Assessment of LNAPL movement from
Transformer leaks in Cottesloe Sand
Kerry Daubermann
Honours Project
Department of Environmental Engineering
The University of Western Australia
Supervised by
David Reynolds
Christoph Hinz
4 November 2002
2
Assessment of LNAPL movement from Transformer leaks in Cottesloe Sand
Kerry Daubermann
Honours Project
Department of Environmental Engineering
The University of Western Australia
4 November 2002
Supervised by
Dr David Reynolds
Dr Christoph Hinz
This research has undertaken on behalf of Western Power Corporation
and the Centre for Water Research
My sincerest thanks goes to David Reynolds and Michelle Hurley who provided me with support,
knowledge and inspiration throughout the entire duration of this project.
“For the things we have to learn before we can do them, we learn by doing them.”
- Aristotle, Nichomachen Ethics
3
Abstract
Transformers owned by electrical utilities use large volumes of transformer oil for
insulating and cooling purposes. Leaks from flanges and gaskets on transformers
occur often over the lifespan of a transformer installation. This research investigates
the migration of transformer oil through the subsurface. Extensive field work was
carried out at a single substation site to gather soil samples, which were in turn tested
in the laboratory for hydraulic conductivity and saturation-pressure constitutive
relationships.
Previous studies have shown that LNAPL migration in the subsurface is largely
influenced by subsurface heterogeneity, therefore three-dimensional random
correlated permeability fields were created for the substation based on permeability
statistics generated from the laboratory results.
A three-dimensional, multiphase numerical model was used to determine the effect of
subsurface heterogeneity and various release characteristics on the behaviour of
simulated spills. Oil migration was found to be relatively insensitive to spill surface
area, infiltration rate, rain and to the geostatistics of the subsurface. This was
primarily due to the relative homogeneity of the aquifer at the tested location. The
results of this study show that the movement of transformer oil in Cottesloe Sand may
be modelled using average subsurface properties.
4
Table of Contents
1.0 Introduction..........................................................................................................................................8
2.0 Literature Review ................................................................................................................................92.1 Transformer Oil Spills at Western Power Substations ..................................................................9
2.1.1 Transformer Foundation.............................................................................................................102.1.2 Properties of Transformer Oil......................................................................................................10
2.2 Site Description .............................................................................................................................112.2.1 Selection.................................................................................................................................112.2.2 Location..................................................................................................................................112.2.3 Physical Environment ............................................................................................................122.2.4 Spill History ............................................................................................................................12
2.3 Factors affecting multiphase flow .................................................................................................142.3.1 NAPL migration at the pore scale ...............................................................................................152.3.2 NAPL migration at the field scale..........................................................................................17
2.4 Modelling Multiphase Flow............................................................................................................202.4.1 Model Development...............................................................................................................202.4.2 Mass Balance ........................................................................................................................212.4.3 Momentum Balance...............................................................................................................222.4.4 Constitutive Relations............................................................................................................222.4.5 Difficulties in multiphase flow modelling ...............................................................................28
2.5 Stochastic Site Characterization...................................................................................................302.5.1 Site Characterization .............................................................................................................302.5.2 Monte Carlo Analysis.............................................................................................................33
2.6 Field Experiments..........................................................................................................................34
3.0 Parameter Measurement ..................................................................................................................353.1 Acquisition of field samples ..........................................................................................................353.2 Permeability ...................................................................................................................................373.3 Capillary Pressure Relations ........................................................................................................40
3.3.1 Measurement of Capillary Pressure-Saturation Curves ............................................................403.3.2 Analysis of Capillary Pressure-Saturation Curves ...............................................................42
4.0 Stochastic Site Characterization ......................................................................................................454.1 Variogram Development ...............................................................................................................454.2 Random Field Generation.............................................................................................................46
5.0 Numerical Simulations ......................................................................................................................495.1 Model Description..........................................................................................................................495.2 Model Inputs ..................................................................................................................................49
5.2.1 Fluid and soil properties ........................................................................................................495.2.2 Boundary conditions ..............................................................................................................495.2.3 Initial conditions .....................................................................................................................505.2.4 Constitutive relations .............................................................................................................51
5.3 Monte Carlo Analysis ....................................................................................................................535.4 Effect of Spill Volume....................................................................................................................575.5 Effect of Spill Area.........................................................................................................................605.6 Effect of Infiltration Rate................................................................................................................625.7 Effect of Rain .................................................................................................................................63
6.0 Implications........................................................................................................................................656.1 Comparison to Field Data .............................................................................................................656.2 Applicability and Further Research ..............................................................................................69
6.2.1 Use of average properties...........................................................................................................696.2.2 Extension to other sites ...............................................................................................................69
7.0 Conclusions.......................................................................................................................................72
8.0 Bibliography.......................................................................................................................................73
5
List of Figures
Figure 2-1 Transformers at Cottesloe Substation – a typical substation transformer layout. ................... 9
Figure 2-2 Location of Cottesloe Substation...............................................................................................12
Figure 2-3 Study spill beneath the north side of Transformer One............................................................12
Figure 2-4 Cable oil beneath Transformer One . ........................................................................................13
Figure 2-5 LNAPL movement in the subsurface(modified from Pinder and Abriola 1986).......................14
Figure 2-6 Wettability configurations for water and NAPL .........................................................................16
Figure 2-7 Capillary pressure-saturation relations of Brooks-Corey and van Genuchten .......................24
Figure 2-8 A typical capillary pressure-saturation curve for porous media............................................... 25
Figure 2-9 Relative permeability-saturation relations of Brooks-Corey and van Genuchten ..................27
Figure 2-10 A typical model variogram fitted to an experimental variogram. ...........................................31
Figure 3-1 Location and arrangement of two sample trenches adjacent to Cottesloe Substation ..........35
Figure 3-2 Methodology for collecting undisturbed samples from the trenches ......................................36
Figure 3-3 Methodology for measuring permeability using the constant-head method ........................... 38
Figure 3-4 Histogram for all 96 permeability measurements.....................................................................39
Figure 3-5 Air-water capillary pressure-saturation drainage curves .........................................................41
Figure 3-6 Scaled and fitted capillary pressure-saturation curves for NAPL-water..................................43
Figure 3-7 Fitted capillary pressure-saturation curve for air-NAPL ..........................................................44
Figure 4-1 Direction of the major and minor principle axes....................................................................... 45
Figure 4-2 Best fit model variogram experimental variogram for the major principal axis. ......................46
Figure 4-3 A vertical slice through the Random Field Four permeability field. .........................................48
Figure 5-1 Geometry and boundary conditions of the simulation domain ...............................................50
Figure 5-2 Penetration depth verses time for all realizations. ...................................................................54
Figure 5-3 Second moments of simulated spills in 15 realizations . .........................................................54
Figure 5-4 NAPL distribution for the homogeneous field in comparison to RF4 .....................................56
Figure 5-5 The natural logarithm of permeability of RF4 in comparison to NAPL saturation ..................57
Figure 5-6 Contour plots for the final distribution of NAPL in the y-z plane for various spill volumes.....58
Figure 5-7 NAPL volume in each layer for different spill volumes. ...........................................................58
Figure 5-8 Depth of penetration for varying volumes of oil spilled in 1 node (0.12m2) ............................59
Figure 5-9 Second moments in the x and y direction for various spill volumes........................................59
Figure 5-10 Contour plots for the final distribution of NAPL in the y-z plane for various spill areas .......60
Figure 5-11 NAPL saturation profile for each entire layer for various spill areas.....................................61
Figure 5-12 Volume of oil in the domain plotted against time for varoius spill area..................................61
Figure 5-13 Contour plots for the final distribution of NAPL for various infiltration rates .........................62
Figure 5-14 NAPL saturation in each depth layer for varying infiltration rates .........................................63
Figure 6-1 Location of core samples taken from beneath Transformer One at Cottesloe Substation ....66
Figure 6-2 Shapes of dye infiltration tests .................................................................................................68
Figure 6-3 Soil types assigned to Western Power Metropolitan Substations...........................................70
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List of Tables
Table 2-1 Physical Properties of Shell Diala Oil B (Shell 1999).................................................................10
Table 3-1 Statistical summary of results of permeability tests conducted on 96 samples ......................39
Table 4-1 Inputs into FGEN91 which was used to create multiple random permeability fields...............47
Table 5-1 Numerical model input parameters used in all NAPL simulations............................................52
Table 6-1 Summary of measured concentrations of TPH on core samples ............................................67
7
List of Appendices
Appendix A Laboratory data for constant head permeability tests
Appendix B Laboratory data for NAPL-air pressure-saturation curve
Appendix C Particle size analysis for Cottesloe Sand
Appendix D Non-dimensionalized NAPL-water curves
Appendix E Location and permeability for all samples
Appendix F Experimental and model variograms for Cottesloe Sand
Appendix G Input code for FGEN91
Appendix H Porosity calculations
Appendix I Initial water saturation profile for simulations
Appendix J Input pressure-saturation-permeability curves for the numerical model
Appendix K Summary of numerical simulations for the Monte Carlo Analysis
Appendix L Summary of numerical simulations for effects of spill volume
Appendix M Summary of numerical simulations for effects of spill area
Appendix N Field data for core samples collected beneath Transformer One
Appendix O Measured oil concentrations from samples collected from Transformer One
Appendix P Dimensions of individual dye bodies and a fitting linear relationship
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1.0 Introduction
Western Power Corporation is currently investigating the extent of possible contamination that may
have been caused by oil leaks from transformers at its substation sites. The investigation was
motivated by the Contaminated Sites Bill 2000, which will require contaminated sites to be identified,
reported and classified so that sites posing potential ecological or health risks can be assigned an
appropriate response (Legislative Assembly Council 2000).
Western Power has addressed the pending legislation with the Substation Strategy so that relevant
sites can be detected and reported to the Department of Environment and Water Catchment
Protection (DEWCP). The strategy is divided into three main phases: Preliminary Screening
Assessment, Screening Assessment and Risk Assessment. The aim of Screening is to determine
whether groundwater below each Western Power substation site is at any risk of contamination by
spilled transformer oil. The Risk Assessment should verify sites that do not pose a risk to ecological
or human health, primarily by determining the maximum possible depth of penetration of transformer
oil.
Bowman Bishaw Gorham (1997) performed a risk assessment on Southern Terminal Transformer
One by extensive sampling and modelling using the Hydrocarbon Spill Screening Model (HSSM). The
study was limited by the assumptions of a homogeneous subsurface, no biological degradation, a
constant water flux through the soil profile and a constant spill rate of oil over spill period. Similarly,
Lukehurst (2001) conducted a study to determine a suitable preliminary screening method for Western
Power transformer spills by comparing the HSSM with a simple field experimentation method. The
HSSM was proclaimed most useful in eliminating sites from further investigation when accurate spill
data was known and worst case parameters were used, and thus may be used for Screening
Assessment.
The purpose of this research is to investigate the subsurface movement of transformer oil, a light non-
aqueous phase liquid (LNAPL), in the context of Western Power substations. Oil migration is
examined in three dimensions using numerical simulations and observed field data for a particular spill
located beneath Transformer One at Cottesloe Substation. Inputs for the numerical multiphase model,
SWANFLOW (Faust 1985), include site-specific data, particularly detailed measurements of the
spatially variable soil characteristics, permeability and capillary pressure-saturation relationships. A
detailed reconstruction of subsurface heterogeneity is necessary for a full investigation, as research
over the past several decades has indicated that spatial variations in hydrogeological properties play
an important part in controlling LNAPL movement. Monte Carlo analysis of simulated oil spills is
conducted to determine the average behaviour of spills in statistically similar permeability fields. Spill
characteristics, including volume, release area and infiltration rate, are also investigated through
numerical simulations as these parameters have also been shown to influence NAPL migration.
This research will determine the effects of subsurface heterogeneity and spill release characteristics
on transformer oil migration in Cottesloe Sand. Results will be discussed in the context of Western
Power transformer spills and recommendations for further work made.
