°
CT = K K K (126)
1 KKK
114
-------
Substituting Equation (126) into (124) and simplifying the result
shows that
K.C 0
(127)
A d+KBCmO+KcCmO)
where KA = k1/K]K2K3
Kg = 1/K2K3
The interfacial concentration term (CO) cannot be measured
directly, also; it must be related to the concentration of oil in
the bulk water phase through Equation (115).
Interfacial Reaction Control Model--
The rate of reaction is
rR - k2(C.S)m-k_2(CniOSm) d28)
Substituting for the adsorbed species using Equations (120) and
(121) gives
rR = mk2K1SCi-mk_2SCmO/K3 (129)
where Sm has been replaced with mS. Equation (129) is simplified
to give
Substituting for S using Equation (123), results in
[mk2K1C.-mk_2CmO/K33S0
If, however, C. is replaced in Equation (131) by using Equation
(126), the result simplifies to
(VKeqK3-k.2/K3)mS0CmO
i ~ Aiii/ /*"" rT_i_ \/ r> A A \ I *5 c
where
11 5
-------
KB - l/KeqK3
Kc = m/K3
Ke = overall equilibrium constant
= KO/ - 2
Equation (132) is the overall rate of dispersion when the
formation of micelles is the controlling step.
Desorption-Control Model --
In Langmurian terms, the rate of desorption is assumed to be
proportional to the concentration of the desorbing specie(s) or
the fraction of the surface occupied, 9. Thus, the rate of
desorption is
rD ' MCm°Sm> - k39 <133>
Substituting for (CmOSm) using Equation (121) gives
rD = mk3K]K2SCi (134)
If S is replaced in Equation (134) with Equation (123), the
result it
D
Substituting for C. using Equation (126) and simplifying gives
KnCmO
D m
D " (1+KB
where
KD = mk_3SQ
B = 2 3
Kp = m/ Ko
This equation is similar to that derived for the case when the
rate of adsorption is the limiting step. Also, Equation (136)
is related to the concentration of oil in the bulk fluid through
Equation (115).
**»»
116
-------
When mixed micelles desorb from the interface, surfactant
molecules are lost from the surface areas. Desorption of mixed
micelles exposes additional areas at the interface. Thus, space
is available for adsorption of surface-active molecules reaching
the interface by diffusion from the bulk oil or water column.
The overall rate of dispersion of chemically treated oil
spills will vary according to the mechanism(s) which is(are)
rate-limiting. Field conditions will determine the mechanism
which is the slowest step.
The Effect of Mixing
Mixing is usually supplied to oil slicks after they are
treated by dispersants by mechanical means and/or water motions
induced by the action of winds, waves, tides, and currents. The
hydrodynamics of the system will vary according to the origin and
intensity of mixing.
The amount of work required to remove completely a unit of
oil from the oil layer is called the work of detergency. The
magnitude of this work for complete detergency is
W . = a +a -o"
d w o ow
(137)
where
W
cl = work of detergency, dynes/cm
aw'CTo'aow
surface tensions of water and oil, and interfacial
tension between oil and water, dynes/cm, respectively
The presence of surfactants at oil/water interfaces causes reduc-
tion in interfacial tension between oil and water and leads to
lower values of Wd< Also, a high energy barrier must be overcome
for mixed micelles to form and desorb from oil/water interfaces;
therefore, the system must be supplied with additional energy for
complete detergency. When the work of detergency is equal to or
less than the work input into the system, complete dispersion may
occur. If the
be complete.
energy input is less than W,, dispersion will not
It is important to be able to estimate the amount of mixing
energy required to achieve a specific degree of emulsification.
Unfortunately, one of the difficulties in effective dispersant
treatment of oil spills is the inability to estimate the fraction
of energy input available to aid detergency. In the field, the
largest part of the energy introduced into the system is dissipa-
ted into the water column. Inadequate mixing has adverse effects
on chemical dispersion as dispersant can be transported through
the water phase before mixed micelles are formed. Therefore, it
117
-------
is not surprising that greater efficiencies are usually reported
for small scale laboratory tests of the effectiveness of disper-
sants, in which the energy input per unit volume of fluid is
large. It is necessary to allow the oil and dispersant to make
sufficient contact prior to agitating the system.
The rate of input of mechanical energy is important as it
influences the total area of oil/water interfaces available for
the mass transfer processes discussed earlier. Additional oil/
water interfaces are created as the oil layer is physically
sheared into droplets according to the following equation
A = Vow "38)
where
W. = amount of energy required to create the interfaces
Stability of the oil droplets is a function of mechanical energy
input and other factors. If the intensity of agitation is low,
oil droplets that are formed will be coarse and unstable.
Unstable phases will tend to remain dispersed only in the
presence of turbulence. In the absence of turbulence, or after
these phases have migrated to regions of low shear, coalescence
is possible; these droplets may coalesce with the parent slick or
form separate patches.
Fine oil droplets will form if a system is agitated suffi-
ciently; these droplets are stable and resist coalescence.
Weathering processes, turbulent diffusion, waves, currents and
tides, and Brownian diffusion transport oil droplets through the
water column to points far from the source of the spill. The
movement of dispersed oil droplets in water depends on hydro-
static and hydrodynamic forces and the sizes of the droplets.
NUMERICAL ANALYSIS OF DISSOLUTION AND SPREADING EQUATIONS USING
EXPERIMENTAL DATA
The dissolution model was tested with experimental data.
The values of four parameters in the segmented model are unknown,
and must be estimated for any oil. These parameters are GS, tm>
K., and K£. For each oil tested, a value for the joint point,
t , was estimated from the experimental data. Since t corres-
ponds to the time when oil concentration is maximum, the data in
columns 2 (Tables 6 and 7) served as input values for t during
the regression analysis. Similarly, C$ corresponds to oil concen-
trations at saturation. The input values for this parameter are
listed in Table 8. The initial estimates for K. and Kr were unity,
118
-------
The equations of spreading are functions of the volume of
oil, the duration of the spill, physical properties of oil and
water phases, and time of spreading. In each equation, only the
value of one empirical constant must be determined from experi-
mental data. Iteration was started with unity as the initial
estimate of the constants in the four spreading equations.
Least-squares regression analysis of the dissolution func-
tions and spreading equations was performed on an IBM 360/370
computer using the SAS (Statistical Analysis System). SAS is a
commercial statistical package that is widely used and highly
documented (SAS Institute, 1979). Minimum programming effort is
required and the package has been tested adequately. The
Marquardt method was used to estimate unknown parameters. This
method is available as an option in the nonlinear parameter esti-
mation program (NLIN) of the SAS package. NLIN regresses the
residuals on the partial derivatives of the functions with respect
to the parameters until the iterations converge. The Marquardt
procedure is an extension of the Gauss-Newton and Steepest Descent
methods and can converge with relatively poor starting guesses
for the unknown parameters (Marquardt, 1963). The least squares
objective function which is minimized is the sum of the squares
of the residuals between the predicted values and experimental
data. The built-in convergence criterion in the NLIN program has
Q
a value of 10 .
The listings of sample computer programs, used to run the
regression analyses and estimate unknown parameters in the disso-
lution and spreading models are given in Tables Fl and F2 of
Appendix F.
119
-------
SECTION 9
RESULTS AND DISCUSSION
DISSOLUTION
The rates of dissolution in water of crude oils and
processed petroleum have been investigated in open static tests.
The tests correspond to the worst condition of an oil spill, e.g.
oil completely covering the surface of a small lake. Oils were
equilibrated with water at 25C for periods of 2 to 3 weeks and
oil concentrations in solution were measured routinely by infra-
red spectrophotometry.
Tap Water Studies
In studies using tap water as the test fluid, 9 crude oils,
2 processed oils and an oil mixture containing 8% crude and the
remaining processed oil were investigated. Experimental data
for oil concentrations and equilibration time have been presented
in Appendix B.
The results of solubility measurements suggest the old adage
"that oil does not mix with water" is false. The concentration
profiles for all oils increased gradually during the first few
days of equilibrium, reached maximum levels within 9 days and
decreased afterwards. Maximum concentration levels were not
achieved after equivalent periods of equilibration, but all oil
concentrations stabilized after approximately 12 days of equili-
bration. Despite variations in maximum solubility levels,
experimental data for all oils showed similar trends, except
Suniland crude which reached maximum solubility in water in the
first day. Since samples were taken daily, it is not known
whether this crude actually achieved maximum solubility earlier.
