Accepted Manuscript Manuscript Assessing the Performance Performance and Cost of Oil Spill Remediation Technologies Technologies Daniel P. Prendergast , Philip M. Gschwend
PII:
S0959-6526(14)00409-0
DOI:
10.1016/j.jclepro.2014.04.054
Reference:
JCLP 42 4260
To appear in:
Journal of Cleaner Production
Received Recei ved D Date: ate: 16 Se Septemb ptember er 2013 2013 Revi Re vise sed d Date Date::
17 Apri Aprill 2014 2014
Accepted Date: 21 April 2014
Please cite this article as: Prendergast DP, Gschwend PM, Assessing the Performance and Cost of Oil Spill Remediation Technologies, Journal of Cleaner Production (2014), doi: 10.1016/ j.jclepro.2014.04.054.
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ACCEPTED MANUSCRIPT
10,406 Words
1
Assessing the Performance and Cost of Oil Spill Remediation
2
Technologies
3
Daniel P. Prendergast and Philip M. Gschwend *
4
a
a
b,
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology,
5
MIT Bldg. 48-123, 77 Massachusetts Ave, Cambridge, MA 02139, USA
6
[email protected]
7
b
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology,
8
MIT Bldg. 48-413, 77 Massachusetts Ave, Cambridge, MA 02139, USA
9
[email protected]
10 11
* To whom all correspondence should be addressed:
12
Philip Gschwend [tel: 617-253-1638 617-253-1638 email:
[email protected]]
[email protected]]
13 14
ACCEPTED MANUSCRIPT
Abstract
1 2
Oil spills are an especially challenging chemical contamination event to remediate. Predicting the
3
fate and effects of spilled oil is a formidable task, complicated by its complex chemical composition and
4
the potential for catastrophically large discharge volumes. The proper choice of cleanup technique is
5
equally complex, and depends on a host of factors, including oil ttype, ype, spill location, spill size, weather,
6
and local regulations and standards. This paper aims to provide a broad review of the current technologies
7
used to remediate oil spills, and the context in which they operate. The chemical characteristics of an oil
8
spill are discussed, including implications for transport modeling, and impacts that arise from short-term
9
and chronic toxicity. The most common remediation technologies (mechanical recovery, dispersants, and
10
in-situ burning) are reviewed, as are emerging technologies (hydrophobic meshes and magnetic sorbents).
11
A comparative analysis is performed on these methods by calculating a maximum oil encounter rate for
12
each device, which is an under-reported performance characteristic critical to planning a response effort.
13
Finally, a review of cleanup cost estimation techniques is used to assess the cost-effectiveness of
14
remediation methods. Analysis shows that that waiving the legal penalty for recovered oil can result in
15
significant cost savings for the liable party, and may drive improvements in recovery-focused technology.
16
The authors suggest continued research into improving oil spill recovery methods and understanding the
17
fate of individual compounds in the spilled oil. This will both minimize potential environmental damages,
18
and reduce the uncertainty of their impacts.
2
ACCEPTED MANUSCRIPT
Highlights Assessing the Performance and Cost of Oil Spill Remediation Technologies: Prendergast, Gschwend
• • • • •
Review of the composition and fate of spilled oil, including modeling approaches. approaches. Calculation of the maximum oil encounter rate for various remediation techniques. Estimation of cleanup costs including cost averted by recovering spilled oil. Net negative cost of cleanup c leanup can be achieved, promoting removal of contamination. Recommend increased development of oil spill recovery methods.
ACCEPTED MANUSCRIPT
10,406 Words
1
Assessing the Performance and Cost of Oil Spill Remediation
2
Technologies
3
Daniel P. Prendergast and Philip M. Gschwend *
a
b,
4
a
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology,
5
MIT Bldg. 48-123, 77 Massachusetts Ave, Cambridge, MA 02139, USA
6
[email protected]
b
7
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology,
8
MIT Bldg. 48-413, 77 Massachusetts Ave, Cambridge, MA 02139, USA
9
[email protected]
10 11
* To whom all correspondence should be addressed:
12
Philip Gschwend [tel: 617-253-1638 617-253-1638 email:
[email protected]]
[email protected]]
13 14
ACCEPTED MANUSCRIPT
1 2
Abstract
Oil spills are an especially challenging chemical contamination contamination event to remediate. Pre Predicting dicting the
3
fate and effects of spilled oil is a formidable task, complicated by its complex chemical composition and
4
the potential for catastrophically large discharge volumes. The proper choice of cleanup technique is
5
equally complex, and depends on a host of factors, including oil type, spill location, spill size, weather,
6
and local regulations and standards. This paper aims to provide a broad review of the current technologies
7
used to remediate oil spills, and the t he context in which they operate. The chemical characteristics of an oil
8
spill are discussed, including implications for transport modeling, and impacts that arise from short-term
9 10
and chronic toxicity. The most common remediation technologies (mechanical recovery, dispersants, and in-situ burning) are reviewed, as are emerging technologies (hydrophobic meshes and magnetic sorbents).
11
A comparative analysis is performed on these methods by calculating a maximum oil encounter rate for
12
each device, which is an under-reported performance characteristic critical to planning a response eeffort. ffort.
13
Finally, a review of cleanup cost estimation techniques is used to assess the cost-effectiveness of
14
remediation methods. When recovering spilled oil averts a fine, and a nd then the fine is subtracted from the
15
cost of the spill, mechanical recovery methods are found to have a negative cost per unit recovered for
16
offshore spills with a variety of oil types and sizes. Waiving the legal penalty for spilled oil that is
17
recovered can result in significant cost savings sa vings for the liable party, and may drive improvements in
18
recovery-focused technology. The authors suggest continued research into improving oil spill recovery
19
methods and understanding the fate of individual compounds in the spilled oil. This will both minimize
20
potential environmental damages, and reduce the uncertainty of their impacts.
2
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1. Introduction
2
The worldwide use and distribution of crude oil and its derivatives continues to impose a
3
potential threat to aquatic environments. Accidental releases can occur from a variety of sources including
4
tankers, pipelines, storage tanks, refineries, drilling rigs, wells, and platforms (Vanem et al., 2008).
5
Fortunately spill frequency and volume from all international sources have decreased since the 1970’s
6
(Burgherr, 2006) due to the identification of management-based risk factors (Bergh et al., 2013),
7
increasing implementation of preventative regulations, and the development of corporate social
8
responsibility practices by the oil production and transportation industries (Rauffleta et al., 2014). Despite
9
these global improvements, there may be an increased risk of spills on a local level due to increased
10
industrial activities in countries with high economic growth, e.g. in the South China Sea S ea (Woolgar, 2008).