9
2.0 Literature Review
2.1 Transformer Oil Spills at Western Power Substations
There are a total of 138 Western Power Substations in Western Australia, with 65 of these located in
the Perth Metropolitan Area. The purpose of these substations is to transfer power by changing
voltages from one level to another. The primary piece of equipment used to perform this transition is a
transformer (TX). There are generally 2 or 3 transformers spaced evenly apart at each substation
(Figure 2.1).
Figure 2-1Transformers at Cottesloe Substation – a typical substation transformer layout. There areusually 2 or 3 transformers spaced evenly apart at all sites.
Inside each transformer exists a chamber filled with a light density fluid commonly known as
Transformer Oil. The oil acts as an electrical coolant, as well as preventing arcing and short circuits.
Oil leaks from gaskets and flanges on transformers are inevitable. A conservator sits above the main
oil chamber to automatically replace oil as it escapes via a random distribution of leaks. When the
level in the conservator is low, personnel are alerted and the oil is physically replaced. The volume of
oil replacement is significant because it reflects the volume lost from the transformer which must
ultimately enter the subsurface. The volume of oil inside each transformer ranges from 10,100 L (TX1
Cottesloe Substation) to 142,881 L (TX1 Northern Terminal), which correspond to conservator
volumes of 757.5 L and 10,716 L respectively (Lukehurst 2001).
Oil spills are sporadic and not often large or instantaneous, which makes the task of documenting
them somewhat difficult. Very few records involving spill incidents exist. Only recent maintenance
records indicate dates of major leaks or low conservator oil levels, but they rarely specify the actual
volume of oil lost or replaced.
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2.1.1 Transformer Foundation
Each transformer sits on a 33cm thick rectangular concrete slab which are surrounded by a
rectangular brick wall called a bund , as can be seen in Figure 2.1. The bund separates the
transformer from the rest of the site and limits the surface spreading of oil, which is particularly
important in the case of an electrical fire.
Due to construction and safety requirements, the subsurface profile inside each bund generally
consists of the following (starting from the surface): 15cm blue metal aggregate; 15cm limestone
chunks; 100cm disturbed compacted construction sand; natural subsurface.
Oil will fall directly onto either the concrete slab or the blue metal aggregate depending on the location
of the leak. Where oil falls beyond the slab and enters the subsurface, flow is unconfined.
Environmental awareness has prompted Western Power to include sealed bunds in all new substation
constructions.
2.1.2 Properties of Transformer Oil
The oil currently used for insulating and cooling in transformers is Diala Oil B (Shell 1999).
Transformer oil is classified as a light non-aqueous phase liquid (LNAPL) because it has a density less
than water. It is a mineral oil with a low viscosity and good dielectric properties to match its purpose.
Bowman Bishaw Gorham (1997) concluded that the oil has a low solubility, is comprised completely of
alkanes and cycloalkanes, and is free from aromatic hydrocarbons. Physical properties of the oil are
tabulated below (Table 2.1).
DESCRIPTION UNITS VALUE
Density @ 15°C kg/L 0.885
Viscosity @ 20°C mm2/s 20.0
Water Content ppm <15
Interfacial Tension mN/m 48
PCB Content ppm <0.03
Gassing Tendency _L/min +10
Molecular Composition1 LEPH n-C10 to n-C18
HEPH n-C19 to n-C32
18%
82%
1 Bowman Bishaw Gorham 1997
Table 2-1 Physical Properties of Shell Diala Oil B (Shell 1999)
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2.2 Site Description
2.2.1 Selection
Cottesloe Substation was chosen at the study substation site for the following reasons:
• A substantial spill volume could be assumed due to the age of the substation and the
presence of relatively large oil stain areas. This would allow simulated oil penetration depths
to be compared to an actual detectable penetration depth.
• Depth to water table was large enough to assume mostly unsaturated flow, as well as
ensuring that deep trenches could be excavated without becoming flooded.
• The geology of the area indicated coastal sand: a simple type of geology in terms of
measuring hydraulic properties and it reflected similar geologies of other substations. This
similarity would aid in the application of the Risk Assessment model to Western Power sites.
• A vacant site, also belonging to Western Power, was situated adjacent to the substation that
would allow excavation of trenches for extensive sampling for soil hydraulic properties.
2.2.2 Location
Cottesloe Substation is situated on the corner of Curtin Avenue and Jarrad Street in Cottesloe, Perth
(Figure 2.2). The substation was built in the 1958 and is a relatively old station due to the age of the
area.
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Figure 2-2 Location of Cottesloe Substation
2.2.3 Physical Environment
Cottesloe Substation lies on Cottesloe Sand, which is a shallow sand derived from Tamala Limestone.
This soil type is yellow and brown, of residual origin, moderately sorted and medium to coarse grained
(Geological Survey 1986).
Bore data from the Water and Rivers Commission show that the water table probably lies between
11.6m and 19.8m below the site. The Perth Groundwater Atlas (Water and Rivers Commission 2002)
gives a depth to water table ranging between 6m to 11m.
Rainfall in Perth falls mostly between May and August and is approximately 850 mm/year (Bureau of
Meteorology 2001).
2.2.4 Spill History
The transformer oil spill investigated in this study is located on the north side of Transformer One
(TX1) at Cottesloe Substation. The spill is comprised of two discrete stains as can be seen in Figure
2.3. The main stain is 1.35m2 in area and imitates the radial shape of the overlying transformer. Due
to the nature of leaks, this is a common spill shape under many transformers. A smaller stain 0.15m2
in area exists just beyond the perimeter of the main stain, and is most probably caused by oil drips
from an over-hanging transformer part. Therefore, the total stain area is approximately 1.5m2.
Figure 2-3 Study spill beneath the north side of Transformer One. Two discrete stains are evident,one large (1.35m2) and one small (0.15m2)).
Considering the age of the substation and the lack of detailed records relating to past spills, it is
difficult to predict with any confidence how much oil has been spilt onto the ground beneath the
13
transformer. The only existing records at Western Power involving Transformer One oil leaks at
Cottesloe Substation indicate the following key events:
• September 1997: Repair minor oil leak. Top up of conservator to correct oil level.
• November 1997: Serious oil leaks. Refurbishment of Transformer One (TX1).
• January 2001: Repair oil leak from low voltage (LV) cable box (196.552L).
The volume of oil held in TX1 is 10,100L and the volume of the above conservator is 757.5L. The
average volume or time period between conservator oil top ups is unknown.
Records from January 2001 show a loss of approximately 200L of oil from the LV cable box. Although
it is important to recognize this incident, it should be noted that cable oil leaks are not identical to
transformer oil leaks. Cable oil has different properties to transformer oil and enters the subsurface in
a different manner to transformer leaks. While transformers oil drips from the transformer in random
places, cable oil leaks from the LV cable box and flows down the cable surface which enters the
ground beside the transformer concrete slab (Figure 2.4). Cable oil leaks are also of concern for
Western Power but will not be included in this study.
Figure 2-4 Cable ground entry and cable oil contamination beneath TX1 at Cottesloe Substation.
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2.3 Factors affecting multiphase flow
When transformer oil is spilled, it flows through the aggregate beneath the transformer and then
penetrates into porous media. On its travels, the immiscible transformer oil, or LNAPL, encounters air
and water phases initially present in the subsurface. This phenomenon is called multiphase flow,
which is defined as the relative movement of two or three immiscible phases, namely gas, water and
non-aqueous phase liquid (NAPL). Components of the LNAPL may exist in the subsurface as four
separate phases: immiscible liquid, volatile gas phase, dissolved aqueous phase and adsorbed to soil
particles.
After release, the immiscible LNAPL moves downwards in the unsaturated zone due to gravity and
capillary forces. Vapour from the LNAPL in the unsaturated zone can move significant distances
through the air-filled pores. If a sufficient volume is released, the LNAPL may reach the saturated
zone. In this instance, a LNAPL will float on the water and spread across the capillary fringe. The
distribution is then a function of LNAPL, air and water pressures and pore size distribution (Mercer and
Cohen 1990). In the saturated zone, soluble components of the LNAPL may dissolve in groundwater
and move as a plume with local flow. The movement of LNAPL in the subsurface is illustrated in
Figure 2.5.
This study is concerned only with the immiscible liquid LNAPL phase of transformer oil and its flow in
the unsaturated zone. This assumption of negligible interphase mass transfer (i.e. transport
phenomena) is common to many models (eg. Faust 1985; Kueper and Frind 1991a; Huyakorn,
Panday and Wu 1994)
Figure 2-5 Schematic representation of LNAPL movement in the subsurface(modified from Pinder andAbriola 1986)
15
Many studies relating to different aspects of multiphase flow systems have been carried out in the past
several decades. Mercer and Cohen (1990) presented a detailed summary and review on previous
work performed on NAPL movement in the subsurface. The review included descriptions of important
properties and mathematical equations to describe NAPL flow.
Multiphase flow is a topic of active research because of the high demand for oil spill simulators for oil
recovery and environmental applications (Hemond and Fechner 1994). However, it is also difficult and
expensive to undertake research in this area. Miller et al. (1998) found that there is an overall lack of
consideration for low NAPL saturation for environmental applications as the study of NAPL flow at low
saturation is not of economic importance for most petroleum applications. The direction of flow of the
NAPL is another major difference between petroleum and environmental applications.
2.3.1 NAPL migration at the pore scale
Multiphase flow processes at the pore scale ultimately controls NAPL movement at the field scale.
Therefore, an understanding of these processes and the determination of factors affecting flow at this
scale provides a foundation for the examination of NAPL migration at larger scales.
Density
The density of a NAPL has a large impact on gravity flow forces. It also determines whether the oil will
float or sink if it reaches the water table (Mercer and Cohen 1990). NAPLs lighter than water
(LNAPLs) will float and NAPLs denser than water (DNAPLs) will sink in water saturated medium.
Viscosity
Internal fluid resistance to flow is measured by viscosity. Fluids with low viscosities penetrate more
rapidly into soil than high viscosity fluids (Mercer and Cohen 1990). If the viscosity of oil is greater
than that of water, then the mobility of water is favoured (Mercer and Cohen 1990).
Interfacial tension
At the boundary between immiscible fluids in direct contact there exists a kind of ‘skin’ arising because
of the difference between molecular cohesion within a phase and adhesion effects between phases
(Schowalter 1979). Interfacial tension is a measure of this difference and influences multiphase flow
because of its direct effect on the capillary pressure across the immiscible fluid interface (Mercer and
Cohen 1990). The units of interfacial tension are energy per area (dyne cm-1).
Wettability
Wettability describes preferential spreading of a fluid onto a solid surface and depends on interfacial
tension (Mercer and Cohen 1990). The wetting fluid will tend to spread over grains in preference to
the non-wetting fluid. The wetting fluid will occupy smaller voids and pore throats, whereas the non-
wetting fluid will be restricted to larger pores (Mercer and Cohen 1990).
Wettability can be measured by the contact angle (_) - the angle between the solid surface and the
tangent of a drop of the fluid at the solid interface. If _ between the fluid and the solid interface is less
16
than 90°, the fluid is said to be wetting. If _ is greater than 90°, the fluid is said to be non–wetting
(Mercer and Cohen 1990) (Figure 2.6).
Figure 2-6 Contact angle for wetting and non-wetting fluids. This diagram shows the wettabilityconfigurations for water and NAPL (modified from Mercer and Cohen 1990)
In multiphase systems, water is generally assumed to be the wetting fluid, followed by NAPL then air.
This is called the wettability sequence, and is a crucial and common assumption to many multiphase
models. However, wettability depends on many factors and so it is spatially variable (Honarpour et al.
1986).