The range of oil concentrations varied from zero to a little
less than 200 ppm. Generally, the processed oils, i.e., #2 and
#6 fuel oils, were less soluble than the crude oils. The rate
and extent of solution of an oil depends on the chemical composi-
tion of the oil. Crude oils from Brass River and Arzew exhibited
similar solubility behavior that differed slightly from the other
crude oils. The rates of dissolution of these two crudes were
stable for the first few days, then accelerated, until maximum
120
-------
solubility levels were reached. Ironically, these two crudes are
from the same geographical area (Algeria). Table 6 shows the
maximum concentrations in solution and the time these maximum
concentrations were reached.
Salt Water Studies
The rates of dissolution of 5 crude oils and one refinery
product were investigated in aqueous solutions containing 3.5%
sea salt. The experimental data are presented in Appendix C.
In general, solubility levels in salt solutions are lower
than those in tap water. Thus, the rates of dissolution are
lower. Longer equilibration periods were also required to
achieve maximum concentrations in salt solution. The only excep-
tion is Brass River crude. Table 7 shows the maximum concentra-
tion levels and required equilibration periods. The last column
shows the percent difference when maximum concentrations in tap
and salt water are compared. The solubilities of #2 fuel oil in
tap and salt water are comparable. Decreases of up to 99%
occurred for Alaska and Brass River crudes. These results indi-
cate that hydrocarbon levels in seawater will be much lower than
in fresh water systems.
Oil concentration levels in salt water represent the levels
that would exist in marine waters with equivalent salt content.
The effect of sea salts is to decrease the solubility of oils by
"salting-out" hydrocarbons. In marine environments, this reduc-
tion in solubility may be offset by the presence of dissolved
organic matter in sea water. These materials can solubilize oils
and increase the solubilities of oils in salt water beyond the
limits of solubilities in tap water.
Saturation Studies
The concentration of oil in water at saturation was deter-
mined for each oil. These tests were conducted in closed vessels
and the oil/water systems were allowed to equilibrate for 3
months.
Oil concentrations at "saturation" are given in Table 8.
For any oil, the concentration at saturation is significantly
greater than the maximum solubility in open water (Table 6). It
is necessary to caution that these values may not be true satura-
tion concentrations; however, they should be close due to the
prolonged equilibration of the oil and water systems in closed
vessels.
121
-------
TABLE 6
Maximum Solubilities of Oils in Tap Water
and Times to Attainment
Oil
Nigerian Crude
Lagunillas Crude
La Rosa Crude
#2 Fuel
#6 Fuel
Sum' land Crude
Alaska Crude
8% Crude
Iranian Crude
Sahara Crude
Brass River Crude
Arzew Crude
Time (t )
(days)
6
9
5
7
2
1
3
2
4
2
8
8
Maximum Solubility
(ppm)
4.5
2.5
3.4
1 .7
0.9
61 .2
152.1
78.6
15.0
24.0
176.0
196.0
Comparison of Predictions by the Dissolution Model and Experimen-
tal Data
During regression, the values of the parameters in the
dissolution equations are adjusted in the iterative process to
give final values that best fit the equations to experimental
data. Convergence was achieved in all numerical analyses. Table
9 summarizes the final values of the four parameters for all the
oils. Statistical tests of the significance of the values of K,
and K,. showed that these parameters are significantly different
2
from zero. The correlation coefficients, R , are close to unity,
indicating that there is good correlation between the model and
experimental data. Correlation coefficients were less than 0.9
in only two cases: Brass River and Arzew crudes.
The final values of the two mass transfer coefficients, K.
and Kr, vary for different oils but all values are smaller than
unity. Variations in the final values of the mass transfer
coefficients are caused by the different characteristics of the
122
-------
TABLE 7
Maximum Solubilities of Oils in Salt Water
and Times to Attainment
Oil
Nigerian
La Rosa, Venezuela
North Slope, Alaska
Brass River, Algeria
Iranian
#2 Fuel
Time (tj
(days)
14*
12-13
4
4
7
5-6
Maximum
Solubility
(ppm)
1 .5
2.5
1 .1
1 .4
1 .5
1 .5
Decrease "*"
(%}
67
26
99
99
90
12
* End of Equilibration
+ Based on Maximum Solubility in Tap Water
soluble and volatile components in the oils. In tests using tap
water, K£ was always larger than K.; but the reverse is true in
tests using salt water. Several factors that were not investiga-
ted influence KE and K,. They are the temperature of the bulk
oil and water phase, salinity, and pH. In the field, KE and K,
are functions of several other factors, such as the wind velocity
profile above the oil layer, turbulence in the water phase, and
water quality. The final values of C , in six out of twelve oils,
converged to the experimental "saturation" concentrations
tabulated in Table 8. The differences were small in those cases
where the values did not agree. The values of C$ in tests
conducted in salt water are smaller than those in tap water and
reflect the lower solubilities of oils in salt water. The final
values of tm correspond to the times required for the oils to
reach maximum solubility in the specific medium. These values
are comparable to those given in Tables 6 and 7.
Comparison of concentration-time profiles, using the disso-
lution model and experimental data, can be made by considering
Figures 15 to 20. Experimental data and model profiles are shown
in Figure 15 for #2 and #6 fuel oils, and crudes from Nigeria,
Lagunillas and La Rosa. The dissolution model predicts experi-
mental data fairly accurately in all cases. The profiles for
Suniland, Sahara and Iranian crudes, and the oil mixture contain-
123
-------
TABLE 8
Oil Concentrations at "Saturation"
Oil Concentration (CV)
(ppm)
Nigerian Crude 29.9
LagunillasCrude 13.7
La Rosa Crude 17.4
#2 Fuel 9'3
#6 Fuel 21'12
Suniland Crude 102.6
Alaska Crude 235.8
8% Crude 120'9
Iranian Crude 23.3
Sahara Crude 35.6
Brass River Crude 270.7
Arzew Crude 306.0
ing 8% crude are displayed in Figure 16. The results show that
the predictions by the model are comparable with experimental
data for Sahara and 8% crudes, but the dissolution model does not
fit the data as well for crudes from Iran and Suniland. Dispari-
ties occur during the later stages of equilibration. Figure 17
compares the results of the model and data for Alaska, Brass
River, and Arzew crudes. The fit between the data and the model
is good for Alaska crude; it is poor for Brass River and Arzew
crudes, because of the significantly different behavior of these
two crudes.
Profiles of the dissolution model and experimental data,
from solubility studies of #2 fuel oil and Iranian and Brass
River crudes in salt water, are displayed in Figure 18. Similar
graphs are shown in Figure 19 for Nigerian, Alaskan and La Rosa
crudes. The model predicts experimental data accurately in all
cases. Figure 20 shows the data and model for Nigerian crude
using the results of tests in tap and salt water. Despite
slightly different behaviors of the crude,in the two test liquids,
the data and models indicate that the final concentrations are
similar.
124
-------
TABLE 9
Comparison of Final Values of Parameters
from Fitting Dissolution Model to Experimental Data
Parameters
Oil
A. Tap Water
Nigerian Crude
La Rosa Crude
Lagunil las Crude
#2 Fuel
#6 Fuel
Iranian Crude
Sahara Crude
Suniland Crude
8% Crude
Alaska Crude
Brass River Crude
Arzew Crude
B. Salt Water
#2 Fuel
Iranian Crude
Brass River Crude
La Rosa Crude
Alaska Crude
Nigerian Crude
KL
(day"1)
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
055
040
025
06
012
42
60
90
71
20
07
07
330
220
299
054
060
120
KE
(day'1)
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0801
090
080
no
098
300
260
951
163
28
601
540
060
01
025
044
06
05
*m
(day)
3
5
8
7
4
4
2
1
1 .5
3
9
8
5
6
3.8
11
3
12
Cs
(ppm)
29.
17.
13.
5.
15.
17.
35.
100.
144.
290.
270.
306.
2.
2.
2.
6.
5.
2.
9
4
7
0
0
0
6
0
6
0
0
0
0
0
0
0
0
0
R2
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
993
989
994
980
948
960
990
922
988
968
860
860
992
996
997
980
962
978
125
-------
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-------
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T3 S-
00
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(Wdd) NOIlVdiN33N03 110
130
-------
s-
i-
Q.r
to
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-------
The rate of dissolution in water of some crude oils and
petroleum-based products has been investigated in open static
tests. The tests correspond to an unlikely worse case of an oil
spill, such that the oil completely covers the water surface.
The experimental data suggests that the dissolution process can
be divided into two phases. Initially, soluble and volatile
organics diffuse into the underlying water; later, some volatile
materials evaporate from solution. Thus, the dissolution process
is influenced by evaporation in the final stages of equilibration.