11
Additionally, catastrophic spills remain a possibility from all sources. Noteworthy examples include: the
12
1989 sinking of the Exxon Valdez oil tanker off the coast of Alaska (Peterson et al., 2003), the subsea
13
blowout in the Gulf of Mexico of the Deepwater Horizon drilling rig in 2010 (Camilli et al., 2011), and
14
the 2010 pipeline spill of diluted bitumen in Michigan (EPA, 2011). The inability of responders to
15
prevent the spilled oil from reaching sensitive areas led to economic, social, and environmental damages.
16
These large-scale spills in highly mobile aquatic environments highlight the need for remediation
17
technologies that can respond swiftly to mitigate potential damages.
18
Oil spill clean-up technology has expanded to include a variety of approaches in the past 50
19
years. Spill response techniques are typically classified as mechanical/physical, chemical, and biological
20
(Dave and Ghaly, 2011). While only briefly described below, detailed reviews of these techniques have
21
been published, including their operational limitations (Ventikos et al, 2004) and a qualitative assessment
22
of their strengths and weaknesses (Dave and Ghaly, 2011). The mechanical/physical class includes
23
deployment of oil booms, which are floating barriers designed to control the movement of surface oil
24
slicks. Skimmers are a broad category of stationary or mobile mechanical devices specifically designed to
3
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recover oil from the water’s surface (Schulze, 1998). To separate the water and oil, they typically take
2
advantage in the difference in density or adhesive properties of water and oil. An example of a chemical
3
technique is the application of dispersants, which are surfactants sprayed on the oil slick from aircraft or
4
boats in order to reduce the water/oil interfacial tension and cause the oil to break-up into smaller drops.
5
This promotes dissolution and biodegradation while limiting movements of large volumes of oils to
6
sensitive receptors such as coastal wetlands. Bioremediation consists of the addition of nutrients and/or
7
oxygen to stimulate the growth of indigenous microbes that can utilize oil as a carbon source. Microbes
8
designed to degrade the oil can also be added, if it is felt that natural oil-degrading strains are not present
9
in sufficient numbers. Most recent research has focused on chemical surfactants or bioremediation
10
applications, in order to improve their efficiency and/or the impact of their addition on the environment
11
(Dave and Ghaly, 2011).
12
Newer techniques are also becoming well-known and applied in the oil spill response community.
13
One such technique, in-situ burning, consists of using specially designed high-temperature boom to corral
14
oil slicks into a smaller area, where it is ignited in a controlled burn (Allen and Ferek, 1993). This
15
technique was widely used in the Deepwater Horizon response (Allen et al., 2011). Absorbents also see
16
widespread use, especially when cleanup goals demand the complete removal of oil. However, due to the
17
difficulty in handling oil-soaked materials, this technique is typically confined to small areas, and is not
18
examined in this paper.
19
Material science offers the potential for innovation beyond current techniques. Skimmers have
20
been modified to have oleophilic surfaces, and this advance has seen widespread implementation in the
21
oil spill response industry (Broje, 2006). Magnetic particles offer many advantages over traditional
22
absorbent techniques. Their high hydrophobicity and oleophilicity makes them extremely efficient
23
separators, and their uptake capacity can match or exceed current absorbents (Chun and Park, 2001). In
24
addition, their inherent magnetic properties provide a facile method of recovering and handing oil-sorbent
4
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amalgam. Another technique originating from materials research involves hydrophobic meshes, which
2
can separate oil and water in-situ without additional energy input (Deng et al., 2013). While these
3
techniques remain largely untested under field conditions, their potential to improve the rate and
4
efficiency of cleanup operations is worth investigating.
5
This paper has three primary objectives. The first is to review the inherent complexity in
6
predicting the fate and impact of spilled oil in the marine environment. Crude oil and its derivatives are
7
extremely complex mixtures of organic chemicals. Recent advances in fate modelling are reviewed, while
8
highlighting the uncertainties and gaps in current knowledge. Ideally, perfect knowledge leads to an
9
optimal response to an oil spill, defined as one that balances response costs with environmental damages.
10
However, the literature shows that quantifying the damage to social, economic, and environmental
11
resources from oil spills is an uncertain endeavor. Thus, the second objective is to review and reanalyze
12
the performance of the major classes of oil spill cleanup techniques in order to assess the current
13
technological capabilities for responding to a large-scale oil spill. Emphasis will be placed the encounter
14
rate of each technique, a common limiting factor for large spills. The third objective is to review how the
15
costs of response efforts are currently estimated. These methods are then used to establish a financial
16
incentive to recover oil, under the hypothetical scenario whereby the responsible party is not fined for oil
17
that is recovered from the environment at or very near the point of discharge. This scenario will highlight
18
the financial benefits of recovering, rather than dispersing or destroying, spilled oil, and show how it
19
complements the mitigation of environmental damage.
20
5
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2. Method of Review
2
This study relies solely on peer-reviewed scientific papers, publically available government
3
reports, and published results of remediation technique performances. Preference was given to recent
4
reviews of a given topic, and papers that first identified a phenomenon. Using this literature, the most
5
common approaches to oil spill remediation are identified, and their performance metrics are compiled. In
6
a parallel effort, the factors controlling the fate and impact of oil spills are identified, as are the
7
quantitative models that predict these factors. Only models that had published the scientific basis and
8
validation of their algorithms are included in this review. These models are assessed for their adherence to
9
physical mechanisms, and ability to predict the transport and impact of oil spills. We then introduce the
10
idea of a theoretical maximum oil encounter rate, and show how the underlying formulation is consistent
11
with published predictive tools currently used by oil spill response community. After identifying the
12
major classes of oil spill response technology, published methodologies for estimating the cost of each
13
response
are
used
to
assess
the
economic
6
implications
of
oil
spill
recovery.