Capillary pressure
Capillary pressure is defined as the difference in pressure between the wetting and non-wetting fluid
phases in a porous medium (Miller et al. 1998; Mercer and Cohen 1990):
WNCNW PPP −= (1)
where
PCNW : capillary pressure [Pa]
PN : non-wetting phase pressure [Pa]
Pw : wetting phase pressure [Pa]
Capillary pressure is dependent on interfacial tension, wettability (contact angle) and the pore size
distribution of the soil:
rP NW
CNW
φσ cos2=(2)
where
r : radius of pore that non-wetting fluid must enter
φ : contact angle [°]
_ : interfacial tension between non-wetting and wetting fluid [dyne cm-1]
17
Capillary pressure is a major aspect of multiphase flow as it causes porous media to draw in the
wetting fluid and push out non-wetting fluid from smaller pore spaces (Bear 1972) and so affects the
shape of a NAPL spill in the unsaturated and saturated zone (Mercer and Cohen 1990).
2.3.2 NAPL migration at the field scale
The vertical and lateral migration of NAPL in the subsurface at the field scale is controlled by both
gravitational and capillary forces (Guarnaccia et al. 1997; Kessler and Rubin 1987; Mercer and Cohen
1990). After release, NAPL flows downward as one continuous phase due to gravity and spreads
laterally due to capillary forces, horizontal bedding and spatial variability (Mercer and Cohen 1990;
Poulsen and Kueper 1992). Lateral spreading is related to penetration depth because an increase in
the horizontal movement of NAPL results in a smaller volume available for penetration (Poulsen and
Kueper 1992).
Factors affecting NAPL movement at this scale can be classified into fluid and porous media
properties, the nature of NAPL release and subsurface heterogeneity.
2.3.2.1 Fluid and porous media properties
Fluid and porous media properties affecting NAPL migration at the field scale include capillary
pressure, saturation and permeability. These three fluid and porous media properties are highly
interdependent, or non-linear, because the relative permeability of a fluid depends on its saturation,
and saturation depends on capillary pressure. These relationships are called capillary pressure-
saturation-permeability relations and are a key element of multiphase flow models. The importance of
these relations will be discussed in more detail in section 2.4.4.
Residual saturation, Sr, is an important aspect of multiphase flow that is related to the capillary
pressure-saturation-permeability relationship. After initial subsurface migration, NAPL may become
immobilised due to residual liquid becoming entrapped in pore spaces causing the flow to become
discontinuous. The saturation of NAPL when the flow stops is called the residual saturation (Hemond
and Fechner 1994):
voids
NAPLr V
VS =
(3)
Values of Ss generally range from 0.10 to 0.30 for mineral oil in sands (Mercer and Cohen 1990).
Residual saturation is controlled by capillary forces (i.e. pore size distribution, interfacial tension,
wettability), as well as porosity, intrinsic permeability and initial water saturation, and is therefore
highly spatially variable. A large capillary pressure, such as a large NAPL pressure head, increases
residual saturation by forcing the non-wetting fluid into smaller pore spaces where it may remain
entrapped if pressure is decreased (Mercer and Cohen 1990). Therefore, in the presence of water in
18
the unsaturated zone, NAPL may be retained as residual, or non-wetting blobs (Mercer and Cohen
1990). In the saturated zone, the fluid viscosity ratio, density ratio and hydraulic gradient also control
residual saturation. Residual NAPL is difficult to remove or remediate and may cause long term
contamination due to slow dissolution or vaporisation.
The displacement entry pressure (Pd) is the capillary pressure that must be overcome for the non-
wetting fluid to enter a wetting fluid saturated media (Mercer and Cohen 1990). This principle explains
perching of potentially mobile pools of NAPL upon lenses containing soil with a small average pore
radius (r). These lenses act as capillary barriers to flow and pathways that require the least capillary
resistance to entry are followed.
Spill penetration depth is partly controlled by residual saturation. If a greater volume of oil can be held
within the pores (residual), then the volume available for further migration is reduced (Poulsen and
Kueper 1992). Van Geel and Sykes (1997) illustrated the effects of residual saturation in predicting
LNAPL distribution in the unsaturated and saturated zone through numerical modelling and laboratory
work.
2.3.2.2 Nature of NAPL release
The nature in which NAPL enters the subsurface has a large effect on the spatial distribution of NAPL
migration paths at the field scale (Poulsen and Kueper 1992; Guarnaccia et al. 1997; Feenstra and
Cherry 1988). Quite often in real spill scenarios, NAPL release history (in particular volume, duration
and infiltration area) are not known, and so investigations into the effects and sensitivity of these
parameters are important .
Poulsen and Kueper (1992) examined the effect of source release rate and porous media
heterogeneity on the spatial distribution and depth of penetration of tetrachloroethylene (PCE) in the
unsaturated zone of a sandy aquifer. They showed that capillary forces dominated the system when
the PCE was released as a drip. Under ponded rapid infiltration (“instantaneous”) release, gravity
forces only appeared dominant directly beneath the release. The drip release penetrated 1.6 times
deeper than the instantaneous release because the cross sectional area was 1000th of the size.
Saturation of the NAPL below the instantaneous release was also much larger than for the drip
release because the pressure due to ponding could force the NAPL into smaller pores. The study
therefore showed that the depth of penetration was a function of source release strength.
In a similar study, Kueper and Gerhard (1995) investigated the effect of source release location, size
and strength (source capillary pressure) on infiltration rates and the degree of lateral spreading of
DNAPL into a saturated heterogenous porous medium. Twenty five numerical simulations in different
spatially correlated random hydraulic conductivity fields showed that infiltration rates for point source
releases were log-normally distributed with a similar variance to the underlying permeability field.
They also showed that lower source capillary pressure releases (i.e. slow, dripping release) of non-
wetting liquids results in greater lateral spreading than a catastrophic, high capillary pressure release.
19
2.3.2.3 Subsurface Heterogeneity
If hydrogeological properties affecting multiphase flow (eg. permeability, porosity) are spatially
variable, then it is intuitive that NAPL distribution in the subsurface will be directly related to this same
pattern of heterogeneity.
Past research has explored the response of NAPL migration to variability in subsurface properties.
Simulations of Kueper and Frind (1991b) demonstrated the sensitive response of NAPL migration
pathways to even relatively minor variations in the capillary properties of the porous medium. They
explored the vertical and lateral migration of NAPL in porous media and the encounter with a lens of
low permeability. In this case, the NAPL will need to build up the required saturation to create the
necessary capillary pressure that will allow the non-wetting fluid to penetrate the lens. Lateral
spreading is also promoted above such lenses because of the increases saturation and the dissipation
of the pressure head.
Poulsen and Kueper (1992) examined the effect of porous media heterogeneity on the spatial
distribution of PCE and also showed that the NAPL migration in sand was sensitive to variations in
permeability and capillary characteristics. Kueper and Gerhard (1995) demonstrated that the order of
encounter of varying permeability lenses influences the infiltration rate of a non-wetting phase release,
and that infiltration rates for equivalent releases in multiple realizations exhibit similar statistical
distributions to the fields themselves. Numerical simulations conducted for point source releases also
resulted in a lower degree of lateral spreading in an equivalent homogenous medium than the entire
ensemble of heterogeneous results. Bradford et al. (1998) generated spatially correlated permeability
fields to examine the effect of chemical and physical heterogeneity on DNAPL migration. They found
that spatial variations in wettability characteristics can greatly influence aspects of DNAPL distribution
such as saturation, lateral spreading and depth of infiltration.
20
2.4 Modelling Multiphase Flow
Numerous models have been developed over the past several decades to simulate the simultaneous
flow of air, water and NAPL in porous media (eg. Abriola and Pinder 1985a,b; Faust 1985; Kuppusamy
et al. 1987; Huyakorn et al. 1994; Panday et al. 1994). Models vary greatly in complexity depending
on the assumptions made, ranging from simple air-water flow (Richards 1931) to compositional three-
phase flow (Miller et al. 1998). Models also range in the number of dimensions modelled (1D, 2D,
3D), numerical methods employed (eg. finite difference vs. finite element approach, iteration
techniques) and purpose of the model (eg. research, oil recovery, environmental applications).
Van Dam (1967) was the first to recognise NAPL movement in groundwater as a two-phase flow
phenomenon. Following this recognition, a suite of models were created but generally assumed
piston-like flow, thus ignoring capillarity effects. Models then began incorporating capillarity, such as
the work of Little (1983). Little’s work was extended by Faust (1985) to include a static air phase - an
important step for NAPL migration modelling in the unsaturated zone. Transport phenomenon (i.e.
volatilisation and dissolution) was included in the 2D model of Abriola and Pinder (1985a,b).
Kessler and Rubin (1987) suggested a general methodology for the development of an oil spill
migration simulator, but this was limited to sandy soil and only several days after spill release. They
also used a numerical model to simulate oil spill migration and performed laboratory measurements
for retention curves, hydraulic conductivity and infiltration rates. Kueper and Frind (1991a) developed
a 2D finite difference model for DNAPL and water movement which produced complimentary
experimental results (Kueper and Frind 1991b). This model was used by Kueper and Gerhard (1995).
Rathfelder and Abriola (1998) performed numerical simulations to explore the sensitivity of numerical
solutions to grid resolution and found that in some cases, grid resolution may need to be 1/5 to 1/10 of
the displacement pressure head. Modelling by Panday et al. (1994) gave evidence of a passive air-
phase formulation, which produced similar saturation profiles to a fully three-phase simulator except
near the surface of the soil column. However, they concluded that “there is still a lack of assessment
as to how well the passive air-phase formulation performs in depicting the three-phase flow behaviour
and saturation distribution.”
Miller et al. (1998) found that common trends in multiphase flow modelling included the frequent
assumption of local equilibrium, simulation sizes of the order of 100 to 10000 nodes and the use of
non-hysteretic forms of capillary pressure-saturation-permeability relations in models in the
environmental field.
2.4.1 Model Development
Computer multiphase models are built from small constant volumes called Representative Elementary
Volumes (REVs). Microscopic processes are averaged over the REV so that discontinuity at this
spatial scale cannot be recognised, so that at each point in the REV it is assumed that there exists a
local thermodynamic equilibrium (Helmig 1997). This enables continuum mechanics (i.e. mass,
momentum, energy balances) to be applied and new parameters, such as saturation, created.
21
Formulating a multiphase flow model involves producing a minimum set of these balance equations for
each phase to describe system behaviour. The momentum equation, a generalized form of Darcy’s
Law, is substituted into a mass balance and the resulting simultaneous equations are solved with a set
of constitutive relations.
However, detailed steps for formulation depend on the specific purpose and required complexity of the
model. When the purpose is clear, assumptions and approximations must then be made so that
computational demands are reduced. Even with a similar approach, models may differ according to
assumptions made, computational methods employed, and the choice of primary variables (a subset
of fluid pressures and saturations). Wu and Forsyth (2001) presented an analysis and general
recommendations for selecting primary variables for multiphase subsurface flow simulations, and
demonstrated that the selection “depends on the sensitivity of the system of equations to the variables
selected at given phase and flow conditions.”
Pinder and Abriola (1986) published a broad overview of the task of modelling NAPL movement in
groundwater. More recently, Miller et al. (1998) compiled a review on the current status of multiphase
modelling, highlighting current research areas. Two aspects of the formulation of flow simulation were
considered: continuum balance (mass and momentum) and closure relations (constitutive relations
and equations of state). This review will not consider equations of state as interphase mass transfer is
assumed to be negligible.