The amounts of these hydrocarbon species vary according to the
composition of the oil, hence, variations exist in maximum solu-
bilities, times to attainment, and dissolution rates. A segmen-
ted dissolution model has been applied successfully to correlate
the experimental data of the oils. Although the goodness-of-fit
of the dissolution model to the experimental data varies, a model
based on the two processes has been shown to be capable of
reasonable predictions of the solubilities of different oils, as
a function of time, in water below a surface slick.
In general, the results of solubility measurements indicate
that these oils exhibit low solubilities in water. The processed
oils, #2 and #6 fuels, are less soluble than the crude oils. The
solubility behavior of oils depends on their chemical composition.
For fuel oils, the extent of refinery processing and additives
are important factors affecting solubility. The data show that
maximum concentrations were not achieved by all the oils after
equivalent periods of contact. In spite of variations in maximum
solubility levels and times to attainment, the experimental data
show similar trends.
The results of the dissolution studies give probable oil
concentration levels in the water immediately under a surface
slick, when these oils are spilled on water. Oil concentrations
are low and may not be hazardous to marine organisms when exposure
is limited. Concentration levels may be dangerous when oils
attain maximum solubilities in water. A class of marine organisms
which has adapted to the sea surface environment is neuston. The
solubility limits established for these oils are important to
bioassay studies of the toxicity of oils to neuston. Oil concen-
trations will be lower in sea water. Also, water movements at sea
will continuously decrease oil concentration by dilution. In
contrast, the dissolved organic matter in the surface microlayers
of the sea will increase oil concentration by solubilization.
SPREADING
The rates of spreading of 12 oils were investigated. The
experimental runs consisted of spilling specific volumes of oil
onto calm tap water. Four different volumes of each oil were
spilled at different flow rates. The effects on spreading of
several parameters, such as the volume of oil spilled, duration
132
-------
of spill and physical properties of the oils, i.e. viscosity,
density, surface tension and interfacial tension between oil and
water, were investigated. These parameters are important in
determining the increase with time of the area of an oil slick
spreading on calm water. Water temperature is a factor in the
rates of spreading of oils but it was not investigated in this
study because the effect of temperature should be determined by
its influence on the properties of the oil and water phases. The
effect of temperature will be proportional to changes in the
values of the physical properties of the two phases. The data
generated in each experimental run include areal extents of the
oil as a function of the time of spreading. Photographic tech-
niques were used and the areas covered by the oils were measured
from photographic images.
All the oils did not spread uniformly and several slicks
developed regions with varying thicknesses of oil. In some
cases, subjective judgment was used to determine the areal extent
of a slick if its profile was not properly defined in the photo-
graphic prints. Spreading patterns vary for different oils and
there is no preference for elliptic or circular geometries. The
initial configurations of a slick during the initiation of
spreading and the final profile at the end of an experiment are
influenced by the rate of oil discharge, the duration of the
spill, thermal convection currents in the water column, proper-
ties of the oil and spreading forces. The configurations and
areas of slicks may vary even when the slicks are formed by the
same oil and under the same conditions.
Spreading equations were derived to correlate experimental
data. The development of these equations parallels Fay's work
and yields four spreading equations: surface-tension/viscous
(STV), surface-tension/inertia (STI), gravity/viscous (6V), and
gravity/inertia (GI). Each spreading equation defines a spread-
ing regime in which only two opposing forces dominate the spreadr
ing behavior of a slick. The equation for each regime is then
derived by equating two forces, one of which accelerates
spreading and the other retarding spreading. The dependent
variable in each equation is the area covered by the spreading
slick and the independent variables include the properties of the
oil and water phases. This information is usually available at
sites of spills or can be determined experimentally. Each
equation contains an empirical constant.
Experimental data from spreading studies are presented in
Appendix D. The spreading equations were fitted to experimental
data to estimate the values of the empirical coefficients. The
final values of the coefficients and the regression statistics
are summarized in Tables 10 to 21. The correlation coefficients
indicate the models are capable of fitting experimental data with
varying accuracies. In general, the order of the goodness-of-fit
of the spreading equations from the best to the worst is
133
-------
GV > STV > 61 > STI. As expected the fit with the surface-
tension/inertia model was the worst; this model predicts that the
area of spreading is independent of the volume of oil spilled.
Thus, this equation is not acceptable as a model for predicting
variation of the area covered by an oil slick with time.
TABLE 10
Summary of Coefficients of Spreading Equations
for Arzew Crude
Equation
1. Surface-Tension/Viscous
2. Surface-Tension/Inertia
3. Gravity/ Viscous
4. Gravity/Inertia
Vol .
25
50
75
100
25
50
75
100
25
50
75
100
25
50
75
100
K
15.695
12.356
11 .400
10.289
0.0392
0.0466
0.0549
0.0603
25.922
18.274
15.908
13.800
3.208
2.541
2.342
2.133
R2
0.966
0.9745
0.9769
0.9580
0.5550
0.5776
0.6040
0.579
0.9895
0.9937
0.9935
0.9720
0.8514
0.8695
0.8804
0.8585
134
-------
TABLE 11
Summary of Coefficients of Spreading Equations
for Brass River Crude
Equation
1. Surface-Tension/Viscous
2. Surface-Tension/Inertia
3. Gravity-Viscous
4. Gravi ty/ Inertia
Vol.
25
50
75
100
25
50
75
100
25
50
75
100
25
50
75
100
K
7.869
4.462
4.533
3.747
0.0183
0.0132
0.0169
0.0189
13.559
7.136
6.901
5.289
1 .705
0.905
0.909
0.799
R2
0.9757
0.9636
0.9479
0.9860
0.7792
0.5845
0.6096
0.7843
0.9528
0.9847
0.9656
0.9739
0.9718
0.8589
0.8547
0.9716
135
-------
TABLE 12
Summary of Coefficients of Spreading Equations
for Alaskan Crude
Equation
1. Surface-Tension/Viscous
2. Surface-Tension/Inertia
3. Gravity/Viscous
4. Gravity/ Inertia
Vol .
25
50
75
100
25
50
75
100
25
50
75
100
25
50
75
100
K
59.989
49.778
28.064
28.304
0.0772
0.0908
0.0664
0.0775
68.238
52.281
27.060
26.332
5.175
4.154
2.402
2.396
R2
0.9953
0.9785
0.9921
0.9847
0.6791
0.6563
0.6582
0.6426
0.9986
0.9901
0.9987
0.9955
0.9278
0.8961
0.9176
0.9024
136
-------
TABLE 13
Summary of Coefficients of Spreading Equations
for Iranian Crude
Equation
1. Surface-Tension/Viscous
2. Surface-Tension/Inertia
3. Gravity/Viscous
4. Gravity/Inertia
Vol .
25
50
75
TOO
25
50
75
100
25
50
75
100
25
50
75
100
K
34.650
24.920
20.314
18.990
0.0573
0.0594
0.0609
0.0670
47.472
30.818
23.619
21 .139
4.399
3.126
2.544
2.373
R2
0.9853
0.7905
0.9676
0.9621
0.6355
0.5918
0.5906
0.5871
0.9966
0.9898
0.9873
0.9817
0.9003
0.8684
0.8648
0.8584
137
-------
TABLE 14
Summary of Coefficients of Spreading Equations
for Sahara Crude
Equation
1. Surface-Tension/Viscous
2. Surface-Tension/Inertia
3. Gravity/Viscous
4. Gravity/Inertia
Vol .
25
50
75
TOO
25
50
75
100
25
50
75
100
25
50
75
100
K
41 .544
28.351
17.955
20.108
0.0616
0.0618
0.0511
0.0642
67.098
41 .554
24.490
26.951
6.555
4.415
2.845
3.056
R2
0.9665
0.9415
0.9739
0.9044
0.5564
0.5437
0.5973
0.5526
0.9905
0.9666
0.9916
0.9226
0.8525
0.8242
0.8746
0.7904
138
-------
TABLE 15
Summary of Coefficients of Spreading Equations
for Nigerian Crude
Equation
1. Surface-Tension/Viscous
2. Surface-Tension/Inertia
3. Gravity/Viscous
4. Gravity/Inertia
Vol .
25
50
75
100
25
50
75
100
25
50
75
100
25
50
75
100
K
10.300
8.342
6.459
7.486
0.0182
0.0193
0.0198
0.0280
15.232
11 .492
8.287
9.429
1 .584
1 .207
0.954
1 .094
R2
0.9674
0.9920
0.9974
0.9849
0.8198
0.6820
0.7542
0.9005
0.9324
0.9987
0.9907
0.9727
0.9868
0.9242
0.9649
0.9944
c
139
-------
TABLE 17
Summary of Coefficients of Spreading Equations
for #6 Fuel Oil
Equation
1. Surface-Tension/Viscous
2. Surface-Tension/Inertia
3. Gravity/ Vis co us
4. Gravity/ Inertia
Vol .