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3. The Composition and Fate of Spilled Oil
2
3.1 Oil Composition and Characterization
3
Oil is not a single-component substance with well-defined physical properties and behavior. For
4
example, crude oil is a mixture of individual chemicals with more than 10,000 unique elemental
5
compositions (Marshall and Rodgers, 2008). Each unique elemental composition, in turn, potentially
6
represents thousands of unique chemical structures. The total number of individual compounds is
7
estimated to be in the billions (Beens and Brinkman, 2000). The compounds mostly consist of
8
hydrocarbons, but also include organic compounds with various heteroatom substituents, notably oxygen,
9
nitrogen, sulfur, and trace metals (Shi et al., 2010). More processed forms of oil, such as diesel fuel,
10
lubricating oils, or diluted bitumen, represent a subset of the composition of crude oil which has been
11
separated or modified to produce desired physical or chemical properties. The origin of biofuels is distinct
12
from that of crude oil, and as such is considered separately in performance and analysis (although they
13
may have many components in common) (Brynolf et al., 2014). Desired properties of any fuel depend on
14
individual chemical composition, composition, which has been limited by the overwhelming complexity of the mixture.
15
Gas chromatography coupled with mass spectrometry (GC-MS) is the conventional method used
16
to elucidate oil composition. The columns used to separate oil components largely do so based on their
17
London dispersive interactions as reflected by their boiling points. In order to resolve compounds with
18
similar boiling points, two-dimensional gas chromatography (GC x GC) can be used (developed by Liu
19
and Phillips (1991), with recent applications by Ventura et al. (2008) and Reddy et al. (2012)), which
20
separates by both the London interactions with the first stationary phase as well as polar interactions with
21
the second stationary phase. Unfortunately, GC is only effective at separating compounds with a boiling
22
point of less than about 400 C. For crude oil, this can represent a significant blind spot: only about half of
23
the mass in the Macondo oil well was resolvable by conventional gas chromatography (McKenna et al.,
7
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2013). Only very recently have these high-boiling point compounds been separated by mass using ultra-
2
high resolution mass spectrometry, but the structure of the individual compounds for a significant fraction
3
of many crude oils remains unknown.
4
Additional characterization methods have been developed in order to empirically link oil
5
composition with bulk behavior. The most widespread technique is SARA fractionation, which separates
6
oil into saturates, aromatics, resins, and asphaltenes (Jewell et al., 1972). Resins and asphaltenes are more
7
polar and differentiated empirically. Asphaltenes are insoluble in heptane or pentane. Saturates are
8
nonpolar saturated hydrocarbons, while aromatic compounds are more polarizable. Heavier oils tend to be
9
enriched in resins while lighter oils tend to be enriched in saturates. Depending on the analytical
10
technique used, different methods may yield different mass fractions for each class (Fan and Buckley,
11
2002).
12 13
Nevertheless, numerous correlations have been developed that link the SARA fractions to the bulk properties of spilled oil. For example, emulsification has been found to be related to SARA
14
information (Fingas (Fingas and Fieldhouse, Fieldhouse, 2012). Emulsification of the oil, where where water droplets become become
15
entrained in the oil phase due to wind and wave action, increases the oil's viscosity, thereby making the
16
oil slick more resistant to skimming and dispersion. Fingas and Fieldhouse (2012) found that the resin and
17
asphaltene fractions of more than 300 crude oils correlate with the ease of such emulsification. In
18
addition, the specific gravity of oil has often been used to predict its un-emulsified viscosity, with more
19
recent correlations utilizing resin and asphaltene content (Hossein et al., 2005). Notably, in both of the
20
above studies, higher asphaltene content was shown to significantly increase the viscosity of the oil and
21
stability of the emulsion. Spilled oil becomes more viscous and emulsified as time passes. Field trials
22
(Figure 1) have shown that in less than 24 h, the water content of emulsified oil can reach up to 80% by
23
volume, and its viscosity can increase by a factor of 100 (Daling et al., 1997). An increase in
24
emulsification or viscosity causes any remediation technique to be less effective. Understanding the
8
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propensity of spilled oil to alter its physical properties under environmental conditions is one key to
2
understanding its fate and choosing the optimal remediation response.
3
4 5 6 7
Figure 1: Field data of the viscosity and water content of crude oil released on the open sea. Water
temperature was 15˚C in the summer and 10˚C in the winter. Lines are added for visualization purposes only. Data taken from Daling et al. (1997), who note that dispersant effectiveness is dramatically reduced for this oil when its viscosity becomes greater than 4000 cP.
8
9
3.2 Modeling Oil Distribution and Fate
10
After release to an aquatic environment, oil undergoes numerous processes collectively known as
11
“weathering” that alter its composition and fate (Blumer et al., 1973). An oil slick both moves with the
12
underlying water currents and spreads relative to the water surface (Fay, 1971). Spreading broadens and
9
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thins the oil slick at a rapid rate controlled by gravity and the oil’s viscosity. As it is exposed to wind and
2
wave action, lighter oil components are transferred to the air via evaporation (Mackay and Matsugu,
3
1973). Simultaneously, Simultaneously, lighter polar constituents dissolve into the water water column (Arey et al., 2007). Both
4
of these processes cause the remaining oil to become enriched with heavier, apolar compounds, which
5
increases the viscosity of the slick. Depending on the composition of the oil, the depletion of lighter
6
compounds can enhance the transformation of a slick sl ick into a water-in-oil emulsion through wind and wave
7
action (Fingas, 1995). Eventually, the oil can entrain so much water (up to 80% by volume) that it breaks
8
up into nearly neutrally buoyant “tar balls”, causing it to sink and be transported hundreds of miles with
9
prevailing currents (Reed et al., 1999). Oil on the surface can undergo photodegradation where it is
10
broken down into smaller components or transformed into oxygenated compounds (Aeppli et al, 2012).
11
Oil can also be broken down by native microorganisms, especially when entrained in the water column
12
(Atlas, 1995). Models that couple all of the transport and weathering process have been developed by
13
various governmental and industry groups. One goal of such models is to predict the physical extent and
14
distribution of a spill in order to plan or implement response operations.
15
The National Oceanographic and Atmospheric Administration (NOAA) has developed two
16
models to this end: the General NOAA Operational Modeling Environment (GNOME) and the
17
Automated Data Inquiry for Oil Spills 2 (ADIOS2).