2.4.2 Mass Balance
The most elementary balance equation derived using the REV approach is the mass balance. A
general mass balance (4) can be written out for each phase _ if it is assumed that there are no
chemical or biological reactions, chemical and physical properties of the NAPL are invariant, mass
exchange between phases is negligible and movement of NAPL is by advection only (i.e. no diffusion
or dispersion):
( ) ( ) 0=⋅∇+∂∂
ααααα υρερεt
(4)
where
_ = soil (s), air (a), water (w), NAPL (n)
__ : mass average velocity of the _ phase (Darcy velocity) [m3 m-2 s-1]
__ : fraction of volume occupied by the _ phase
__ : density of the _ phase [kg m-3]
∇ : differential operator
The first term on the left hand side of equation (4) represents the accumulation of mass in phase _
and the second term describes the movement of mass due to advection of the phase. Equation (4) is
subject to following constraint:
1=∑α
αε (5)
22
If the gas phase is assumed to remain at atmospheric pressure and the porous medium is assumed to
be rigid (i.e. porosity is steady-state), then equations for the gas and soil phase are not needed. If
fluids are assumed incompressible (i.e. density does not change in time or space), then density terms
are not needed. Following these assumptions, (4) simplifies to:
( ) ( ) 0=⋅∇+∂∂
ααα υnSSt
n(6)
where
n : porosity
2.4.3 Momentum Balance
A momentum balance for the continuum is developed to specify fluid velocities as a function of fluid
pressures and saturations. This is achieved with the use of a macroscopic form of the momentum
equation, Darcy’s Law:
( )zgPkkr ∇−∇−= αα
α
αα ρ
µυ
(7)
where
k : intrinsic permeability [m2]
kr_ : relative permeability of the _ phase [-]
µ_ : dynamic viscosity of the _ phase [Pa s-1]
P : pressure of the _ phase [Pa]
z : elevation [m]
Darcy’s law (7) is then substituted into (6) and the resulting equation is written out for water (_ = w)
and NAPL (_ = n):
( ) ( ) 0=
∇−∇⋅⋅∇+
∂∂
zgPkk
St
n www
rww ρ
µ
(8a)
( ) ( ) 0=
∇−∇⋅⋅∇+
∂∂
zgPkk
St
n nnn
rnn ρ
µ
(8b)
For three-phase flow, equation (8) is subject to the constraint:
1=++ gnw SSS (9)
Equation (8) can be solved with the substitution of capillary pressure - saturation - relative permeability
relations, also known as constitutive relations.
2.4.4 Constitutive Relations
Constitutive relations express the functional relationship between capillary pressure, saturation and
relative permeability of fluids in a multiphase system. Development of these relations are a key
23
component of multiphase models because they enable closure of the system of balance equations
through the determination of unknowns with accessible parameters (Miller et al. 1998). The relations
depend on pore structure, media and fluid characteristics and are usually empirically based (Miller et
al. 1998). Numerous investigations into capillary pressure - saturation - permeability relations for
multiphase flow systems have been published (eg. Dullien 1992; Corey 1994; Demond et al. 1996;
Wipfler and van der Zee 2001). However, research in this area is often limited by the difficulty,
expense and time needed for the development of a full set of relations for three-phase systems (Miller
et al. 1998).
Capillary pressure-saturation relations for three phases are usually determined by measuring the
relation for two fluid pairs and then using a scaling procedure (Lenhard and Parker 1987) to extend
these to the third fluid pair. The extension of two-phase relations to three-phases is based on a crucial
assumption called Leverett’s assumption (1941) which is discussed in section 2.4.4.3. Along with the
direct measurement of permeability and the use of a pore network theory (eg Burdine 1953; Mualem
1976), capillary pressure-saturation relationships are often used to resolve the associated saturation-
relative permeability relationship for two-phase systems. The relative permeability-saturation relation
of NAPL in three-phases is commonly computed from two-phase relations using the approaches of
Stone (1970, 1973) or the approach by Parker (Parker and Lenhard 1987; Parker et al. 1987).
Detailed steps for developing constitutive relations for a water-wet, hysteretic three-fluid system were
outlined by Miller et al. (1998).
2.4.4.1 Capillary Pressure-Saturation Relations
Saturation is a macroscale property and a vital parameter of multiphase flow. Model formulations are
often based around saturation because it can be directly correlated to capillary pressure and relative
permeability.
The relationship between capillary pressure and saturation of a continuous fluid phase is known as the
capillary pressure-saturation relation, or retention curve. Such a relation describes the adhesion
between the liquid and solid fractions (i.e. capillarity of the system) and quantifies this at the
macroscale (Kessler and Rubin 1987). The Brooks-Corey (1964) and van Genuchten (1980) models
are the two most popular and commonly employed empirical models that relate capillary pressure to
the saturation of fluid phases (i.e. determine an equation for the retention curve).
The Brooks-Corey (BC) model is:
( )λ
=
−−=
c
d
wr
wrwce p
p
S
SSpS
1 for pc ≥ pd
(10)
The van Genuchten (VG) function is:
( ) ( )[ ] mnc
wr
wrwce p
S
SSpS
−⋅+=
−−
= α11
for pc > 0(11)
24
where
Ss : effective saturation
Sw : wetting fluid saturation
Swr : residual wetting fluid saturation
_ : BC parameter [-]
pd : BC parameter (entry pressure) [Pa]
n : VG parameter [-]
m : VG parameter (usually defined as m = 1 – 1/n) [-]
_ : VG parameter [1/Pa]
The formulas can be rearranged to expresses capillary pressure as a function of effective saturation:
Brooks-Corey:
( ) λ1
−= edwc SpSp for pc ≥ pd
(12)
van Genuchten:
( ) ( ) nmewc SSp
/1/1 11 −= −
α for pc > 0
(13)
The typical shapes of the two capillary pressure-saturation functions are presented in Figure 2.7, and
highlights the discrepancy between them.
Figure 2-7 Capillary pressure-saturation relations of Brooks-Corey and van Genuchten with equalphysical conditions (taken from Helmig 1997)
Many studies have made comparisons between the Brooks-Corey and van Genuchten fitting
functions. Lenhard et al. (1989) developed correlation formulas to relate the parameters between the
two relations. Oostrom and Lenhard (1998) presented an investigation into the two common
constitutive relation models in developing parameters used to model LNAPL in sandy porous media.
Rathfelder and Abriola (1998) performed numerical simulations to explore the use of fitting capillary
25
retention data with the Brooks-Corey and van Genuchten models. They found that differences
resulting from fitting function selection occurred mainly due to the representation of capillary pressure
below entry pressure near Sw = 1. The Brooks-Corey model exhibits a distinct entry pressure whereas
the van Genuchten does not. It is for this reason that Brooks-Corey generally produces better results
for sands with a narrow pore size distribution and van Genuchten is more appropriate for fine textured
soils with a large pore size distribution (van Genuchten and Nielsen 1985). Rathfelder and Abriola
also showed that Brooks-Corey solutions exhibited greater spreading, less inclination to penetrate
semi-permeable layers and poorer spatial convergence.
Capillary pressure-saturation relations depend on saturation history (i.e. if the porous media has
previously been drying or wetting to reach the present saturation content). This is called hysteresis.
Drainage occurs when the non-wetting fluid invades pores, taking the place of the wetting fluid.
During this time, wetting fluid in large pores drain first while smaller pores drain reluctantly due to
capillary retention, and pores do not even drain at all (residual saturation). During wetting, or
imbibition, the smaller pores are filled up first with the wetting fluid and the large pores fill up last.
Therefore, there exists a lower capillary pressure curve with saturation as is shown in Figure 2.8.
Figure 2-8 A typical capillary pressure-saturation curve for porous media. Hysteresis is illustrated bya lower secondary wetting curve than the main drainage curve (A,B,C) of the wetting fluid (taken fromKueper et al. 1993).
Models that incorporate a hysteretic relationship must use a separate fitting function for imbibition and
drainage curves and use these to determine separate parameters with a fitting function.
2.4.4.2 Saturation-Relative Permeability Relation
When more than one phase exists in porous media, the flow of each phase is restricted due to
competition for pore space (Mercer and Cohen 1990). Therefore, the conductivity of each fluid in the
system is a function of its mobile saturation and is measured by relative permeability, a dimensionless
number ranging from 0 to 1. The relative permeability of NAPL is 0 at residual saturation and 1 at
26
100% saturation. At intermediate saturations, the permeability of both fluids is reduced such that the
sum of their relative permeabilities does not equal 1.
The effective permeability of each competing fluid in a system can be calculated by multiplying the
relative permeability of the fluid by the intrinsic permeability of the soil:
( ) ( )θθ rikkk = (14)
where
k(_) : effective permeability of the fluid at saturation _ [m2]
ki : intrinsic permeability at complete saturation respectively [m2]
kr : relative permeability [-]
Multiphase models require the development of the relationship between relative permeability and
saturation. Due to the difficulty and expensive processes used to derive three–phase site-specific
saturation-permeability curves, it is often necessary to rely on parameterization (Helmig 1997). This
can be achieved through the development of empirical potential functions of effective water saturation
(Se), but more often by the development of functions differentiated on the basis of the pressure-
saturation relations (pc(Sw)) and a theoretical model of the pore network. The latter is based on the
theory that pressure-saturation relations and saturation-permeability relations are influenced by the
same pore structure.
The common empirical models used to fit retention data, Brooks-Corey and van Genuchten, are
extended with pore network theorems to provide estimations of the relative permeability-saturation
function. Both formulations include parameters already defined from the capillary pressure-saturation
relations which make them convenient and simple to apply.
The Brooks-Corey model is usually applied in conjunction with the pore network of Burdine (1953):
λλ32+
= erw Sk(15)
( )
−−=
+λ
λ22 11 eern SSk
(16)
The van Genuchten model usually incorporates Mualem Theorem (1976):
21
11
−−=
m
meerw SSk ς
(17)
( )m
meern SSk
21
11
−−= γ
(18)
The form parameters, _ and _, describe the connectivity of the pores (Mualem 1976) and are generally
taken to equal 1/2 and 1/3 respectively (Busch et al. 1993). Figure 2.9 shows a typical relative
27
permeability-saturation relationship for water and NAPL in porous media, as well as demonstrating the
difference between the two fitting functions. Like capillary pressure-saturation, saturation-permeability
relations also exhibit hysteresis.
Figure 2-9 Relative permeability-saturation relations of Brooks-Corey and van Genuchten with equalphysical conditions (taken from Helmig 1997)
2.4.4.3 Scaling of Constitutive Relations
Extending two-phase constitutive relations to three-phases with a scaling procedure was first suggest
by Leverett (1941) who argued that interfacial curves are fixed by the pore size distribution for a
monotonic displacement process. He also proposed that in a three-phase system, the interface
between the continuous gas and liquid phase, as well as the continuous NAPL and water phase, are
independent of the number and proportions of liquids in the porous medium. In this way, the capillary
pressure at the water-NAPL interface (Pcnw) defines the water saturation, and the capillary pressure at
the NAPL-air interface (Pcan) defines the total liquid saturation:
wncnw PPP −= (19)
nacan PPP −= (20)
where Pw, Pn, and Pa are the water, NAPL and air pressure, respectively.
The theory is based on the fundamental assumption that water is a continuous and perfectly wetting
fluid, NAPL is the intermediate wetting fluid and air is always least wetting. This order of wetting is
known as the wettability sequence. Many models involving pressure-saturation-permeability relations
where fluid pairs are scaled to three phase fluid relations are based on this wettability sequence and
the assumptions made by Leverett (1941). Scaling constitutive relations has the advantages of self
consistency and also that only a minimum set of parameters need to be determined to develop a full
set of curves.
28
Lenhard and Parker have made a significant contribution to this area of research through predictions
and laboratory measurements of constitutive relations based on the work of Leverett. Lenhard and
Parker (1987) concluded that sets of capillary pressure-saturation relations for any two fluid pairs in
multiphase systems could be determined by scaling a single set of two-phase measurements with
interfacial tension data. Lenhard and Parker (1988) validated the procedure of scaling two-phase
capillary pressure-saturation relationships to three-phases through measurements of monotonic
drainage saturation paths.
Leverett (1941) also proposed a dimensionless form of the capillary pressure-saturation relation (Pcd),
Leverett’s scaling function, which correlates permeability, porosity, interfacial tension and capillary
pressure functions (Kueper and Frind 1991b):
2/1
=
nkP
P ccd σ
(21)
However, the scaling function assumes that the contact angle is not important, as well as a rigid
porous medium, negligible fluid-surface interactions and negligible NAPL residual saturation in the
unsaturated zone. Richardson (1961) improved on the function by incorporating a function of the
contact angle in the numerator:
( ) 2/1
=
n
kfPP c
cd σφ (22)
where f(_) represents a function of wettability (contact angle). Richardson also made some
assumptions so that this scaling could also be applied to a three-phase system. Zhou and Blunt
(1997) used the modified Leverett scaling function to predict LNAPL distributions of continuous
LNAPL, water and air from a single capillary pressure function curve. Their predictions matched
measurements in areas where NAPL saturation was greater than 10%.