25
50
75
100
25
50
75
100
25
50
75
100
25
50
75
100
K
5.552
6.440
5.219
6.329
0.0021
0.0041
0.0045
0.0059
4.709
4.809
3.607
4.288
0.182
0.220
0.182
0.213
R2
0.9846
0.9425
0.8590
0.9448
0.7443
0.9012
0.9658
0.8994
0.9680
0.8960
0.7998
0.9090
0.9598
0.9977
0.9595
0.9867
141
-------
TABLE 18
Summary of Coefficients of Spreading Equations
for 8% Crude
Equation
1. Surface-Tension/Viscous
2. Surface-Tension/Inertia
3. Gravity/ Viscous
4. Gravity/ Inertia
Vol .
25
50
75
100
25
50
75
100
25
50
75
100
25
50
75
100
K
30.991
27.293
25.342
25.264
0.0488
0.0567
0.0644
0.0730
39.925
32.973
28.636
27.895
3.657
3.024
2.791
2.700
R2
0.9141
0.9917
0.9987
0.9907
0.9111
0.8410
0.7748
0.7715
0.8634
0.9780
0.9918
0.9905
0.9878
0.9887
0.9700
0.9433
142
-------
TABLE 19
Summary of Coefficients of Spreading Equations
for Lagunillas Crude
Equation
1. Surface-Tension/Viscous
2. Surface-Tension/Inertia
3. Gravity/Viscous
4. Gravity/ Inerti a
Vol .
25
50
75
100
. 25
50
75
TOO
25
50
75
100
25
50
75
100
K
21 .614
13.338
35.032
35.032
0.0112
0.0102
0.0351
0.0351
19.840
11 .085
26.719
26.719
0.953
0.587
1 .462
1 .462
R2
0.8623
0.8745
0.9761
0.9761
0.9555
0.9549
0.8423
0.8423
0.7976
0.8149
0.9470
0.9470
0.9696
0.9756
0.9949
0.9949
143
-------
TABLE 20
Summary of Coefficients of Spreading Equations
for La Rosa Crude
Equation
1. Surface-Tension/Viscous
2. Surface-Tension/Inertia
3. Gravi ty/Vi scous
4. Gravity/Inertia
Vol .
25
50
75
100
25
50
75
100
25
50
75
100
25
50
75
100
K
61 .194
56.427
57.586
53.202
0.0798
0.1001
0.1327
0.1378
60.062
51 .190
48.649
44.097
4.261
3.739
3.869
3.442
R2
0.9835
0.9754
0.9839
0.9465
0.7458
0.6488
0.6840
0.6597
0.9662
0.9864
0.9884
0.9540
0.9636
0.8920
0.9163
0.8620
144
-------
TABLE 21
Summary of Coefficients of Spreading Equations
for Suniland Crude
Equation
1. Surface-Tension/Viscous
2. Surface-Tension/Inertia
3. Gravity/Viscous
4. Gravity/Inertia
Vol .
25
50
75
100
25
50
75
100
25
50
75
100
25
50
75
100
K
52.768
30.937
27.396
24.414
0.0701
0.0673
0.0717
0.0751
73.803
38.545
32.233
27.386
6.179
3.742
3.254
2.908
R2
0.9516
0.9958
0.9818
0.9852
0.5720
0.7414
0.6645
0.6569
0.9726
0.9918
0.9896
0.9999
0.8437
0.9527
0.9060
0.9083
145
-------
The values of the coefficients differ for each oil and
spreading regime. Within each spreading regime slight to large
differences can be seen in the values of the coefficients for the
four oil volumes spilled. These differences are caused by experi-
mental error due to variations in thermal convection currents in
the water and, perhaps, air motions which are unavoidable even in
the laboratory environment. It is probable that for each spread-
ing regime, the mean of the four coefficients is a more accurate
value for the empirical constant.
The experimental data and predictions by the four spreading
equations are given in Figures 21 to 32 for #2 fuel oil, Nigerian
and Alaskan crudes. The data and model profiles show that oil
slicks spread faster initially and spread more slowly as the
slicks age.
The effects of oil properties, i.e. density, viscosity,
surface tension and interfacial tension between oil and water can
be judged from the spreading equations. Increases in density and
viscosity have negative effects on the spreading behavior of oils
The net effect of surface tension varies according to whether it
is positive (accelerates spreading) or negative (retards spread-
ing). Data for #6 fuel oil and Lagunillas crude show that
viscous oils spread more slowly than less viscous oils. As the
ratio of the density of oil-to-water decreases, spreading rate
increases. Since spreading of oils on water persists longer than
the duration of the spill, the initial effect of the rate of oil
discharge is cancelled by the total volume of the oil spilled.
Therefore, the rate of discharge of oil is important in the early
stages of a spill and in situations where the oil is discharged
continuously, e.g., oil seeps.
The mathematical models used here are valid only for spread-
ing on calm seas. The results of the experiments have shown
that, even for this simple situation,oi1s behave differently.
Information on the behavior of a greater variety of oil types is
needed. In the open sea, gross oil transport commences almost
immediately after oil is spilled. The transport processes due to
turbulence created by wind, current, wave and tidal forces will
be superimposed on natural spreading. The rates of these
processes are at present difficult to quantify, however, these
modes of transport are of importance in evaluating the potential
damage to marine ecosystems by oil slicks.
CHEMICAL DISPERSION
When oil slicks are agitated by turbulent forces at sea,
they break up into small droplets that disperse into the water.
The formation and dispersal of oil droplets can be aided by
application of chemical dispersants to the slick. Thus, infor-
mation on the mechanisms leading to dispersion of droplets is
146
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essential to planning appropriate clean-up operations, using
commercially available dispersants.
This study has identified the principal and secondary mass
transfer processes that are important in chemical dispersion. A
theoretical formulation has been proposed to explain these
mechanisms of chemical dispersion. This theory is based on
detergency and catalysis concepts. Mathematical models were
derived to quantify the principal mechanisms according to the
steps that are rate limiting. The models must be judged on their
merits as they were not verified by experimental data, due to
lack of accurate input data. Because of the variety of commer-
cially available dispersants, knowledge of the mechanisms of
chemical dispersion is essential to establishing a rationale for
dispersant selection. This work has identified these mechanisms.
As this study progressed, the limitations of modeling became
apparent. For example, the chemical structure and the degree of
association or micel1ization of surface-active compounds in
commercial dispersant preparations must be known. This informa-
tion is proprietary. The properties of the surfactants are useful
for determining the rate controlling steps. This study under-
scores the importance of basic data utilizing known surface
active compounds in free form and mixtures of surfactants. The
results of the experimental data from dispersion tests using 5
commercial dispersants and 3 oils are discussed next.
Current practices in chemical dispersion tests report the
effectiveness of chemical dispersants in terms of the percent
dispersion. The percent dispersion is based on the concentration
of oil in solution, following violent agitation of an oil/water/
dispersant system, as a fraction of the concentration of oil that
would result if all the oil were dispersed in the water. This
practice is not followed here because it has little merit and it
does not reflect accurately the efficiency of dispersants. A
brief explanation follows.
Usually, dispersants are formulated in hydrocarbon or
aqueous solvents. Hydrocarbon-base dispersants have some advan-
tages over aqueous-base dispersants. For instance, hydrocarbon
solvents are easily miscible with oil slicks. This may lead to
faster dispersion of oil slicks.
Furthermore, the sources of hydrocarbon in an oil/water/
dispersant system are the slick material and the dispersant.
Thus, a hydrocarbon-base dispersant will contribute a larger
amount of hydrocarbon to the system than an aqueous-base disper-
sant containing the same surface-active compounds. Since
commercial dispersants contain a variety of surface-active com-
pounds and additives with hydrocarbon molecules, the fraction of
hydrocarbons in different dispersants will vary with the structure
of the surface-active compounds (the hydrophobic group), and the
1 59
-------
concentration of surfactant, hydrocarbon solvent and additives.
A water sample from a dispersion test will contain some
hydrocarbon from all the sources. Analytical techniques do not
discriminate between the hydrocarbon fractions contributed by the
hydrocarbon solvent, the hydrophobic group of the dispersant, and
the oil slick. Surely, a hydrocarbon-base dispersant will show
higher oil levels in aqueous solutions even though the efficiency
may be identical to the aqueous-base dispersant containing the
same surface-active compounds and additives. The effect of the
type of solvent on the efficiency of dispersants could be
partially resolved through use of calibration curves based on
oil and dispersant mixtures.