18
GNOME focuses on predicting the trajectory of an oil spill using a 2D Lagrangian approach
19
(Beegle-Krause, 2001). The model accounts for wind, current, oil spreading, and beaching along
20
shorelines (Zelenk et al., 2012). It also takes into account evaporation by idealizing the oil as a mixture of
21
three pseudocomponents, each assigned an independent degradation half-life. Users may select one of six
22
included oils with predetermined component fractions and half-lives, or specify oil with custom
23
characteristics. Other inputs include local wind velocities, currents, bathymetry, maps, and extent of the
24
oil spill. The program models the development of the spill’s spatial extent over time. The model does not
10
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take into account any losses besides evaporation, and thus likely overestimates the total slick volume at
2
any given time. NOAA also acknowledges that the trajectory model is simplistic and sensitive to the
3
accuracy of the local current data, but that it includes tools to estimate the uncertainty of a predicted
4
trajectory (NOAA, 2013).
5
ADIOS2 (Lehr et al., 2002) focuses on the weathering process of spilled oil, rather r ather than its spatial
6
distribution. Using a database of over 100 oils, the program tracks the macroscopic properties of the oil
7
(specifically density, viscosity, and water content) as it undergoes evaporation, spreading (to determine
8
thickness), emulsification, dispersion (entrainment of oil droplets into the water column), and beaching. It
9
also simulates the effects of clean-up techniques, including skimming, in-situ burning, and application of
10
dispersants. Inputs to the program include wind speed, a uniform current, oil type, and the details
11
regarding the cleanup operations. The main program outputs are the evolving properties of the spilled oil
12
and remaining volume. Predictions do not extend for more than five days, and so they do not consider
13
effects of biodegradation or phototransformations. ADIOS2 also does not model the formation of tar
14
balls, which is the final fate of much of the heavier, nonpolar components of the oil. In addition, many of
15
the algorithms are based on empirical studies where the properties of interest were simulated in a
16
laboratory with a limited set of oils, rather than a field trial. Lehr et al. (2002) note that validation of the
17
model has been limited to basic observations of 40 small oil spills, and they recommend that it be used as
18
a rough guide for cleanup planning.
19
Oil spill models have also been developed by nongovernmental agencies. The Spill Impact Model
20
Application Package (SIMAP) was developed by Applied Science Associates, Inc. as part of an
21
ecological risk assessment process required by the Department of the Interior (French-McCay, 2004). As
22
a result of this developmental goal, SIMAP is unique insofar as it combines a physical fate model with a
23
biological effects model. The physical model predicts slick transport, evaporation, component
24
concentrations in the water column, sorption to sediments, and shoreline fouling. The model still
11
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simplifies the oil composition by treating it as an eight component mixture, but the pseudo-components
2
have been chosen to emphasize the toxic, volatile, and residual natures of a given oil. The algorithms used
3
to model the physical degradation resemble those in the AIDOS2 model, and so suffer from the same
4
limitations. The biological effects model uses the output from the physical fate model to determine the
5
extent of exposure of local wildlife (birds, fish, marine mammals, and reptiles), invertebrates, and plant
6
communities (French-McCay, (French-McCay, 2009). A toxicity model (Di Toro et al., 2000) is then used to determine the
7
percent mortality, which is in turn fed into a food web model to determine overall ecological impact.
8
SIMAP does not take into account chronic toxicity or changes in the behavior of birds and wildlife.
9
Validation has been undertaken with at least 20 spill events (French-McCay, 2009), but most cases were
10
limited to observation of wildlife.
11
Modeling the outcome of an oil spill faces many challenges. Many of the algorithms used to
12
predict physical processes rely on parameters derived from empirical studies. These parameters are based
13
on a limited dataset, and it is unclear if or when the models extrapolate from that dataset. Another major
14
challenge to developing accurate fate models is the difficulty of validation. Oil spills can cover a large
15
area, with complicated local ecosystems and physical environments. Collecting appropriately detailed
16
spatial and temporal field data is a challenging, time-consuming, and expensive endeavor. Future
17
modeling efforts should focus on validation, particularly by hindcasting the effects of a past spill where
18
extensive fieldwork was undertaken.
19
3.3 Environmental Impact of Spilled Oil
20
The environmental damage caused by spilled oil is probably its least understood aspect, owing to
21
the combined complexity of both the oil and the environment. The toxicity of the individual compounds
22
can vary greatly. Quantitative structure-activity relationships (QSARs) have been developed to correlate
23
the n-octanol-water partition coefficient (a measure of a chemical’s tendency to partition into nonpolar
12
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media from aqueous solution) to the nonspecific toxicity of hydrocarbons, which is caused by the build-
2
up of oil components in the membranes membranes of cells (Di Toro et al., 2000). The nonspecific toxicity can also
3
be determined solely through GC x GC analysis of the oil, without the need to identify individual
4
components (Tcaciuc et al., 2012). In addition, compound-specific compound-specific QSARs often contain correction
5
factors for chemicals with unique toxicity mechanisms, such as polycyclic aromatic hydrocarbons
6
(McGrath et al. 2005).
7
However, our knowledge of toxicity mechanisms is incomplete. First, byproducts can form after a
8
spill is released into the environment. For example, as first noted by Hansen (1975) and recently reviewed
9
by Lee (2003), compounds produced by photodegradation can be toxic to aquatic animals and
10
microorganisms, yet this aspect is not typically tracked as part of an oil fate model. Second, there is some
11
evidence that the bioassays used to test for chemical toxicity do not fully expose the test organisms to
12
fraction of the oil that is not resolved by GC (Hong et al., 2012). Weathered oil is enriched in high
13
molecular weight compounds, and its toxicity relative to fresh oil is still being debated. Finally, most
14
experiments can only determine the acute toxicity of chemicals, since exposure times rarely last longer
15
than 96 hours (Weber, 1993). This has led to instances where chronic exposure to low levels of pollutants
16
caused lasting adverse effects on the local ecosystem, such as in Prince William Sound following the
17
Exxon Valdez oil spill (Peterson et al., 2003). In general, the complexity, variability, and incomplete
18
characterization of oil compounds magnify the uncertainty in predicting the impact of a spill.
19
4. Technical Assessment of Oil Spill Response Technologies
20
4.1 Overview of Response Techniques
21
A broad review of the operational limitations of various countermeasure techniques has been
22
reported by Ventikos et al. (2004), ( 2004), including mechanical barriers/booms, skimme skimmers, rs, skimmer vessels,
23
sorbent materials, and chemical dispersants. They provide quantitative performance limits for all 13
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techniques based on environmental conditions: wind speed, current velocity, wave height, and sea state.
2
For recovery techniques (skimmers and sorbents) additional data are provided for oil viscosity, recovery
3
efficiency (ratio of oil encountered to oil recovered), sensitivity to debris, recovery capacity, and nominal
4
recovery rate (range of possible volumetric recovery rates). For dispersants, rougher numbers are given
5
for the application ratio (volume of dispersant/oil) and the effectiveness. These values will be used as the
6
basis of subsequent analysis here.