Leverett’s scaling function can be applied to cope with the impact of heterogeneous systems on
constitutive relation variability (eg. Kueper and Frind 1991b), which exists at the scales at which
constitutive relations are developed and parameters measured (Miller et al. 1998).
2.4.5 Difficulties in multiphase flow modelling
Huyakorn, Panday and Wu (1994) concluded that a “comprehensive, flexible and robust simulator is
essential for practical investigations.” In addition to this, multiphase models should ideally be
computationally efficient and have achieved some kind of agreeance with field data. However,
accurately modelling NAPL movement in three-phase flow remains a challenging task, primarily due to
difficulties arising with parameter inputs and computational methods.
Over-simplified or incorrect parameters weaken the integrity of a model. Sound parameter values rest
on the correct representation of pressure-saturation-permeability relations and local natural
29
heterogeneity characteristics (Miller et al. 1998). Complex data such as this is not only difficult and
costly in terms of money and time, but also carry with them a certain level of uncertainty.
Computational methods also play a crucial role in accurate modelling because of the difficulty inherent
with solving the system of coupled partial-differential balance equations. Non-linear discrete algebraic
expressions for each REV (or node) are solved using an iterative approach such as the Newton-
Raphson method. Associated with this difficulty is the extensive computational resources required,
particularly for field applications. Although accuracy of numerical multiphase models can generally be
improved with refinement of the numerical grid with the use of smaller discretization steps (Helmig
1997), there needs to be a balance between the level of detail and computational intensity. This can
be achieved by choosing an appropriate discretization scheme and developing simple and efficient
algorithms, which will vary depending on the scale and purpose of the simulator (Helmig 1997).
Other important aspects of numerical methods are error estimates, stability and convergence. Factors
affecting the convergence of models include problem complexity, discretization scale, numerical
discretization of the differential equations, linearization of the system of equations and the choice of
solution algorithm (Helmig 1997).
Multiphase flow models are evolving and will continue to rely on advanced computer machinery. It is
believed that because models are presently limited by modern software methods, advancement in this
area, along with the development of clever algorithms, will continue to minimize computational
demands (Miller et al. 1998).
30
2.5 Stochastic Site Characterization
“In reality, subsurface hydrogeological parameters rarely posses uniform
properties…their properties vary in a discrete or continuous manner on a multiplicity
of scales from one location to another.” (Elfeki et al. 1997).
Subsurface hydrogeological parameters, such as permeability and porosity, and their spatial variability
have a strong influence on the flow of NAPLs (eg. Kueper and Frind 1991; Kueper and Gerhard 1995).
Although multiphase flow is approached deterministically by continuum mechanics (i.e. conservation
of mass and momentum), numerical techniques often solve these balance equations with stochastic
parameters (Elfeki et al. 1997). Miller et al. (1998) argued that multiphase systems themselves must
be stochastic in nature because of the types of geological processes that originally create them.
Research has also demonstrated the influence of subsurface heterogeneity on NAPL migration (see
2.3.2.3), highlighting the need for multiphase models to incorporate site specific data on the spatial
variability of subsurface hydrogeological parameters.
2.5.1 Site Characterization
Site characterization refers to the description of the local heterogeneity of an aquifer, and can be
achieved through either a deterministic or stochastic approach.
2.5.1.1 Deterministic Approach
The deterministic approach involves reconstructing the subsurface to produce the ‘most probably
picture’ using a finite set of observations (i.e. interpolation). The basic theory of interpolating can be
shown with equation (23) which says that the estimated value of a function z (eg. permeability) at
location x, E[z(x)], can be calculated by summing each value of z at surrounding points, z(x),
multiplied by a probability coefficient, Pi (Kitanidis 1997).
( )[ ] ( )ii
i zPzE xx ∑= (23)
Kriging is one method of interpolation which allows the best estimate of z(x). A major advantage of
kriging over other interpolation techniques is that the probability coefficients are calculated according
to how the function varies in space (Kitanidis 1997). Kriging is a best linear un-biased estimation
(BLUE) technique such that the mean square error is calculated for estimated points.
A prominent feature of kriging is the structural analysis of spatial variations in subsurface properties
which are examined through variograms. Variograms demonstrate how a property, such as
permeability, between two points becomes increasingly uncorrelated as the distance between them
increases. In this way, variograms can be related to the covariance function (Kitanidis 1997).
The variogram, γ, can be mathematically expressed by (Kitanidis 1997):
31
( ) ( ) ( )( )[ ]2
2
1izzEh xx −=γ
(24)
where h is the physical distance between two points.
The development of variograms for a field allows correlation lengths to be estimated. These lengths
represent the maximum physical distance that a property can be assumed to be correlated.
Theoretically, property values have an influence on surrounding points only within the correlation
length. This is the key concept behind kriging.
Finding the interpolated solution for a field requires the development of a variogram model. This is
obtained by selecting a model form and manually altering parameters to match the model to a
variogram built from real data called the experimental variogram. There are four main types of model
variograms to choose from: Exponential, Gaussian, Power and Spherical. Parameters that define the
chosen model variogram include nugget, contribution and range. The value of the range corresponds
to the correlation length. An example of a model variogram fitted to an experimental variogram is
shown in Figure 2.10
Figure 2-10 A typical model variogram fitted to an experimental variogram. This example shows thebest fit of a spherical model to an experimental vertical variogram for data collected from the BordenAquifer in Canada (modified from Turcke and Kueper 1996).
Kriging and the associated variogram development are fundamental tools in the field of geostatistics.
The identification of correlation lengths in three-dimensions as a preliminary step of kriging, can be
extended to a stochastic description of subsurface properties as outlined in the following section. For
more information on kriging and associated geostatistics, the reader is referred to the text by Kitanidis
(1997).
32
2.5.1.2 Stochastic Approach
Aquifer properties, such as permeability and capillarity relations, can be described by both a
deterministic and a stochastic component corresponding to the very nature of geological processes
(Robin et al. 1993). Stochastic comes from the Greek language and means “skilful at aiming or
guessing” (Haldorsen et al. 1987). The stochastic approach to site characterization involves the
generation of multiple lots of synthetic geological structures. Each of these “guesses” is called a
random correlated field or realization. Sudicky (1986) demonstrated with field data that stochastic
theory using the statistical properties of the permeability distribution was successful.
Stochastic models used to create realizations are called Random Field Generators (RFGs). RFGs
take advantage of the rules of probability in that a given set of circumstances will not always lead to
the same outcome (i.e. no deterministic regularity), but will lead to different outcomes which have
statistical regularity (Robin et al. 1993). The development of random correlated fields is done using a
stochastic description of the system and is a useful tool to examine the spatial variability of aquifers.
Inputs for RFGs include the mean and variance of the data set, as well as the correlation lengths
which can be obtained from variograms. Although random fields strive to resemble reality, they
cannot replace actual measurements (Robin et al. 1993).
The stochastic approach can be divided into two types of models: discrete and continuous. Discrete
models identify heterogeneities as individual natural formations and describes them as geometric
shapes. Continuous models use parametric variability to describe local variations of soil properties,
such as permeability and porosity. Stochastic subsurface hydrology frequently uses the continuous
approach (Elfeki et al. 1997). There are several methods used for stochastic field generation: multi-
variate, nearest neighbour turning bands, spectral, source point and Fourier transform method (Elfeki
et al. 1997). Robin et al. (1993) presented a computer algorithm to cogenerate pairs of three-
dimensional, cross-correlated random fields using the Fourier transform method.
Sudicky (1986) presented an examination of the spatial variability of hydraulic conductivity of the
Borden Aquifer in Canada. This paper is significant because it triggered off many other studies of a
similar nature near the same site, and also contained extremely detailed hydraulic conductivity
measurements at that time. Permeability measurements were conducted on 32 cores along two cross
sections. Statistics of the measurements and a derived covariance model was used to describe the
variability of the natural logarithm of the permeability, ln(k). The study was completely re-examined by
Woodbury and Sudicky (1991) who described variability with variograms instead of autocorrelation
functions as was used by Sudicky (1986). They showed that outliers caused difficulties in both
variogram estimation and determining population statistics. They also demonstrated the effects of
using different variogram estimators on sampled data and showed that both a normal and exponential
distribution for log conductivity could be used to model the data. Further still, Turcke and Kueper
(1996) conducted a detailed analysis of the Borden permeability field also with the extensive use of
variograms. Robin et al. (1991) studied the same site to investigate the correlation between K and Kd
(distribution coefficient). They showed that, unlike variograms, spectral analysis was a powerful tool
that could provide independent estimates.
33
2.5.2 Monte Carlo Analysis
Monte Carlo analysis is a technique used to analyse the impact of spatial variability on flow (Essaid
and Hess 1993). This type of analysis is often used for risk assessment investigations to estimate
uncertainty in the response variables (Elfeki et al. 1997). Numerous spills are simulated using multiple
random correlated fields with the same statistical characteristics as the real one. Analysis of a large
number of outputs provides a valuable set of statistics such as the mean, variance and covariance for
each spatial node in the grid (Elfeki et al. 1997). Results can then be pulled together to describe likely
outcomes for features such as final penetration depth and period of infiltration. Disadvantages of
other techniques, such as spectral analysis and small-perturbation methods, are that the variability
must be relatively small and boundaries must be far from the edge of interest. Although Monte Carlo
methods are superior in these areas, they are limited by the huge computational efforts required
(Essaid and Hess 1993).
Essaid and Hess (1993) studied the effect of spatial variability of sediment hydraulic properties on
multiphase flow by performing 50 Monte Carlo simulations with 50 different spatially variable
permeability realizations and corresponding spatially variable retention curves. They suggested that
for the type of correlation structure studied (typical of glacial outwash deposits), the use of mean
hydraulic properties reproduces the ensemble average oil saturation distribution obtained from the
Monte Carlo simulations.
34
2.6 Field Experiments
Many features of NAPL migration in the subsurface have been highlighted through numerous
laboratory experiments (eg. Kueper et al. 1989) and numerical simulations (eg. Kueper and Frind
1991a,b). However, these studies are controlled and as such are “hampered by an inability to
recreate the spatial variability of physical and chemical properties associated with naturally occurring
geologic deposits” (Kueper et al. 1993).
Field studies have usually been limited to accidental spills of NAPLs because of the difficulty and
restrictions on the controlled release of these substances. The major problem with studying accidental
spills is the lack of knowledge on the nature of the spill, in particular, the volume of NAPL released.
Transient monitoring of NAPL migration is also not possible when contamination of the site is
discovered well after the release, which is usually the case when attempting to study an accidental
spill. Nonetheless, some extremely valuable controlled releases have been previously conducted in
the field to examine the effect of subsurface heterogeneity. The majority of these few studies have
been performed in the Canadian Forces Base Borden which features a fine to medium grained sand.
Poulsen and Kueper (1992) released two lots of 6L spills into an unsaturated sandy aquifer at Borden
to examine the effect of source release rate and porous media structure on the ultimate distribution
and penetration depth of tetrachloroethylene (PCE) – dense non-aqueous phase liquid (DNAPL).
Excavation of the area was done one day after release and the distribution was recorded through
photographs and with the aid of a 5cm grid frame. They found that the PCE was distributed
heterogeneously right down to the millimetre scale.
Six hundred metres east-north east of the unsaturated zone field experiment conducted by Poulsen
and Kueper (1992), Kueper et al. (1993) performed a field experiment to study the behaviour of PCE
below the water table. This involved the release of 230.9 L of PCE into an isolated 3m x 3m x 3.4m
deep cell in a saturated, unconfined aquifer. The PCE entered the cell at a rate of 8 L hour-1 through a
plastic pipe with a constant head of 1.23m of PCE. Twenty eight days after release, the upper 0.9m of
the cell was excavated and samples as small as 2cm3 were tested for PCE using a
spectrophotometer. Sampling revealed high spatially variable distribution of PCE pools and residual
and that were generally present in coarser grained horizons. NAPL saturation ranged from 1% to 38%
of pore space.