Even when the structure of the surfactant and its concentra-
tion in the dispersant solution are known, it is not easy to
determine the fraction of oil introduced into solution by treating
the surface slick. The possible sinks for surfactants in the
system are a) the bulk oil phase and dispersant solution,
b) adsorption at the oil/water interface, as free or mixed
micelles, and c) the bulk water phase, as unaggregated molecules
or in mixed micelles. It is impossible to determine these con-
centrations separately. Therefore, development of a meaningful
criterion to rank commercial dispersants without information on
the composition of the formulations remains a major task.
The trends in experimental data gathered from the dispersion
of 3 oils with 5 dispersants under different test conditions will
be discussed. Slicks formed by spilling 300 mis of oil were
dispersed with dispersants in 1:1, 5:1 and 10:1 oi1-to-dispersant
ratios. The experimental data have been presented in Appendix E.
Figures 33 to 35 are concentration-time profiles for the disper-
sion of #2 fuel oil with the five products at 1:1, 5:1, and 10:1
oil-to-dispersant ratios, respectively. The maximum oil concen-
tration represents the average oil and dispersant concentration K
in the bulk fluid immediately after agitation was stopped. An
analogy to current practice of using percent efficiency can be
made by normalizing the maximum oil concentration by the oil
concentration that would result if all the oil was completely
dispersed in the volume of the aqueous phase. Therefore, 100%
dispersion corresponds to 425 ppm. The profiles show decreases
in oil concentration with sampling time for all products. The
greatest decrease occurred with product B. Oil concentrations
stabilized after about 2 hours. If all the products are assumed
to contain equal concentrations of the same solvent, the order of
the relative ease of dispersion of #2 fuel oil is given below
0/D Ratio Dispersion of #2 Fuel Oil
1:1 D>B>A>C>E
5:1 D>A>B>C>E
10:1 D>B=A>C>E
160
-------
ro
to
Q
CO
*
«c
to
u
3
-o
o
S-
Q.
r -M
t- 1C
o a:
a> c
3 (O
CM O)
=tt= a.
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c o
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I I
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S- -I-
CO
ro
(U
(Wdd) NOIiVdlN33N03 110
161
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CO
ce
ID
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1C
res
o
c
ro
O
CO
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u
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^ 03
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I 4J
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-------
CO
ID
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^x
UJ
ro
UJ
-O
c
ro
a
CO
10
!->
u
3
T3
O
S_
Q-
r- O
r- re
r- CC
o
(!) ro
3 10
U- S_
0)
CM Q.
=te 10
r-
<4- Q
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O
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ai
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r- O
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i-
en
(Wdd) NOI1VH1N33N03 110
163
-------
This sequence was determined on the basis of stabilized oil
concentration levels in the liquid phase. Product B indicates
that initial dispersion is efficient but, because stable emulsions
are not formed, coalescence occurs readily. Migration of
coalesced droplets to the surface reduces the concentration of oil
in the liquid phase. On the other hand, product D forms fairly
stable emulsions. The rates of dispersion for products C and E
are lower than for product A.
The effect of varying the ratio of oi1-to-dispersant can be
seen in Figures 36 to 40. In general, higher rates of dispersion
occurred as the volume of dispersant added was increased. The
rate of dispersion increased significantly when the volume of
Product A added was increased. Other dispersants were less effec-
tive. Products B and E did not significantly increase rates of
dispersion when the oil-to-dispersant ratio was increased from
10:1 to 5:1. These results seem contrary to some manufacturers
claims that oil slicks can be completely dispersed at oil-to-
dispersant ratios as low as 100:1. Number 2 fuel oil is one of
the easiest oils to disperse, but complete dispersion was not
achieved with the dispersants tested, even when oil-to-dispersant
ratio of 1:1 was used.
The concentration-time profiles displayed in Figures 41 and
42 represent the dispersion of Iranian crude and #6 fuel oil,
respectively. Both oils are more difficult to disperse than #2
fuel oil. The degree of difficulty is reflected in the levels of
oil concentrations that result from the dispersion of the oils
with the 5 products. The concentration levels for each product
are least when #6 fuel oil is dispersed. The behavior of the
products in these tests was similar to their behavior in the
dispersion of #2 fuel oil. Oil concentration decreased with
sampling time. This series of tests was performed at a 5:1 oil-
to-dispersant ratio and the following order indicates relative
dispersion efficiency of the products:
<
I rani an Crude D>B>A>C>E
#6 Fuel Oil D > B > C > A > E
When the relative efficiencies of the products are compared, on
the basis of these dispersion studies with the 3 oils, an impor-
tant conclusion can be drawn: the relative efficiencies of the
products do not depend on the type of oil. This conclusion is
significant, also, as manufacturers tend to classify their
products according to specific oils. It follows that a good
dispersant will be effective in dispersing both "easy" and "tough"
oils.
Product B was investigated in a further series of tests.
Figure 43 shows the experimental data when #2 fuel oil and
Iranian crude were dispersed in calm water. Low levels of oil
164
-------
CO
o:
UJ
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c
o
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concentrations are achieved. In contrast, oil concentrations
shown in Figure 44 are high because agitation was provided
throughout the sampling period. Figures 43 and 44 suggest the
importance of providing mixing to oil/water/dispersant systems,
-to increase rates of dispersion. Higher rates of dispersion
result if the system is agitated continuously. This appears to
be the ideal method to disperse oil slicks. Because of high
costs associated with providing mixing energy continuously to
chemically treated oils, this method of dispersion is impractical
During high sea states, mixing energy can come from gross water
movements.
Finally, Figure 45 describes the dispersion of #2 fuel oil
and Iranian crude in salt water. The behavior in salt water was
similar to that in tap water. Except at high dilution sea salts
may not have a significant effect on rates of chemical dispersion
ofoilslicks.
173
-------
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3 O
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rtJ
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-------
100.0
LU
o
m
cc
o
CO
m
l.R cell: 1 cm
Corr. Coefficient: .9999
50.0 100.0 150.0 200.0 250.0 300.0
OIL CONCENTRATION (PPM)
Figure Al . Calibration Curve for Nigerian Crude
using 1 cm cuvets.
189
-------
100.0
Ifl
L
60.0.
LU
O
DO
cn
o
CO
GO
40.0
20.0
0.21
. 1.R cell: 5 cm
Corr. Coefficient: .9998
_ 1 i
0.0 20.0 40.0 60.0 80.0 100.0
-OIL CONCENTRATION (PPM)
Figure A2. Calibration Curve for Nigerian Crude
using 5 cm cuvets.
190
-------
O
<
00
a:
o
CD
100.0
.0
60.0
40.0
20.0
0.3
l.R cell: 10 cm
Corr. Coefficient: .9995
0.0 10.0 20.0 30.0 40.0 50.0
OIL CONCENTRATION (PPM)
Figure A3. Calibration Curve for Nigerian Crude
using 10 cm cuvets.