7
A more comprehensive, but qualitative, review has been completed by Dave and Ghaly (2011). In
8
addition to the techniques reviewed in Ventikos et al. (2004), Dave and Ghaly (2011) included chemical
9
solidifiers, in-situ burning, and bioremediation. The authors listed qualitative advantages and
10
disadvantages for each technique, then assigned a weighted score based on a variety of criteria, including:
11
efficiency, time, cost, impact on marine life, level of difficulty (to operate), weather, reliability, oil
12
recovery, effect on oil characteristics, and the need for post-remediation treatmen treatment. t. Their work provides
13
insight into the less quantifiable aspects of implementing each technique.
14
4.2 Maximum Oil Encounter Rate
15
Currently, the recovery capacity of oil spill remediation techniques is reported as the Effective
16
Daily Recovery Capacity (EDRC) (USCG, 1997). This value is used in the design of oil spill response
17
plans, and is required by the Oil Spill Protection Act. The calculation is as follows:
EDRC = T · 24 h · E
(1)
18
19
where EDRC is in bbl/d, T is is the nameplate na meplate recovery capacity in bbl/h as defined by AS ASTM TM F2709
20
(2008), and E is is an efficiency factor, which must be at most 20%. The nameplate recovery capacity is the
21
maximum rate that a collection system can recover rec over oil, given optimal conditions. Thus, the EDRC
22
represents a corrected estimation of a day’s worth of recovery efforts. Unfortunately, the correction factor 14
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is the only parameter than can be adjusted for irregularities in spill conditions, and it does not explicitly
2
take into account variable oil viscosity and thickness, emulsified oil, dispersant addition, or other
3
complicating factors (Lee, 1993). In terms of assessing the potential of spill technology, it
4
overemphasizes the importance of the nameplate recovery capacity. An important missing parameter is
5
the oil encounter rate. A framework for assessing this parameter is developed below.
6
In simple terms, a device cannot recover more oil than it encounters. Thus, the volumetric
7
recovery rate of any system will be the lower of either its EDRC or the encounter rate. The encounter rate
8
for a given spill is dependent on the physical distribution of the spill and the capacity of the remediation
9
technique. In order to focus on the potential of a technology t echnology,, it is assumed that the recovery system s ystem is
10
always in contact with an oil slick, making this framework an estimation of the maximum oil encounter
11
rate (MOER). Furthermore, the slick is characterized by its average thickness, which accounts for both its
12
volume and spatial distribution. Thus, the MOER is described in units of area/time. This approach
13
quantifies the limiting factor for large spills spread over a wide area. In contrast, for confined spills the
14
rate of recovery is more likely to be limited by the E EDRC. DRC. The methodology of this approach is consistent
15
with previously developed spill response operations planning tools, such as the Response Operations
16
Calculator (Dale et al., 2011) and the Estimated Recovery System Potential (ERSP) Calculator (Allen et
17
al., 2012).
18
The MOER is designed as a complementary metric for assessing oil spill technologies, not an
19
improvement of the EDRC. Below (sections 4.2.1 to 4.2.4), we develop a MOER expression for major
20
classes of remediation technologies, and estimate representative values. Unless otherwise noted, these
21 22
calculations do not take into account the preparation time, transport time, or post-operational processing. The MOER is oil encounter rate under optimal conditions. In-situ burning is an exception because it relies
23
on a two-step technique of corralling the oil, followed by a stationary burn. S Sorbents orbents were not included in
15
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1
this analysis, since they are generally more suited for confined spills where complete oil removal is
2
necessary (Dave and Ghaly, 2011).
3
It is important to emphasize that a MOER estimation assumes the technique is in constant use,
4
which is never the case. For example, aircraft applying dispersants are often only over the spill for about
5
20% of operational time (Fingas, 1999). Thus, by focusing on the maximum encounter rate possible, the
6
MOER is an overestimation of actual performance. The calculated MOER values are intended to be
7
representative of the technique’s potential; the unique circumstances of a given spill will degrade the
8
actual encounter rate.
9
10
4.2.1 Skimmers
For skimmers, the MOER is simply the product of the maximum operational water velocity
11
(relative to the skimmer) and the width of the skimmer opening. For mobile skimmers that operate in
12
conjunction with a boom, the boom is assumed to funnel the encountered oil with perfect efficiency,
13
giving the skimmer an effective swath equal to the width of the boom opening. The maximum feasible
14
swath of a boom is about 1000 ft, or 300 m (Allen et al., 2012), and the maximum speed a boom can be
15
towed under optimal sea conditions without losing oil is about 0.5 m/s (Amini et al., 2008). Thus, the
16
MOER for a boom-skimmer system is 150 m2 /s, or 54 ha/h.
17
4.2.2 Dispersants
18
Dispersants are typically applied from fixed-wing or rotary-wing aircraft, covering c overing a wide area
19
using specially designed application equipment (ASTM, 2013). The MOER can be found directly from
20
previous operational reports of areal coverage rate (Fingas, 2011). At a 1:20 dispersant-to- oil ratio,
21
typical values for rotary- and fixed-wing aircraft are 300 ha/h and 800 ha/h, respectively.
16
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4.2.3 In-situ Burning
2
In-situ burning is a two-step process. The first step involves collecting oil within a boom, which
3
would have the same encounter rate as the skimming system described above. The second is the
4
controlled burn, which requires the boom to remain re main stationary. In calculating the MOER for in-situ
5
burning, it is assumed that the time required to seal the boom and ignite the collected oil is negligible
6
compared to the total collection and burn time. t ime. In addition, the boom assumes the shape of a catenary
7
curve (Wicks, 1969), and a collection is ceased when oil occupies one third of the total enclosed area. The
8
oil burns downward from the surface of the enclosed slick at a typical rate of 3 mm/min (Fingas, 2011),
9
although this value may be slightly lower for emulsified oil (Evans et al., 1990). Given a capacity, C (m (m3),
10
of a boom configuration, the time required to collect the oil (T 1) and to burn the oil ( T 2) is given by:
T 1 = C / S ; T 2 = C / (A · B)
(2)
11
12
where S is the encounter rate (m3 /s) when moving, A is the area occupied when the boom is at 1/3
13
capacity (as recommended by Allen (1991)), and B is the burn rate, noted above. The total encounter rate
14
is given by dividing the capacity of the boom by the total time required to fill and burn it:
-
EnR = C // (T 1+T 2) = C / [(C / S ) + (C / AB)] = [(1 / S ) + (1 / AB)]
(3)
15
16
Normalizing by the spill thickness h and introducing parameters for tow speed u and swath width w gives:
-1
-1
MOER = EnR / h h = [(h / w·u·h) + (h / AB)] = [( 1 / w·u) + (h / AB)]
(4)
17
18
Booms used for in-situ burning are intentionally towed such that the opening width is about 30% of the
19
boom length (Allen, 1991). As outlined by Wicks (1969), ( 1969), a catenary boom with a known length and
17
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1
width-to-length ratio has a fixed area, A (see Appendix). Using a 300 m long boom with a 90 m wide
2
opening (Allen, 1991), the area is found to be approximately 3000 m2.