Brewster et al. (1995) observed the migration of a controlled release of 770 L of PCE within the
saturated zone of a sandy aquifer. PCE was released into a 9m x 9m x 3.3m deep cell by a constant
head in a PVC standpipe and migration was monitored over 984 hours using a variety of geophysical
techniques. A pool of PCE spreading over an area of greater than 32m2 was formed at a depth of
approximately 1m. This study highlights the significant effect natural heterogeneity has on NAPL flow,
particularly lateral spreading.
35
3.0 Parameter Measurement
Accurate multiphase simulations require detailed knowledge about the variability of underlying
hydrogeological properties. Through the collection and geostatistical analysis of permeability data,
random permeability fields were created to capture natural heterogeneity and consequently used as
the media for spill simulations. Pressure-saturation relations were measured for a limited number of
samples for two fluid pairs (air-water and air-NAPL). These relations are spatially variable, and so the
base curves were scaled such that they could be applied to any location of known permeability.
Saturation-permeability relationships were also generated using scaling techniques and parameters
extracted from the measured pressure-saturation curves.
This section discusses how samples were acquired in the field, as well as how they were tested in the
laboratory to produce useful data sets of permeability and constitutive relations.
3.1 Acquisition of field samples
To enable permeability and pressure-saturation relations to be measured, samples representing the
sand beneath the oil spills at Cottesloe Substation needed to be collected. For this reason, two
orthogonal trenches approximately 3m deep and 8m long were excavated in a vacant area adjacent to
the substation (Figure 3.1). Three steps were cut into one long side of each trench for safety and easy
access to bottom steps for sample collection. Within the two trenches, samples were collected from a
total of 104 sites located in an evenly spaced grid-type pattern. Two adjacent samples were collected
from each site so that both permeability and capillary pressure tests could later be conducted.
Figure 3-1 Location and arrangement of two sample trenches adjacent to Cottesloe Substation
Physical sampling techniques were conducted in a manner to ensure minimal disturbance and
remained consistent over the two days of sampling (see Figure 3.2). At each step and location
(horizontal position along the step), a clean vertical scarp and horizontal stage on top of the step were
created with a shovel. Two or three horizontal floors could be created at each step and location
depending on the step height. Each sample was acquired and retained in a 30mm long metal cylinder
36
with an internal diameter of 53mm. Two of these cylinders were placed one on top of the other upon
and then pushed vertically into the stage. The sample was retained by sliding thin square metal plates
above and below the ring. The enclosed sample was then withdrawn from the trench and secured
with tape. Individual samples were labelled according to trench, step and location.
(a) (b)
(c) (d)
Figure 3-2 Methodology for collecting undisturbed samples from the trenches (a) a vertical scarp andhorizontal stage were created with a shovel (b) two cylinders were placed on top of each other anddriven into the stage (c) metal plates were slid above and below the cylinder (d) the sample wasremoved from the surrounding sand, taped and labelled
Simple surveying techniques were used to attach a three-dimensional coordinate to each sample. All
measurements were scaled to a datum arbitrarily set towards the north-east corner of the site and at
the deepest measurement for z. This ensured that all locations were assigned a positive coordinate
for all three directions for the sake of simplicity. The maximum distance between samples was 9.07m,
17.53 m and 2.52 m in the x, y and z direction respectively.
37
3.2 Permeability
Permeability (k) is an important parameter in multiphase flow and needs to be determined at many
points to enable the generation of random permeability fields. It is a property of the pore-space
geometry and is generally measured in m2 or µm2 (i.e. 10-12 m2). Hydraulic conductivity (K) is a
property of both the fluid and porous media and is measured as a flux (m3m-2s-1). The simple
measurement of hydraulic conductivity allows the permeability of a soil column to be calculated with
the following formula (Klute 1986):
gK
kρ
η=(25)
where
η : dynamic viscosity of water (1.14 x 10-3 kgm-1s-1)
ρ : density of water (1000 kgm-3)
g : gravity (9.81 ms-2)
Constant head hydraulic conductivity tests were conducted on a total of 96 samples from the trenches
following the methodology suggested by Klute (1986) (see Figure 3.3). Each sample was unpacked
and placed on a wooden ‘stool’. A metal cylinder, identical to the one containing the sample, was
placed on top of the sample and secured with parafilm and tape to prevent movement and leakage. A
plastic piston was inserted into the top cylinder to allow the sample to be lifted, rotated and transferred
into a Buchnar funnel in which a circle of mesh had been inserted. Saturation of the sand was
achieved by blocking the bottom of the funnel and filling the it to a water level just below sample
height. This allowed the sand to be saturated by capillary rise from the bottom of the sample, ensuring
minimal air entrapment in pore spaces. A Marriott bottle was set-up at an appropriate height adjacent
to the funnel to maintain a constant head. Water from the bottle was delivered directly above the
sample via a plastic tube and so care was taken to avoid scouring of the top of the sample. When
steady state flow and a constant head above the sample was maintained, a volume of water was
collected in a beaker beneath the funnel and the time for this recorded.
The hydraulic conductivity for each sample was then calculated using Darcy’s Law:
H
L
At
VK
∆=
(26)
where
K : hydraulic conductivity [cm/s]
V : volume of water [cm3] collected in time t [s]
A : cross sectional area of the sample [cm2]
L : length of the sample [cm]
∆H : constant head imposed on the sample [cm]
38
(a) (b)
(c) (d)
Figure 3-3 Methodology for measuring permeability in the laboratory using the constant-head method(a) the sample was unpacked, placed on a wooden stool and adjoined to an identical metal ring withparafilm and tape (b) the sample was transferred to a Buchnar funnel with the aid of a plastic piston (c)the sample was saturated from the bottom and a constant head and flow rate maintained (d) flow wasmeasured by recording the time with a stopwatch and volume of water by weighing the collectionbeaker
Each sample was 3.0cm in length with a cross-sectional area of 22cm2. The time of each test was
measured with a stopwatch. The volume of water collected during this time was measured by
subtracting the dry weight of the beaker from the weight of the beaker and water at the end of every
test and dividing the weight by the density of water (1000 kgm-3). The constant head for each test was
simply measured with a metal ruler and ranged from 0.5cm to 3.0cm.
Hydraulic conductivity values were then converted to permeability using equation (25). These
calculations, along with laboratory data, are included in Appendix A. A brief statistical summary of the
permeability of all 96 samples is presented in Table 3.1. A histogram of the natural logarithm of
permeability was constructed for all 96 samples and shows a lognormal distribution (Figure 3.4).
39
Table 3-1 Statistical summary of results of permeability tests conducted on 96 samples collected fromthe trenches.
Statistic Value (m2)
Mean 3.43 x 10-11
Median 3.38 x 10-11
Range 4.05 x 10-11
Minimum 1.68 x 10-11
Maximum 5.73 x 10-11
Standard Deviation 8.70 x 10-12
0
5
10
15
20
25
1.5
- 2.
0
2.0
- 2.
5
2.5
- 3.
0
3.0
- 3.
5
3.5
- 4.
0
4.0
- 4.
5
4.5
- 5.
0
5.0
- 5.
5
5.5
- 6.
0
Permeability ( x 10E-11) m^2
Nu
mb
er o
f O
bse
rvat
ion
s
Figure 3-4 Histogram for all 96 permeability measurements exhibiting a fairly lognormal distribution.
Mean permeability values for step 1, 2 and 3 (where 1 was the bottom step), were 2.92 x 10-11m2, 3.29
x 10-11m2 and 3.98 x 10-11m2 respectively. This shows a decreasing average permeability with depth,
which is expected due to greater compaction in lower layers and more macropores and organic matter
in upper layers.
40
3.3 Capillary Pressure Relations
The importance of developing capillary pressure-saturation relationships for oil migration
investigations was discussed in section 2.4.4. The relations can be established by determining a
series of equilibrium points between fluid pressures and saturations. The imposed pressure is usually
achieved by a head of the same fluid. Laboratory methods for determining this relation, know as the
retention curve, are outlined by Klute (1986).
Although over one hundred samples were collected with the intention of measuring capillary pressure-
saturation relations, only seven curves were developed. Time constraints and the difficulty of
measuring pressure-saturation with the available laboratory equipment precluded the generation of
curves for each sample. Nonetheless, scaling techniques allowed individual (although not
independent) pressure-saturation curves to be developed for locations with a known permeability (see
2.4.4.3).
3.3.1 Measurement of Capillary Pressure-Saturation Curves
Drainage capillary pressure-saturation curves for air-water and NAPL-air in Cottesloe Sand were
measured. Although the additional measurement of imbibition curves would have produced fully
hysteretic curves for the sand, the drainage curves reflected the nature of the transformer spills
themselves (i.e. imbibition of the non-wetting fluid) and the numerical model employed was incapable
of handling hysteretic constitutive relationships.
3.3.1.1 Air-Water
Individual air-water pressure-saturation drainage curves were generated for three high and three low
permeability samples by Mullen (2002). Each sample was placed in a pressure cell above a 1 bar
pressure plate. Pressure at 20cm increments between 0cm and 100cm of water were generated
using a pressure hose. The volume of water collected in a vial below the sample during equilibration
between pressure readings determined the change in saturation. Evaporation losses were
considered.
The capillary pressure-saturation curves for the 6 air-water tests are shown in Figure 3.4.
41
0
20
40
60
80
100
120
0.0 0.2 0.4 0.6 0.8 1.0
Saturation (Sw)
Pc
(cm
wat
er)
k = 5.73E-11k = 5.68E-11k = 5.56E-11k = 2.02E-11k = 1.86E-11k = 1.68E-11
Figure 3-5 Air-water capillary pressure-saturation drainage curves developed for various samplestaken from the sample trenches
3.3.1.2 Air-NAPL
Only one air-NAPL retention curve was developed for a sample taken from the middle step of trench 2,
which was found to have a permeability of 3.22 x 10-11 m2. The apparatus used to measure pressure-
saturation equilibrium points was constructed from a pressure cell, plastic tubing and a burette. The
undisturbed sample was transferred with some difficulty into the bottom half of the pressure cell, and
the top half was then screwed on tightly. Directly below the sample, but still contained within the cell,
lay a ceramic pressure plate with a 1 bar entry pressure. The top of the cell remained at atmospheric
pressure at all times by a small open outlet. The bottom of the cell was connected to plastic tubing
which was attached to a burette at the other end. Oil completely filled the tubing from beneath the
pressure plate to a level in the burette which allowed the position of the oil free surface to be
accurately read. The sample was then saturated with oil from the bottom of the cell by a falling head
of oil in the burette and capillary rise. Readings of the burette before and after saturation allowed the
initial saturation and porosity to be calculated.
Drainage pressure-saturation data was collected by altering the NAPL pressure and recording the
subsequent change in saturation. Negative pressure (suction) was created and altered in the
pressure cell by lowering the elevation of the connected burette, and hence the free oil surface.
Earlier attempts to develop a pressure-saturation curve for air-NAPL revealed that the system was
extremely sensitive to equilibration time. Therefore, after each change in pressure, the system was
left to equilibrate for exactly 12 hours, after which time pressure and saturation readings were
recorded. Capillary pressure was measured by the head difference between the centre of the sample
and the oil level in the burette. Saturation was measured by the corresponding increase of oil level in
the burette.
The final results of the test (Appendix B) were processed to develop a plot of air-NAPL capillary
pressure against effective saturation so that a model could be fitted to it and parameters extracted.