191
-------
APPENDIX B
SOLUBILITY DATA IN TAP WATER AT 25C
Time
(Days)
0
1
2
3
4
5
6
7
8
9
10
n
12
13 -
14
15
16
17
18
19
20
21
Oil Concentration (PPM)
Nigerian
0.0
1 .5
3.5
4.3
4.5
3.5
3.2
3.0
2.8
2.4
2.4
2.4
2.2
- 2 . 1
1 .8
1 .6
1 .5
-
1 .5
1 .3
1 .3
1 .2
Iranian
0.0
6.0
9.8
11.6
15.0
10.0
6.8
3.5
2.7
2.7
2.6
2.5
2.3
2.3
2.1
2.1
2.0
-
1 .8
1 .7
1 .5
1 .5
#2 Fuel
0.0
0.7
0.9
1 .0
1.2
1 .3
1 .4
1 .7
1 .5
1 .3
1 .2
1 .0
1 .0
1 .0
0.9
#6 Fuel
0.0
0.3
0.4
0.5
0.6
0.9
0.5
0.4
0.4
0.4
0.4
0.4
0.3
0.3
0.3
La Rosa
0.0
0.8
1 .1
1 .5
2.3
3.4
2.8
2.3
2.4
2.1
2.0
1.9
1 .9
1 .6
1 .5
1 .2
Sahara
0.0
14.0
24.9
20.7
13.4
11 .9
10.8
7.0
3.7
3.1
2.6
2.2
0.9^
0.9^
0.8
192
-------
V..-
APPENDIX B (Continued)
SOLUBILITY DATA IN TAP WATER AT 25C
Time
(Days)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Oil Concentration (PPM)
Laguni 1 1 as
0.0
0.5
0.7
1 .1
1 .2
-
1 .9
1 .9
2.3
2.5
2.2
2.1
1 .9
1 .7
1 .6
1 .5
Suniland
0.0
61 .2
15.2
12.4
8.9
6.9
6.5
6.3
5.4
4.7
4.8
4.2
4.1
4.1
4.2
8% Crude
0.0
73.4
78.6
73.9
47.6
37.3
36.0
32.9
28.4
26.8
26.3
20.6
17.9
13.0
11 .8
Alaska
0.0
59.1
81 .6
152.1
75.4
70.3
60.9
52.6
28.5
20.1
19. 8
18.2
15.4
15.2
13.9
14.6
Brass
0.0
8.2
8.5
11.0
13.3
37.6
91 .5
108.9
176.0
159.1
77.9
52.6
11 .3
5.8
5.3
Arzew
0.0
12.5
13.0
16.0
28.2
58.2
83.4
131 .8
196.0
89.5
30.5
23.5
13.5
13.4
11 .0
193
-------
APPENDIX C
-SOLUBILITY DATA FOR SELECTED OILS IN SALT WATER AT 25C
Time
(Days)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Oil Concentration (PPM)
Nigerian
0.0
0.4
0.6
0.9
0.9
0.9
1 .0
1 .1
1 .2
1.2
-
-
1 .3
1 .3
1 .5
Iranian
0.0
0.6
0.7
1 .0
1 .1
1 .2
1.4
1 .5
1 .4
1 .4
1 .4
1 .4
1 .4
1 .4
1 .3
#2 Fuel
0.0
0.9
1 .0
1.2
1 .4
1 .5
1 .5
1 .4
1 .4
1 .3
1 .2
1 .0
1 .0
1 .0
1 .0
La Rosa
0.0
0.7
1.2
1 .3
1 .4
1 .4
1 .6
1 .7
2.0
2.3
-
-
2.5
2.5
2.4
Alaska
0.0
0.4
0.7
0.8
1 .1
0.6
0.5
0.6
0.5
0.5
0.5
0.5
0.5
0.5
0.5
Brass
0.0
0.7
0.7
1 .2
1 .4
1 .3
1 .3
1 .2
1 .2
1 .2
-
-
1 .1
1 .1
1 .0
194
-------
APPENDIX D
EXPERIMENTAL DATA FOR THE SPREADING OF OIL SLICKS
ON CALM WATER AT 20C
TABLE 01. AREA OF OIL SLICKS FORMED BY ARZEW CRUDE
Time
(mins)
0
2
3
4
5
6.
8
10
15
20
25
30
35
Area (ft2)
25+
1.75*
0
3.89
4.39
4.94
4.96
5.08
5.20
5.22
5.25
5.29
5.32
5.35
5.44
50+
2.00*
0
4.47
4.81
5.14
5.61
5.94
6.08
6.20
6.27
6.33
6.38
6.40
6.46
75+*
3.27
0
4.79
5.27
5.82
6.30
6.80
6.97
7.05
7.20
7.35
7.50
7.65
7.79
100+
6.08
0
4.95
5.38
5.75
6.14
6.61
6.89
7.23
7.48
7.67
7.82
-
7.99
+ Volume of oil spilled, cm
* Duration of spill, min
o
195
-------
TABLE D2. AREA OF OIL SLICKS FORMED BY BRASS RIVER CRUDE
Time
(min)
0
2
3
4
5
6
8
10
15
20
25
30
35
Area (ft2)
25+
2.5*
0
0.16
1 .09
1 .67
1 .92
2.07
2.17
2.31
2.63
2.93
3.27
3.38
3.45
50+
4.55*
0
1 .04
1 .65
2.00
2.05
2.08
2.11
2.13
2.15
2.16
2.22
2.24
2.28
75+
7.00*
0
0.12
1 .85
2.21
2.44
2.74
2.80
2.81
2.82
2.83
2.86
2.87
2.89
100+
4.53*
0
0.07
1 .20
1 .56
1 .76
2.12
2.35
2.56
2.86
2.88
3.08
3.49
3.75
^
+ Volume of oil spilled, cm
* Duration of spill, min
196
-------
TABLE D3. AREA OF OIL SLICKS FORMED BY ALASKA CRUDE
Time
(min)
0
2
3
4
5
6
8
10
15
20
25
30
35
25+
1 .12*
0
4.64
5.22
5.46
5.63
5.73
5.83
6.07
6.69
7.36
7.80
8.20
8.56
Area (ft2)
50+
6.23*
0
4.13
5.20
6.08
7.11
7.30
8.01
8.20
8.77
8.99
9.17
9.33
9.49
75+
2.92*
0
3.74
4.18
4.73
4.92
5.20
5.41
5.90
6.23
6.46
6.69
6.89
7.08
100+
4.15*
0
4.26
4.76
5.39
6.10
6.47
6.64
7.12
7.43
7.62
7.80
7.96
8.10
Volume of oil spilled, cm'
* Duration of spill, min
197
-------
TABLE D4. AREA OF OIL SLICKS FORMED BY IRANIAN CRUDE
Time
(min)
0
2
3
4
5
6
8
10
15
20 ..."...
25
30
35
Area (ft2)
25+
3.00*
0
4.47
4.97
5.25
5.41
5.45
5.60
6.23
6.52
6.71
6.97
7.18
7.36
5°+*
3.20*
0
5.13
5.60
5.97
6.23
6.34
6.46
6.56
6.71
6.91
7.20
7.35
7.49
75 +
3.40*
0
5.17
6.16
6.29
6.34
6.39
6.45
6.56
6.93
7.19
7.43
7.53
7.66
100+
3.67*
0
6.22
6.64
6.70
6.99
7.08
7.13
7.33
7.67
7.84
8.05
8.28
8.48
+ Volume of oil spilled, cnT
* Duration of spill, min
198
-------
TABLE D5. AREA OF OIL SLICKS FORMED BY SAHARA CRUDE
Time
(min)
0
2
3
4
5
6
8
10
15
20
25
30
35
Area (ft2)
25+
1 .55*
0
8.58
9.03
9.45
9.94
10.32
10.56
10.77
10.84
10.86
10.90
10.97
11 .06
50+
4.00*
0
9.33
9.87
9.99
10.11
10.19
10.36
10.58
10.80
10.92
10.97
11 .01
11 .03
75+
3.12*
0
6.49
6.70
7.49
7.61
7.98
8.22
8.37
8.77
8.94
9.12
9.28
9.45
100+
7.52*
0
9.14
9.43
10.21
10.48
10.66
11 .12
11.15
11 .20
11 .29
11 .35
11 .46
11 .54
4.