3
Equation 4 shows that, due to the time required to remain stationary and to burn the oil, the
4
MOER for in-situ burning must depend on the thickness of the oil encountered. In order to show the range
5
of possible values, two MOER values are calculated: one for a relatively thick oil slick of 5mm, and one
6
for a relatively thin slick of 50 µm, Using a tow speed of 0.5 m/s, those values are 18 ha/h and 45 ha/h,
7
respectively.
8
4.2.4 Hydrophobic Mesh
9
Hydrophobic mesh acts much like a filter: it allows oil to pass through the mesh while rejecting
10
water. This process is passive, utilizing the difference in interfacial energy to drive the separation step.
11
However, oil must still be collected and removed from the interior of the mesh to perpetuate the process.
12
Deng et al. (2013), using bench-scale bench-scale tests, found that the rate of oil recovery was faster than th thee
13
spreading rate of relatively inviscid oils. Thus, much like a skimming system, field-scale devices
14
incorporating hydrophobic mesh will need a way to store recovered oil, as well as continuously move the
15
mesh to unrecovered oil. Although such devices have been yet to be developed, this assessment envisions
16
a device that is handled like a skimmer, with a wide booming system in place to tow the mesh across
17
floating oil slicks, maximizing the oil encountered. In this case, hydrophobic meshes would have a
18
MOER equivalent to those of skimmers. They would also likely be classified as a mechanical recovery
19
technique.
20
4.3 Discussion
21
Table 1 contains a summary of the calculated MOER values. Dispersants applied with aircraft
22
clearly have the largest MOER. This is not unexpected, since aircraft can move much faster than marine
18
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1
vessels towing boom, and do not need to handle the oil after encountering it. Burning and recovery
2
methods cannot encounter oil at the same rate ra te dispersants can. However, due to the time required to reach
3
and return from a slick, typical application rates are 20% of this maximum potential (Fingas, 1999). Even
4
with this practical limitation, if time is the only consideration, dispersants will likely continue to be the
5
fastest way to protect vulnerable resources.
6 7
μ
Table 1: Oil encounter rates normalized by b y spill thickness for various oil spill remediation technologies
operating under optimal operational conditions except applying a 20% factor to dispersant use.
8 9
In this analysis, in-situ burning has a lower MOER than mechanical recovery.This is the opposite
10
of what is typically observed in practice (e.g. Allen et al., 2011). Both utilize a boom to collect oil, but
11
only in-situ burning must collection be (in theory) periodically stopped to burn it off. Most common
12
skimmer systems cannot recover continuously, and must also stop when onboard oil capacity is reached
13
(Schulze, 1998). In addition, the MOER increased when the slick thickness decreased. This result
14
indicates that it is more efficient e fficient for the fire-resistant boom to remain mobile for as long as possible.
15
Additionally,, according to Equation 3, only the area of the boom affects the encounter rate, not the Additionally
16
boom’s volumetric capacity. A deeper draft is a tradeoff: it allows a re responder sponder to collect more oil, but it
17
also means the boom must remain stationary for longer l onger during the burning step. The only way to increase
18
the area of the boom is to use longer boom, or drag it in a wider configuration (see Equation A.3 in the
19
Appendix).
19
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1
Unlike the EDRC, a MOER calculation can compare recovery and non-recovery remediation
2
techniques. The previous calculations compare the implementation of a new technique (hydrophobic
3
meshes) to well-established methods, under the assumption that it could match the recovery recover y capacity of a
4
skimmer system. Unfortunately, Unfortunately, there is a lack of quantitative studies on the separation capabilities of
5
hydrophobic meshes, especially under the harsh conditions of a marine environment (Liu and Jiang,
6
2011). Matching the EDRC of a boom/skimmer boom/skimmer system may require unmanageably large areas of the
7
mesh to be brought into contact with the oil slick.
8 9
Nonetheless, there is reason to believe that hydrophobic meshes have a higher potential MOER. A skimming apparatus is relatively small, and relies on a wide boom swath to encounter oil at a useful
10
rate. In contrast, large areas of hydrophobic mesh may be fabricated, and may potentially be incorporated
11
along the entire length of a boom. Additionally, boom failure usually occurs when the oil slick is pushed
12
at a high velocity relative to the underlying water (Amini et al., 2008). A boom that recovers oil along its
13
entire length reduces that relative velocity, and enables the system to be towed at a faster rate.
14
Incorporating hydrophobic mesh could increase both the MOER and the EDRC of a towed-boom system.
15
An improved determination of the MOER will allow this new technology, or any other, to be more
16
thoroughly assessed for remediation potential than by an EDRC calculation alone.
20
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1 2
5. Cost of Response
3
Cost is important in determining the effectiveness of a remediation technique. A full analysis
4
would consider both the cost of implementing a remediation technique, as well as the cost averted by by
5
preventing the oil from damaging the environment. While these two factors can be difficult to estimate,
6
the balance between the two provides an optimization objective. A spill should not be cleaned in the least
7
expensive manner; rather, an optimal spill response minimizes both environmental damages and cost of
8
operations. This section reviews methods by which the cost of oil spills is typically calculated, and
9
provides additional analysis regarding the choice of response techniques.