42
3.3.2 Analysis of Capillary Pressure-Saturation Curves
Lenhard and Parker (1987, 1988) demonstrated that by using interfacial tension data, it was possible
to scale capillary pressure-saturation curves for one fluid pair to another. Leverett’s scaling function
(1941) also allows scaling such that pressure-saturation curves may be non-dimensionalized (i.e.
effects of porosity, interfacial tension and permeability removed) so that a single fitting function may be
applied. Both of these scaling techniques are applied in this study.
3.3.2.1 NAPL-water
Water saturation in multiphase systems is assumed to be controlled by the NAPL-water interface
(Leverett 1941). However, air-water pressure-saturation relations are much easier to measure than
for NAPL-water. Therefore, the six air-water retention curves developed by Mullen (2002) were
converted to equivalent NAPL-water curves using Leverett’s scaling function (1941):
AW
NWCC AWNW
PPσσ=
(26)
where
_NW : NAPL-water interfacial tension (48 dyne cm-1)
_AW : air-water interfacial tension (72 dyne cm-1)
This scaling simply converted the measured capillary pressures for the air-water system to the
capillary pressures for the NAPL-water system. As this conversion only involved a constant scaling
factor (i.e. interfacial tension ratio), the shape of the curves remained identical.
The six new capillary pressure-saturation curves for the NAPL-water system were then non-
dimensionalized so that a single empirical model function could be fitted. This process allows the data
to be made useful for any point in the system and not just the samples that the curves were developed
for. The non-dimensionalizing process is based on the empirical Leverett scaling function (21) which
relates permeability, porosity and interfacial tension to a dimensionless capillary pressure. Using this
function, a set of scatter points were developed from the NAPL-water curves by assuming a porosity
(n) of 0.4, knowing the air-NAPL interfacial tension (_) to be 48 dyne cm-1, and knowing the
permeability (k) of the sample (which is assumed to be the same as the measured permeability of the
adjacent sample from the trench).
2/1
=
nkP
P ccd σ
(21)
Scatter points of dimensionless capillary pressure against effective saturation were then plotted and
fitted with the van Genuchten function. This methodology mimics that of Kueper and Frind (1991b)
who non-dimensionalized 7 laboratory derived capillary pressure-saturation curves for samples of
different permeabilities, and then fitted this with a Brooks-Corey curve. However, the van Genuchten
model for retention data was employed in this study because of the nature of the data near Sw = 1 and
the representation over the full range of Pc(Sw). The developed curves did not exhibit a distinct entry
pressure which made the use of Brooks-Corey inappropriate. It would seem, however, that because
43
the sand was shown to have a fairly uniform particle size distribution (Appendix C) it should display a
fairly distinguishable entry pressure (van Genuchten and Nielsen 1985). The reason this did not occur
may be due to macropores in the samples due to organic matter, but more likely, disturbances or
cracking of the sample. The choice of the van Genuchten model is also supported by the fact that
Brooks-Corey solutions exhibited greater spreading and less inclination to penetrate semi-permeable
layers (Rathfelder and Abriola 1998). As this study is interested primarily in the penetration depth of
NAPL, then the van Genuchten parameterization can be assumed to model the “worst case scenario.”
The model van Genuchten function (equation 13) was fitted to the set of dimensionless capillary
pressures for a reference permeability of 10-11 m2 (Figure 3.7). Values of the van Genuchten
parameters _nw, n and m were altered to produce a best fit and were found to be 0.033, 4.6 and 0.783,
respectively. The correlation coefficient between the observed scatter points and the fitted function
was 0.927. A table of observed and fitted dimensionless capillary pressure is included in Appendix D.
0.0E+00
2.0E-06
4.0E-06
6.0E-06
8.0E-06
1.0E-05
1.2E-05
1.4E-05
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Effective saturation (Se)
Dim
ensi
onle
ss c
apill
ary
pres
sure
(Pcd
)
observed
fitted VG
Figure 3-6 Scaled capillary pressure-saturation curves for NAPL-water with the fitted van Genuchtenfunction and reference scaling permeability of 10-11 m2
3.3.2.2 Air-NAPL
As there was only one curve developed for the air-NAPL capillary pressure-saturation relation, there
was no need to scale this to a dimensionless form. Instead, the van Genuchten model was fitted
directly to the Pcan(Se) curve, yielding a _an value of 0.028. As expected, the value of n and m
remained unchanged (i.e. 4.6 and 0.783 respectively) due to the mathematical nature of the fitting
function. The correlation coefficient between the experimentally derived curve and the fitted function
was 0.994. This is higher than the correlation coefficient for the observed and fitted NAPL-water data
(0.927) because the model was fitted to only 1 data set as opposed to 6. The fitted van Genuchten
model for air-NAPL is shown in Figure 3.8.
44
0
20
40
60
80
100
120
0.0 0.2 0.4 0.6 0.8 1.0
Effective saturation (Se) NAPL
Dim
ensi
onle
ss c
apill
ary
pres
sure
(Pcd
)
observed
fitted VG
Figure 3-7 Capillary pressure-saturation curve for air-NAPL with the fitted van Genuchten function.
45
4.0 Stochastic Site Characterization
A set of 96 permeability measurements with associated three-dimensional coordinates were
developed from sample collection and permeability tests (Appendix E). This data set was imported
into GMS® (Groundwater Modelling System). The permeability field was characterized using a
stochastic rather than a deterministic approach. One reason for this decision was that the
permeability data was determined for the sample trenches which were located approximately 50m
away form the actual study spill. More importantly, a stochastic description allows for uncertainty and
risk assessment using Monte Carlo analysis.
4.1 Variogram Development
Variograms for the permeability data were developed for the identification of correlation lengths for
three principle axes. Experimental variograms were computed for three directions.
The number of lags for each experimental variogram was altered to produce the most ‘sensible’
variograms with the longest ranges. All variograms were developed using 10 lags and a unit
separation distance of 40cm in the horizontal x and y directions, and 5cm in the vertical z direction. By
adjusting the azimuth angle in the horizontal plane, the major principal axis (i.e. the azimuth angle
producing the longest range) was identified as 120° from the y-axis. The minor principal axis was
required to be perpendicular to the major principal axis so was set at an angle of 30°. Experiments
with the dip angle were done to check its effect on the variograms. However, changes in the dip
showed little or no effect on the variograms, which supported the assumption of a horizontally lying
permeability field and so the currently defined z direction remained valid. The azimuth bandwidth was
set at 2 m for the x and y directions and the dip bandwidth was set at 40cm for the z direction.
Figure 4.1 shows the directions of the principal horizontal axes in relation to the originally defined x-y
coordinate system for the two trenches. Thus, the major principal axis (i.e. longest correlation length)
was found to lie on a bearing of 217° and the minor principal axis on a bearing of 127°.
Figure 4-1 The direction of the major and minor principle axes which were determined by finding themaximum and minimum correlation lengths with the use of variograms.
46
Model variograms were manually fitted to each of the three experimental variograms by manipulating
the model parameters, as well as the model function. The most appropriate model function that best
fitted all three experimental variograms was the exponential model. Values for the contribution and
range for each model variogram were determined by adjustment to produce the best fit. It should be
mentioned that model variogram fitting is often quite subjective because matching the model
variogram to the experimental variogram is achieved by visual assessment only. Variogram fitting is a
conceptual approach and so numerical techniques do not allow freedom of interpretation of the
experimental variograms.
The range of each variogram was assumed to equal the correlation length (_i) in that direction (as
discussed in 2.5.1.1). Therefore, correlation lengths were found to be 3.08m in the x-direction, 1.09m
in the y-direction and 0.39m in the z-direction. Figure 4.2 shows the experimental and model
variogram for the major principal axis. The variograms for all directions, as well as the direction data
and model parameters, are included in Appendix F.
Figure 4-2 Best fit model variogram (smooth line) to experimental variogram (joined dots) for themajor principal axis.
4.2 Random Field Generation
“Random fields are multi-dimensional stochastic processes…a mathematical way to
describe spatial variations of properties of a physical phenomenon.” (Haldorsen,
Brand & MacDonald 1987)
Random permeability fields for the sample area were generated using the random field generator,
FGEN91 (Robin et al. 1993). Inputs into the program included correlation lengths in three directions
and the mean and variance of the natural logarithms of the permeability data. The size of the domain
and discretization lengths also needed to be specified.
The correlation lengths were determined by fitting model variograms to experimental data (see 4.1).
The mean and variance of the natural logarithm of all 96 permeability values were easily computed
47
from the raw data. Taking into account both the determined correlations lengths and computational
resources, the domain size of the random fields were chosen to be 10m in the x-direction (_x = 0.4m;
25 nodes), 3.9m in the y-direction (_y = 0.3m; 13 nodes) and 5m in the z-direction (_z = 0.1m; 50
nodes). The number of nodes per correlation length were therefore 8, 3 and 4 for the x, y and z
direction, respectively. Although the minimum number of nodes per correlation length is ideally 4, this
compromise had to be made to balance computational efficiency with accuracy. The number of nodes
in each domain totalled 16,250 and generation time was approximately 30 seconds.
Input parameters for FGEN91 are summarized in Table 4.1 and the input file (*.gen) included in
Appendix. G.
Table 4-1 Inputs into FGEN91 which was used to create multiple random permeability fields
Input Value
Ensemble statistics:
Mean ln(k) -24.13
Variance ln(k) 0.06756
Correlation lengths:
_x (m) 3.08m
_y (m) 1.09m
_z (m) 0.39m
Domain size:
x-direction 10.0m
y-direction 3.9m
z-direction 5.0m
Nodal discretization:
x-direction 0.4m
y-direction 0.3m
z-direction 0.1m
Number of nodes:
x-direction 25
y-direction 13
z-direction 50
FGEN91 used the input parameters and the specified domain size and discretization to assign
permeabilities for each node in the domain using the direct Fourier transform method. A total of fifteen
three-dimensional random permeability fields were generated with identical inputs, except that the
starting random seed was altered at the tope of the data file. The purpose of this seed was to
introduce randomness in the synthetic construction of each field, such that no two realizations were
the same, but instead all realizations possessed identical geostatistics (i.e. stochastic approach).
Each random field generated therefore represented a possible or realistic picture of the subsurface
structure of Cottesloe Sand. Output statistics of the fields were calculated and were approximately
48
equivalent to the input mean and variance for all realizations. The created permeability fields served
as input files for spill simulations as discussed in the following section.
Although direct measurements gave evidence that permeability generally decreased slightly with
depth (see end of section 3.2), the random field generator cannot accommodate this variation. The
effect of this would be minor in any case because the variation with depth is very slight and more
importantly, the presence of local permeability layers would have a greater immediate affect on NAPL
migration.
A cross-section taken from the centre of Random Field Four was plotted to provide a visual example
of what the underlying permeability configuration at Cottesloe may look like (Figure 4.3). Evidence of
discrete individual blocks demonstrates the resolution of the domain.
Figure 4-3 A vertical slice through the Random Field Four permeability field.
49
5.0 Numerical Simulations
5.1 Model Description
A numerical multiphase model, SWANFLOW (Faust 1985), was employed to simulate the migration of
transformer oil in Cottesloe Sand for various spill scenarios. The three-dimensional model uses a
finite-difference approach and operates in three phases. The air-phase is assumed to be passive (i.e.
air always remains at atmospheric pressure), which is a common assumption in many multiphase
models (eg. Kuppusamy et al. 1987; Kueper and Frind 1991a,b). Panday et al. (1994) gave evidence
of a passive-air-phase formulation producing similar NAPL saturation solutions to a fully three-phase
simulation. SWANFLOW also uses non-hysteretic forms of capillary pressure-saturation-permeability
relations as do most older multiphase models in the environmental field (Miller et al 1998).
The model is formulated around two primary unknowns: NAPL pressure (Pn) and water saturation
(Sw). Pressure and saturation for air, NAPL and water is calculated for each node for each time step
and printed out at a specified interval. Two runs were required to complete each simulation. The first
run allowed a specified volume of NAPL to be injected into the domain by a constant NAPL pressure
at the source node(s). This driving pressure was removed in the second run and the oil was allowed
to naturally distribute itself in the porous media for a further 100 days.