Volume of oil spilled, cm'
* Duration of spill, min
199
-------
TABLE D6. AREA OF OIL SLICKS FORMED BY #2 FUEL
Time
( m i n )
0
2
3
4
5
6
8
10
15
. 20
25
30
35
Area (ft2)
25+
1.83*
0
4.08
5.23
5.92
6.24
6.69
6.88
6.96
7.09
7.21
7.32
7.45
7.57
50+
3.70*
0
2.87
3.86
4.64
5.34
6.02
6.44
6.59
7.12
7.40
7.85
8.32
8.74
75+
6.73*
0
3.69
5.32
6.20
6.57
7.10
7.40
8.03
8.58
8.97
9.28
9.52
9.75
100*
7.22*
0
4.81
7.34
8.05
8.78
9.32
9.54
9.82
10.58
10.62
10.90
11 .14
11 .33
+ 3
Volume of oil spilled, cm
. * Duration of spill, min
200
-------
TABLE D7. AREA OF OIL SLICKS FORMED BY NIGERIAN CRUDE
Time
(min)
0
2
3
4
5
6
8
10
15
20
25 ' ~"
30
35
Area (ft2)
25+
1 .88*
0
0.47
0.73
1 .10
1 .53
1 .68
1 .83
2.07
2.48
2.77
2.99
3.12
3.23
50+
4.88*
0
1 .19
1 .64
1 .99
2.16
2.37
2.57
2.66
2.77
2.87
3.11
3.17
3.19
75+
4.63*
0
0.70
1.18
1 .68
1 .80
2.02
2.44
2.55
2.80
3.04
3.19
3.30
3.39
100+
9.88*
0
0.45
1.05
1 .31
1 .64
1 .97
2.26
2.64
3.34
4.00
4.57
5.03
5.40
Volume of oil spilled, cm
* Duration of spill, min
201
-------
TABLE D8. AREA OF OIL SLICKS FORMED BY #6 FUEL
Time
( m i n )
0
2
3
4
5
6
8
10
15
20
2:5
30
35
Area (ft2)
25+
1 .50*
0
0.04
0.10
0.13
0.15
0.16
0.17
0.18
0.19
0.20
0.22
0.23
0.26
50+
1 .88*
0
0.07
0.14
0.15
0.17
0.18
0.20
0.26
0.32
0.38
0.43
0.49
0.55
75+
2.00*
0
0.08
0.09
0.12
0.14
0.16
0.19
0.20
0.27
0.34
0.43
0.55
0.72
100+
3.23*
0
0.13
0.22
0.24
0.27
0.30
0.32
0.35
0.40
0.47
0.57
0.70
0.88
+ 3
Volume of oil spilled, cm
* Duration of spill, min
202
-------
TABLE D9. AREA OF OIL SLICKS FORMED BY LAGUNILLAS CRUDE
Time)
( mi n )
0
2
3
4
5
6
8
10
15
20 :
25
30
35
Area (ft2)
25 +
1 .57*
0
0.14
0.19
0.25
0.31
0.35
0.42
0.57
0.94
1 .17
1 .36
1 .51
1 .63
1
50+
2.30*
0
0.13
0.19
0.25
0.29
0.37
0.40
0.53
0.83
1 .05
1 .23
1 .37
1 .50
75+
3.47*
0
0.35
0.65
0.91
1 .13
1 .34
1 .48
1 .79
2.51
2.97
3.33
3.60
3.86
100+
3.30+
0
0.68
1 .24
1 .51
1 .88
2.14
2.50
2.85
3.24
3.74
4.11
4.42
4.72
Volume of oil spilled, cm
* Duration of spill, min
203
-------
TABLE DID. AREA OF OIL SLICKS FORMED BY 8% CRUDE
Time
(min )
0
2
3
4
5
6
8
10
15
20
25 ''"~:~K:
30
35
Area (ft2)
25+
3.0*
0
0.65
1.07
1 .16
1 .67
2.33
2.75
3.49
4.87
5.57
6.31
6.75
7.08
50+
6.57*
0
1 .15
2.08
2.76
3.11
3.81
4.05
4.53
5.76
6.76
7.13
7.46
7.98
75 +
5.52*
0
1 .95
2.95
3.77
4.34
4.84
5.50
6.09
7.14
7.61
7.99
8.30
8.59
100+
8.7*
0
2.58
3.76
4.70
5.42
5.65
5.98
6.86
7.57
8.26
8.90
9.49
10.06
+ Volume of oil spilled, cm
* Duration of spill, min
204
-------
TABLE Dll. AREA OF OIL SLICKS FORMED BY LA ROSA CRUDE
Time
( m i n )
0
2
3
4
5
6
8
10
15
20
25
30
35
Area (ft2)
25 +
2.7*
0
1 .47
2.15
2.91
3.59
4.15
4.88
5.69
5.95
6.35
6.53
6.56
6.70
50+
5.33*
0
4.52
5.17
5.68
6.03
6.31
6.51
6.90
7.47
7.50
7.82
8.11
8.43
75+
4.57*
0
6.13
6.77
7.11
7.24
7.49
7.84
7.98
9.84
10.09
10.53
11 .09
11 .25
100+
8.7*
0
6.51
7.17
7.80
8.00
8.34
8.39
9.09
10.21
10.52
10.90
11 .42
11 .48
Volume of oil spilled, cm
* Duration of spill, min
205
-------
TABLE D12. AREA OF OIL SLICKS FORMED BY SUNILAND CRUDE
Time
( m i n )
0
2
3
4
5
6
8
10
15
20
.... _;..
25
30
35
Area (ft2)
25+*
4.07*
0
7.13
7.29
7.39
7.48
7.69
7.95
8.11
8.31
8.51
8.70
8.79
8.97
s°:
5.0
0
3.19
4.54
4.66
5.07
5.51
5.87
6.57
7.44
8.44
8.90
8.93
9.05
75+
5.0*
0
5.12
5.69
6.09
6.37
6.75
7.26
7.90
8.28
8.72
9.06
9.31
9.46
100+
4.4*
0
5.26
5.91
6.43
6.77
7.15
7.68
8.35
9.00
9.42
9.58
9.63
9.70
+ 3
Volume of oil spilled, cm
* Duration of spill, min
206
-------
APPENDIX E
DATA FOR THE DISPERSION OF OILS WITH OIL DISPERSANTS
St.-''
TABLE El. DISPERSION OF #2 FUEL WITH
SELECTION OIL DISPERSANTS (0/D 1:1)
Sampl ing
Time
(Hours)
0.0
0.25
0.50
0.75
1 .0
1 .5
2.0
3.0
4.0
Concentration of Organics (PPM)
A
0.0
74.8
54.1
39.5
31 .9
30.8
24.6
24.1
19.8
B
0.0
377.4
225.1
138.1
108.2
68.1
57.6
57.2
50.3
C
0.0
20.1
19.5
19.1
18.6
17.3
16.5
16.1
15.3
D
0.0
165.1
163.3
160.4
158.1
153.4
145.2
138.8
131 .6
E
0.0
18.8
18.7
14.8
9.7
9.4
6.4
6.2
6.1
207
-------
TABLE E2. DISPERSION OF #2 FUEL OIL WITH SELECTED
OIL DISPERSANTS (0/D 5:1)
Sampl ing
Time
(Hours)
0.0
0.25
0.50
0.75
1 .0
1 .5
2.0
3 . Q _
4.0
Concentration of Organics (PPM)
A
0.0
47.4
34.0
22.5
20.4
17.7
15.7
14.7
12.8
B
0.0
82.1
44.5
28.2
21 .7
20.1
14.5
10.7
6.9
C
0.0
16.2
10.3
9.1
8.5
7.7
7.3
7.3
7.0
D
0.0
75.7
69.4
63.1
57.5
46.5
45.9
45.1
43.0
E
0.0
5.9
3.9
2.5
1 .6
1 .6
0.7
0.6
0.5
208
-------
TABLE E3. DISPERSION OF #2 FUEL OIL WITH SELECTED
DISPERSANTS (0/D 10:1)
Sampl ing
Time
(Hours)
0.0
0.25
0.50
0.75
1 .0
1 .5
..2.0;
3.0 :;::
4.0
Concentration of Organics (PPM)
A
0.0
25.0
14.4
9.9
8.5
6.0
6.0
6.0
6.0
B
0.0
36.7
24.5
16.4
10.2
9.0
6.8
6.2
5.8
C
0.0
6.7
5.6
4.8
4.5
4.1
3.8
3.8
2.9
D
0.0
89.4
60.1
43.3
32.7
32.0
31 .8
26.6
26.3
E
0.0
2.5
2.3
1 .4
1 .3
0.8
0.8
0.8
0.8
209
-------
TABLE E4. DISPERSION OF IRANIAN CRUDE OIL WITH
SELECTED DISPERSANTS (0/D 5:1)
Sam pi ing
Time
(Hours)
0.0
0.25
0.50
0.75
1.0
1 .5
2.0
,3.0 _
4.0 '----
A
0.0
12.8
9.1
7.6
7.3
7.2
6.4
6.3
5.9
Concentration
B
0.0
71 .9
40.1
26.0
21 .9
20.2
19.6
9.3
8.5
of Organi
C
0.0
6.5
6.2
5.4
5.4
5.2
4.5
4.3
3.4
cs (PPM)
D
0.0
37.3
34.0
33.8
33.1
32.3
32.1
29.6
29.9
E
0.0
0.5
0.3
0.3
0.2
0.2
0.2
0.2 .
0.1
210
-------
TABLE E5. DISPERSION OF #6 FUEL OIL WITH SELECTED
DISPERSANTS (0/D 5:1)
Sampl ing
Time
(Hours)
0
0
0
0
1
1
2
3
4
.0
.25
.50
.75
.0
.5
.0
.0^:
.0
0
1
1
1
1
1
1
1
1
A
.0
.7
.6
.5
.5
.4
.4
.3
.2
Concentrate
B
0.
35.
32.
21 .
16.
16.
12.
9.
7.
0
0
7
7
9
7
5
6
9
ion of Organics (PPM]
C D
0.
5.
3.
3.
3.
3.
2.
2.
1 .
0
8
6
6
1
1
4
0
7
0.
24.
18.
17.
16.
14.
12.
11 .
10.
0
9
4
8
5
3
2
8
6
I
E
0.
0.
0.
0.
0.
0.
0.
0.
0.