10
A variety of cost analyses for oil spills have been performed in the last 30 years (Kontovas and
11
Psaraftis, 2008). These studies were undertaken to quantify the full cost of pollution incidents incidents in a manner
12
that was valuable to risk management decisions and conflict mitigations (Yang et al., 2014). In general,
13
the studies found that the cost of the spill, on a per-weight-spilled basis, depended largely on oil type,
14
weather, location (both in terms of geography and national jurisdiction), extent of shoreline oiling, and
15
cleanup technique. In addition, the types of cost tended to vary, but could be largely classified as cleanup
16
(removal, research, etc.), socioeconomic losses (tourism, marketable resources lost), and environmental
17
(deaths of flora and fauna, ecosystem impacts) costs. According to Kontovas and Psaraftis (2008), ( 2008), the
18
determination of total cost for a spill always uses historical data, but has taken different approaches:
19 20 21 22 23
1. Estimating and adding up all relevant cost components (cleanup, socioeconomic, and environmental). 2. Estimating cleanup costs, and then t hen estimating the environmental and socioeconomic costs through a modeled comparison ratio. 3. Estimating total costs directly, but controlling for various influencing factors. 21
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1
4. Estimating total costs based on compensation eventually paid to claimants.
2
Additional efforts have been made to develop a single relationship between the total cost and volume of
3
oil spilled, despite the often-acknowledged complexity inherent to these approaches. As a result, r esult, the
4
regression analysis of Kontovas et al. (2010) showed significant variability, even when outliers are
5
removed and the form of the fitting equation was varied. The cost variability often exceeded an order of
6
magnitude for a given spill size.
7
The model of Etkin (2000) (a Type 3 approach) handles this variability by accounting for
8
different spill scenarios. This model was derived from historical cost data of worldwide oil spills and
9
validated with multiple case scenarios. Cost data were initially obtained from the OSIR O SIR International Oil
10
Spill Database (ITOPF, 2012), which also tracks the characteristics of the oil spills (size, oil type, etc.).
11
The model takes into account oil type, t ype, extent of shoreline oiling, size of tthe he oil spill, location type,
12
country where the spill occurs, and primary cleanup method. The model predicts that the per-weight cost
13
of oil spill cleanup increases with: decreasing spill size, proximity to shore, extent of shoreline oiling, and
14
oil viscosity (reflecting a larger composition of non-volatile, sparingly-soluble components). The trend in
15
costs for shore proximity and spill size is counter-intuitive. However, Etkin (2000) notes that the high
16
per-volume cost of small spills is likely due to a variety of fixed costs related to response resources that
17
are required by law (environmental monitors monitors,, stand-by crews), but not always fully implemented for a
18
small spill. In any case, by statistically controlling for influencing variables, this model allows a
19
straightforward comparison of a variety of oil spill scenarios.
20
A simplified form of the main equation of the model is:
C lili = C n t i si mi
(5)
22
ACCEPTED MANUSCRIPT
1
where C llii is the response cost per unit spilled for scenario i, C n is the average response cost per unit
2
spilled in nation n, t i is the oil type cost modifier for scenario i, si is the spill size cost modifier for
3
scenario i, and mi is the cleanup method cost modifier for scenario i. The cost modifiers represent the
4
median percentage difference in cost for a given scenario with that characteristic from the overall median
5
spill cost.
6 7
Overall, Etkin (2000) showed that the most expensive cleanup techniques are (in increasing order) “natural cleansing”, in-situ burning, dispersants, mechanical recovery, and manual cleanup. The
8
analysis in this work only compares dispersants, in situ burning, and mechanical recovery, which are the
9
three most likely options for a large, offshore spill. Accordingly, the spill location type is limited to
10
offshore, and the extent of shoreline oiling to zero kilometers, since this factor is a reflection of the cost of
11
shoreline remediation techniques, not on-water cleanup techniques. A final summary of the cost modifiers
12
considered in this analysis is shown in Table 2 below.
13
14
No. 2 Fuel (Diesel) 0.18 < 34 t 2.00 In-Situ Burning Light Crude 0.32 34-340 t 0.65 Dispersants Crude 0.55 340-1,700 t 0.27 Mechanical Recovery Heavy Crude 0.65 1,700-3,400 t 0.15 No. 6 Fuel 0.71 3,400-34,000 t 0.05 No. 4/5 Fuel 1.82 > 34,000 t 0.01 Table 2: Cost modifiers (ti, si, mi) used in this analysis. Taken from Etkin (2000).
0.25 0.46 0.92
Etkin (2000) found that the average cost per unit of oil spilled varied greatly depending on the
15
nation in which it was spilled. For example, in 1999 USD, the average cost of a spill in the United States
16
was approximately $25,600/t, while in Singapore it was only $390/t. This large l arge variation was attributed to
17
a variety of factors, fact ors, including spiller liability, liability, cleanup standards, la labor bor costs, and the scarcity of data for
18
some regions. Assuming the cost of the average spill has only been aaffected ffected by inflation, the current value
19
(2013 USD) for the United States is $35,800/t, calculated from the consumer price index (BLS, 2013). 23
ACCEPTED MANUSCRIPT
1 2
The cost of the t he spill usually falls upon the party responsible for the incident. This cost includes any fines imposed by regional laws. Although the exact amount of the fine and method of calculation
3
varies between regions, in the United States the Oil Pollution Act of 1990 imposes a civil penalty of
4
$1,100 per barrel spilled (about $8,070/t). This fine increases to $4,300 per barrel spilled (about
5
$31,600/t) if the liable party was found to be “grossly negligent” in its actions (33 U.S.C. 40 §2716a).
6
This system ensures the responsible party has an incentive to minimize any damages resulting from the
7
spill. The Etkin model includes these fines within the listed cost c ost of the spill.
8
A hypothetical scenario is now proposed. If the liable party were fined for each barrel spilled,
9
minus each barrel recovered during cleanup operations, this could greatly influence the choice of
10
cleanup method. In other words, the liable party is fined only for each unit of oil remaining in the
11
environment. The reasoning for this suggestion is straightforward: if the oil does not remain in the
12
environment, and is confined to an offshore location near where it was spilled, much of the potential
13
damage is mitigated, and the liable party should receive a lesser penalty.