0
4
4
4
3
3
2
2
2
211
-------
TABLE E6. DISPERSION OF #2 FUEL AND IRANIAN CRUDE
OIL WITH PRODUCT B (SALT WATER, 0/D 5:1)
Sampling Time
(Hours)
0.0
0.25
0.50
0.75
1 .0
1 .5
2.0
~3.0^
4.0
Concentration of Organics (PPM)
#2 Fuel Oil
0.0
28.6
23.0
15.7
12.9
11 .8
8.0
7.5
5.6
Iranian Crude Oil
0.0
73.6
52.8
38.4
30.6
30.4
22.9
20.0
13.6
212
-------
TABLE E7. DISPERSION OF #2 FUEL AND IRANIAN CRUDE
OIL WITH PRODUCT B (0/D 5:1) WITH AND
WITHOUT AGITATION
Sampl ing
Time
(Hours)
0.0
0.25
0.50
0.75
1 .0
1 .5
2.0
3.0
4.0 ~:
Concentration of Organics (PPM)
#2 Fuel Oil
Without
Agitation
0.0
2.6
2.3
1 .5
1 .3
1 .3
1 .3
1.0
1 .0
Continuous
Agitation
0.0
158.6
170.4
170.8
175.4
241 .2
248.4
285.0
327.4
Iranian Crude Oil
Without
Agitation
0.0
1 .8
1 .8
1 .6
1 .6
1 .5
1 .5
1 .4
1 .4
Continuous
Agitation
0.0
36.5
41 .9
43.1
69.0
72.2
73.4
84.1 fc
84.7
213
-------
APPENDIX F
COMPUTER PROGRAMS FOR NUMERICAL ANALYSIS
OF EXPERIMENTAL DATA
TABLE Fl
Computer Program for Fitting Experimental Data
to Dissolution Equations
00100 DPT IDNS LS=SOJ
00200 DRTR;
00300 INPUT T C;
00400 PPDC NLIN BEST=10 METHOD=r-1RRQUl=iRDT;
00500 PRRRMETERS KL=.01
00600 KE=.04
00700 TM=3
f i n :-: fi n f: :":=£9.95
00900 EDUHDS CS>0~TM>OJ
01000 IF TOTM THEN DO?
01100 MODEL C=CS+a. 0-EXP C-KL*T» j
01eoo END;
01300 ELSE DD;
01400 MODEL C=CS* <1. 0-EXP C-KL*TM> > -*-EXP <-KE* -;T-TM» J
01500 END;
01600 OUTPUT DUT=NEl..l PREDICTED=CHRT;
01700 PRDC PRINT;
pisoo vflR T c CHRT;
01-913CO PRDC PLOT;
02 0013 PLOT C*T CHRT*T=''*'VDVERLflY;
214
-------
TABLE F2
Computer Program for Fitting Experimental Data
to Spreading Equations
0 0 1 d 0
00 £00
00300
00400
00500
no Ann
00700
00800
nn900
01000
01100
01200
01300
01400
01500.
~0160ti
01700
0 1 '3 0 0
01900
nsnnn
02100
02200
02300
02400
02500
02600
02700
02800-
02900
03000
03100
03200
03300
03400
03500
DPT I QMS LS=80;
DflTfiJ
IHPUT T fl;
IMFILE Ti;
PRDC ML IN METHOD=MflRQIJflRIiT;
PflRflMETERS K=i;
VT=255
TD= 105.0?
Q=VTXTD;
STW=73.4;
STD=£8. 0?
STDW=29.7;
S I GMfl=STI...I-STD-STOI..J 5
VISD=. 01594?
IF T=TD THEN V=VTJ
MODEL fl=K+
OUTPUT DUT=NEW PREDICTED=ftl 5
PRDC PRINT;
VflR T fl Hi?
PRDC PLDT;
PLOT H+T fll*T='*xxDVERLflY;
PRDC NLIN METHDD=MflRQUflRDT;
PflRflMETERS K=1J
VT=25;
Tn=io5. o;
Q=VT-'TD;
STW=73.4?
28. 05
-T2. 0x7. 0>
03700
03800
03900
04000
SI GMfl=ST W-STD-STDW ?
SPD=.797;
IF T=TH THEN V=VTJ
MODEL fl=K> < *'» C2. 0x3. 0> >
OUTPUT OUT=NEW PREDICTED=ft2;
PRDC PRINT;
VflP T fl fl2;
PRDC PLOT;
PLOT fl+T fl£+T=-" + '-xDVERLflY;
215
-------
TABLE F2 (Contd.)
04100 PRDC MLIM METHOri=MRRQURRnT?
04200 PflRflMETERS K=l?
04300 VT=25?
04400 TD=105.0?
04500 Q=VTxTD?
04600 Gp=9ftn;
04700 SPD=.797;
04800 SPW=1.0?
049 0 0 nEL=SPDxSpl.,.l;
05 0 0 0 VISD=.01594 ?
05100 IF T| =TD THEM V=VT?
053 0 0 MODEL R=K> < CGR+SPD*- < 1. 0-DEL>
05400 OUTPUT OUT=NEW PREBICTEIi=fl3?
05500 PRDC PRIMT?
05600 VfiR T fl R3?
05700 PRDC PLDT?
05800 PLDT fl+T R3*T=-'*"'xDVERLRY;
059HO PRDC MLIM METHDH=MflRQUflRDTJ
-136000" "PflRflMETERS K=l? - - -
=96100^ VT=25?
06200 TD=105.0?
06300 Q=VTxTD?
06400 GR=980?
06500 SPO=.797?
06600 SPW=1.0?
06700 DEL=SPOxSPW?
06800 IF T | =TD THEM V=VT?
07 00 0 MDDEL R=K> < * V*-*
07100 OUTPUT DUT=NEW PREDICTEIi=fl4;
07200 .PRDC PRIMT?
07300 ;MfiR T R R4?
07400 PROC PLDT?
07500 PLOT R+T R4*T=-'* -xDVERLRY?
C2.
l. 0»
0x
216
-------
TECHNICAL REPORT DATA
iu.vr read /«ii/i/(V/>»'V :in l/ic reverse bcjorc fo
,i , T>. 1 rvO
_ EPA-600/2-,
. L A\U-S-UBTI I Lt
DISPERSAL MECHANICS
6. PERFORMING ORGANIZATION CODE
AUTHORS) "
Chukwuka A. Osaiaor and
Robert C. Ahlert
PERFORMING.OHGANIZATION NAME AND ADDRESS
Dept. of Chemical & Biochemical Engineering
Rutgers, The State University of New Jersey
New Brunswick, New Jersey 08903
12. SPONSORING AGENCY NAML AND ADDRESS
Municipal Environmental Research Laboratory-Cin.,OH
Office of Research & Development
U.S. Environmental Protection Agency
Cincinnati, Ohio 45268
3. RECIPIENT'S ACCLSSION-NO.
5. REPORT DATE
September 1981
six
1H
8. PERFORMING ORGANIZATION REPORT NO
10. PROGRAM ELEMENT NO.
AUN1K
11. CONTRACT/GRANT NO.
Grant No. R-805901
13. TYPE OF REPORT AND PERIOD COVERED
Final
14. SPONSORING AGENCY CODE
EPA/600/14
15. SUPPLEMENTARY NOTES
Project Officer - Leo T. McCarthy, Jr. (201) 321-6630
16. ABSTRACT
This study investigates the spreading and dissolution behavior of small oil slicks
brmed from spills of 12 oils. The increases in area covered by the oils during spread-
ing experiments were determined using photographic techniques. Spreading equations were
derived and used to correlate experimental data. Derivation of the equations parallels
Fay's development.
The rate of dissolution of the oils in tap water at 25°C were investigated by equi-
librating oils with water in open static tests. Limits of solubilities have been estab-
lished for the oils from results of long-term equilibration in closed vessels. Six oils
were also equilibrated with salt water. A segmented mathematical model has been arrived
ind used to correlate experimental data. The model describes two processes that occur
during equilibration: soluble and volatile components of oil leach into solution
initially, and later evaporate from solution.
y^ detailed description of the mass transfer process occurring during chem-
cal dispersion of oil spills has been made. The primary mechanisms have been quanti-
ied by analogy to homogeneous and heterogeneous catalysis and detergency. To evaluate
the effectiveness of five commercial dispersants, a large-scale laboratory system has
Deen designed. Parameters investigated include oil and dispersant types, oil-to-
iispersant ratios, degree of agitation, and the effect of salt water. __
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
Dispersal
Spreading
Dissolution
Miceles
Chemical Dispersion
b.IDENTIFIERS/OPEN ENDED TERMS
Mechanisms
Dispersal Processes
Petroleum
COSATi Held/Group
3. DISTRIBUTION STATEMENT
Release to Public
19. SECURITY CLASS (Tlus Report)
Unclassified
21. NO. OF PAGES
237
20. SECURITY CLASS (This page)
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
217
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