14
Under this legal scenario, one can analyze the cost of cleanup as follows. For remediation efforts
15
utilizing dispersants or in-situ burning, the oil components are merely transformed or moved to a different
16
phase, and still have the potential to damage the environment. The cost associated with these methods will
17
be assessed using Equation 5. In contrast, mechanical recovery of the oil rremoves emoves it from the
18
environment, and thus would not be fined per unit spilled. This cost would be determined by
C lili = C n t i si mi – F
(6)
19
where F is is the fine per unit of oil spilled (but not recovered). C n was taken as the overall average cost for
20
the United States ($35,600) multiplied by the cost factors for an offshore spill (0.46) and 0-1 km of
21
shoreline oiling (0.47). Figure 2 shows the results of comparing the prices of tthe he three original types of
22
cleanup methods (mechanical recovery, dispersants, and in-situ burning) with mechanical recovery with 24
ACCEPTED MANUSCRIPT
1
two types of fines: $1,100 per barrel, and $4,300 per barrel. The costs have been sorted by spill scenario
2
(oil type and spill volume, 6 each) and ordered from lleast east to most expensive per unit oil spilled (top-to-
3
bottom and left-to-right). A complete list of the costs can be found in the Supplementary material. The
4
cost could be further reduced by the value of the recovered oil. However, even if the costs c osts of processing
5
this recovered oil were not included, the market price of oil, about $100/bbl at the time of this writing, is
6
an order of magnitude less than the fine associated with spilling it. Thus, our cost estimate is slightly
7
conservative by not taking this value into account.
8 9 10 11 12 13
Figure 2: Graphical representation of the estimated cost per tonne (t) to remediate oil spilled in the open
ocean. Each square in the 6x6 grids represents the cost of an oil spill for a given type of oil and spill size, as indicated in the blank Scenario Grid (upper left). For example, the bottom-left corner of every grid estimates the cost, per weight of oil spilled, to remediate a spill of No. 4 or 5 fuel oil that was less than 34 t in size. Results were derived using a model developed by Etkin (2000). Included are two hypothetical
14
scenarios whereby the value of an averted fine is taken into account, reducing the cost (lower ri right). ght).
25
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1
The most apparent result is that all mechanical recovery operations with the larger fine averted
2
operate at a negative ne gative cost. Equivalently stated, this model always estimates that the cost of recovering oil
3
from an offshore spill with no shoreline oiling is less than the value of the fine associated with leaving
4
that spill in the environment. No non-recovery technique has a negative cost per unit oil cleaned,
5
including a “no action” alternative, which requires monitoring, monitoring, modeling, and decision-making. Thus, this
6
cost model indicates that mechanical recovery with an averted fine is the most cost effective technique,
7
even without directly taking into account the socioeconomic and environmental damages prevented.
8 9
When the fine is at the lower value of $1,100 per barrel, this model also estimates negativ negativee costs in 31 out of the 36 scenarios. These five remaining r emaining scenarios were under the most costly conditions,
10
having both small spill sizes and heavy oil types. However, even in these remaining scenarios, mechanical
11
recovery was still less expensive than dispersants in four instances, and in-situ burning twice. In addition,
12
these scenarios are examples of where the most cost-efficient technique determined by the model may not
13
be the one chosen by responders. Dispersants and in-situ burning are the least effective at remediating
14
small spills of heavy oils; the oils tend to emulsify and resist burning or dispersion. Thus, mechanical
15
recovery would likely be the method of choice based on effectiveness, which is not directly accounted for
16
in this cost model.
17
These rough cost estimations showcase the value of only imposing a fine for unrecovered spilled
18
oil. Such flexible regulations, regulations, in combination with a competitive industry industry,, have been shown to foster
19
technological innovation (Ford et al., 2014). In this case, by providing a specific financial incentive for
20
liable parties to remove as much oil from the environment as possible, in a manner that is cost effective in
21
a directly observable way, two goals are accomplished. First, potential damages from the spill are
22
minimized. The more oil that is removed from the environment, the less damage it causes. Second, oil
23
recovery decreases the uncertainty associated with impacts from the accident. As outlined in Section 1,
24
the exact numerical value of socioeconomic and environmental damages it not well known, and varies
26
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1
greatly based on many factors unique to a given spill. This uncertain value often becomes the focus of
2
debates that decide how much compensation should be rewarded, and to whom (Yang et al., 2014). By
3
reducing the number of impacted parties, the uncertainty in assigning just compensation is diminished diminished..
27
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1
2
3 4
5. Conclusions
A review of the oil spill literature showcased the challenges in fully understanding an oil spill. Oils are complex mixtures with varied bulk properties that substantially affect our remediation re mediation
5
approaches. Viscosity and tendency to emulsify (water content) are the most important properties to
6
identify for spill remediation efforts. In order to better assess the potential of different cleanup
7
technologies in large spills, the concept of a maximum oil encounter rate (MOER) was developed, which
8
reflects the ability to remediate oil under perfectly optimal conditions. Representativ Representativee MOER values for
9
common spill technologies were calculated, showing that dispersants had a significantly higher MOER,
10
followed by skimming and in-situ burning. Determining the MOER for hydrophobic meshes, a new oil
11
recovery technology, highlighted the inability of the EDRC to assess the benefits gained from improving
12
the encounter rate of systems.
13
As a complementary assessment, a cost model was implemented to understand the cost-
14
effectiveness of a given remediation technique under various spill conditions. Mechanical recovery
15
methods were the most costly under various spill sizes and volume. However, if the penalty imposed per
16
unit of spilled oil were waived for any recovered oil, the cost of recovering the oil would be smaller than
17
the averted penalty. Care should be taken in waiving this penalty, since the components in oil vary in their
18
fate and impact. But, creating this t his financial incentive would encourage removal of the spilled oil from the
19
environment, reduce the uncertainty of its impact, and may spur the development of better recovery rec overy
20
technologies. To this end, the authors recommend a heightened effort to develop oil spill recovery
21
techniques, as well as additional research into understanding the fate of individual oil components.
22
28
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3 4
Appendix – Additional MOER Calculations for In-Situ Burning
Wicks (1969) derived a series of equations describing the geometry of towed boom. For a catenary shaped section of boom, its length L and opening width W are are related by
L = 2a · sinh(wL / 2a)
(A.1)
5
where a is a constant that reflects the steepness of the curve. If the ratio of boom length to opening width
6
is specified, the value of a can be found numerically.
7
The sag d of of towed boom is the perpendicular distance from its apex to the open end. A boom
8
with a smaller opening width to length ratio will have a deeper curve, and thus a larger value of d . The
9
sag is given by:
d = = a(cosh( L L /2a) – 1)
10
The area enclosed by b y the boom can then be found from the sag, boom length, and opening width:
A = W (a + d ) – a L
11
(A.2)
Note that the area A used in Section 4.2.3 is one third of the area calculated with Equation A.3.
12
29
(A.3)
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