5.2 Model Inputs
Input parameters for the numerical model included site specific soil and fluid properties, geometry and
nodal spacing of the simulation domain, initial values of primary variables (Pn and Sw) for every node
and two sets of pressure-saturation-permeability curves with associated scaling parameters.
A complete list of model input parameters used in all simulations is shown in Table 5.1.
5.2.1 Fluid and soil properties
Physical fluid properties that influence multiphase flow, namely density, viscosity and interfacial
tensions for water and NAPL, were found in the literature (Shell 1999) and entered into the data file.
For each simulation, a previously created permeability field (see section 4.2) was called upon to
incorporate the effects of the spatially variable permeability and pressure-saturation characteristics of
the porous media. Porosity was assumed to be 0.4 for the whole domain; a reasonable assumption
based on simple laboratory measurements (Appendix H).
5.2.2 Boundary conditions
The size and discretization of the three-dimensional solution domain for spill simulations was made to
match that of the generated permeability fields (i.e. 10m x 3.9m x 5m deep) with the number of nodes
for each of these lengths being 25, 13 and 50, respectively. Thus, the number of nodes in the domain
50
totalled 16,250. The geometry and boundary conditions of the solution domain are visually
represented in Figure 5.1.
The water table lies on the bottom layer of the domain (z = 0) where Pw is assumed to be zero.
Vertical sides of the domain were specified as no-flow boundaries, although this is irrelevant as the
NAPL body kept within the boundaries for all simulations performed in this study. The source node (or
nodes for multi-nodal source area simulations) lies in the middle of the top layer.
A NAPL injection head of 2602 Pa (equivalent to 30cm of oil) at the source was employed to ensure a
substantial driving force for NAPL migration. This pressure is called the source strength and although
it too plays an important role in NAPL migration (Poulsen and Kueper 1992), it was kept constant for
all simulations. Using the air-NAPL pressure-saturation curve, this pressure corresponded to a NAPL
saturation of 0.661 in the source node.
Figure 5-1 The geometry and boundary conditions of the simulation domain for a one node sourcerelease area.
5.2.3 Initial conditions
Pressure
Initial water pressure was assumed to be hydrostatic, and therefore linear. Water pressure, Pw,
equalled 0 at the water table (z = 0) and -48,020 Pa at ground level (z = 5m). The pressure at each z
location was calculated by:
ghP wρ= (27)
The initial NAPL-water capillary pressure, Pcnw, is assumed to equal zero because there had not yet
been any invasion of the non-wetting fluid into the field:
51
0=−= wncnw PPP (28a)
wn PP =∴ (28b)
Therefore, NAPL pressure, Pn, is initially identical to the linear water pressure. Air pressure, Pa, is
equal to atmospheric pressure at all times because of the passive air phase assumption, which may
be considered the most significant simplifying assumption of the model formulation (Faust 1985).
Saturation
The initial air and water saturations in the domain were calculated using the air-NAPL capillary
pressure-saturation curve because this was initially equivalent to the air-water curve, as demonstrated
by equation 28. Air saturation could be directly read off the Pcan curve for each water pressure
increment and the corresponding water saturation calculated by:
aw SS −= 1 (29)
Equation 29 is valid because before NAPL is released, only the water and air phases are present in
pores so that the sum of their saturations must equal unity. Appendix I includes the initial vertical
water saturation profile. The initial NAPL saturation was zero everywhere in the domain except for the
source node, where the saturation was calculated using the air-NAPL pressure-saturation curve.
5.2.4 Constitutive relations
Capillary pressure-saturation-permeability curves for NAPL-water and air-NAPL were required in the
simulation data file. These were calculated using the van Genuchten equations with parameters _, n
and m derived from fitting the van Genuchten model function to laboratory measurements (see section
3.3).
NAPL-water curves were formulated for equal increments in NAPL saturation (Sn). Values of Sn
ranged from 0.0 to 1.0 and the corresponding capillary pressures, Pcnw, were calculated using the van
Genuchten model (equation 13). Associated relative permeabilities for NAPL (krn) and water (krw) were
also calculated using van Genuchten (equation 17 and 18). Air-NAPL curves were formulated for
equal increments in capillary pressure (Pcan). The corresponding air saturations (Sa) and relative
permeabilities for NAPL (krn) and air (kra) were also calculated using the van Genuchten equations 11,
17 and 18, respectively.
Also included in the model data file was the reference porosity for Leverett scaling (0.4) and Leverett’s
exponent (0.5). The reference permeability for Leverett Scaling (which is the permeability that the
inputted curves were calculated for) was entered erroneously as the mean permeability (3.43 x 10-11
m2 ). Actual reference permeabilities were in fact 10-11 m2 for the NAPL-water curves and 3.22 x 10-11
m2 for the air-NAPL curve. Due to time constraints, a sensitivity analysis to examine the effect of a
different set of input curves on simulation results was unable to be performed. Although it is expected
52
that this slight error would have minimal effect on numerical outputs, a quantitative sensitivity analysis
is necessary. A table of the set of pressure-saturation-permeability curves used for all simulations, as
well as the revised curves with the correct reference permeability, are included in Appendix J.
Table 5-1 Numerical model input parameters used in all NAPL simulations
Parameter Value
Number of nodes (x) 25
Number of nodes (y) 13
Number of nodes (z) 50
Nodal spacing (x) 0.4 m
Nodal spacing (y) 0.3 m
Nodal spacing (z) 0.1 m
Water density, _w 1000 kg m-3
NAPL density, _n 885 kg m-3
Water dynamic viscosity, _w 0.0010 Pa.s
NAPL dynamic viscosity, _w 0.0177 Pa.s
Air-NAPL interfacial tension, _an 30 dyn cm-1
NAPL-water interfacial tension, _an 48 dyn cm-1
van Genuchten parameter, _an 0.028
van Genuchten parameter, _aw 0.033
van Genuchten parameter, n 4.60
van Genuchten parameter, m 0.783
Leverett’s scaling exponent, _ 0.5
Reference porosity for Leverett scaling, _ 0.4
Reference permeability for Leverett scaling, k 3.43 x 10-11 m2
NAPL pressure at source nodes(s) 2602 Pa
NAPL saturation as source node(s) 0.661
53
5.3 Monte Carlo Analysis
5.3.1 Description
A Monte Carlo analysis was performed to evaluate the effect of spatial variability of subsurface
properties on transformer oil migration in Cottesloe Sand. Of primary interest was the vertical, and to
a lesser extent horizontal, migration of oil because of the ultimate concern of transformer oil leaks
reaching the water table. For this reason, the rate of NAPL infiltration and the movement with respect
to time has not been investigated in great detail.
Fifteen spatially correlated random permeability fields were generated using FGEN91 (Robin et al.
1993) with identical statistics but different random seeds (see section4.2). Spills with identical release
conditions were simulated in each realization, allowing the influence of spatial variability of
permeability on final oil saturation distribution to be evaluated. Each simulation was run with a spill
volume of 100L through a single source node of area 0.12m2 located in the middle and top of the
domain. An equivalent simulation was performed in a homogeneous medium where the average
permeability (3.43 x 10-11 m2) was used for all nodes in the domain. Comparison between results
obtained from the homogeneous field simulation to those simulations incorporating variable
permeability enabled the extent of heterogeneity influence on migration to be evaluated. Analysis of
the shape of each NAPL body at the last time step is aided by the calculation of spatial moments
which provide estimates on the movement of the centre of mass of the body (first moments), as well
as the amount of spreading which has occurred (second moments) (Brewster et al. 1995). A brief
summary table of results are included in Appendix K.
5.3.2 Vertical and Lateral Migration
Maximum penetration depths of NAPL after 100 days of migration were found to be 1.0 m in 11
realizations, 1.1 m in 4 realizations, and 1.0 m in the homogeneous field. Figure 5.2 presents a plot of
depth of penetration against time for all realizations as well as for the homogeneous case. Only the
first 5000 seconds (83 minutes) were plotted because some NAPL body fronts only penetrated to their
greatest depth some 90 hours later. The rapid decrease in the rate of penetration at larger times is
due to the removal of the injection force. From Figure 5.2, it is evident that the rates of penetration of
the NAPL front in each simulation are not identical which is a result of the stochastic nature of the
underlying permeability fields. The time scale of this variability is in the order of hours. The
homogeneous case exhibits a fairly average rate of NAPL front penetration.
The centre of mass in the vertical direction reflects the overall vertical position of the NAPL body and
was calculated for all realizations at the last time step. Values ranged between 32.9cm and 36.3cm,
with the homogenous simulation exhibiting a vertical centre of mass of 34.3cm. The latter value lies
extremely close to the ensemble average of 34.5cm which is not surprising due to the stochastic
generation of the permeability fields. Figure 5.3 shows the final second moment for the x direction and
y direction for all realizations, as well as for the homogeneous field and the ensemble average.
Second moments provide information about the amount of spreading about the centre of mass. This
54
figure illustrates the small range in variability between realizations, and more importantly the similarity
between the spreading of the NAPL body in the homogeneous field and the ensemble average of the
realizations. Monte Carlo simulations performed by Essaid and Hess (1993) also illustrated that the
use of mean properties reproduces the ensemble average.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 1000 2000 3000 4000 5000
Time (seconds)
Pen
etra
tion
dept
h (m
)
Figure 5-2 Penetration depth for the first 5000 seconds of migration. The thick dark line representsthe homogeneous case.
0.205
0.210
0.215
0.220
0.225
0.230
0.235
0.230 0.240 0.250 0.260 0.270
Second Moment in x (m2)
Sec
on
d M
om
ent
in y
(m
2)
RF1 - RF15
Homogeneous
Ensemble average
Figure 5-3 Plots of spatial second central moments of simulated spills in 15 realizations and also in ahomogeneous field exhibiting mean properties. Illustrated is the similarity between use of meanproperties and the ensemble average.
55
Maximum spatial lateral spreading for each realization occurred in the upper most horizontal layer in
the domain. For all simulations, the boundaries of NAPL in this layer exhibited an identical shape and
size, measuring 2.8 m in the x direction and 2.7 m in the y direction (i.e. radius of approximately 1.4m).
This radius represents the extent of lateral spreading from the point source and can therefore be seen
to exceed vertical penetration (i.e. 1.0 m – 1.1 m) in all cases. Upon initial consideration, one may
explain this phenomenon by the presence of slightly lower permeability lenses in the domain, which
would consequently bring about lateral spreading. This phenomenon is illustrated in similar previous
studies such as Kueper and Frind (1991b) and Brewster et al. (1995) who demonstrated that lateral
spreading is a function of the permeability contrasts encountered and the lateral extent of low
permeability layers.
In the context of the numerical simulation performed in this study, lateral spreading cannot be
explained by permeability contrasts. The reason for this is not only because of the extremely low
magnitude in permeability variation in the field, but is evident upon examination of the NAPL
distribution in the homogeneous field. In this case, a constant average permeability is assigned to
every node in the domain producing an isotropic field, yet lateral NAPL migration is still seen to
exceed vertical penetration. Equivalent capillary forces are acting in both the vertical and horizontal
directions but gravity also contributes to vertical penetration. Isotropic media must therefore exhibit
greater vertical penetration than horizontal migration of oil, or must at least be equivalent in each
direction if gravity effects are negligible.
The only resulting explanation for why maximum lateral spreading of NAPL exceeds vertical
penetration in the homogeneous field simulation involves the spatial discretization of the domain. The
nodal spacing in the z direction is 0.1 m as opposed nodal spacings of 0.4 m and 0.3 m for the x and y
direction, respectively, so NAPL migration can therefore be captured at a finer level in the vertical.
Lateral spreading of NAPL at distances of 1.0 m or 1.1 m from the point source (i.e. the maximum
vertical penetrations for all realizations) would mean that with the present nodal separations,
horizontal migration will be recorded as 1.2 m in both the x and y direction. This is precisely the case
in all the Monte Carlo simulations. The main conclusion from this discovery is that because lateral
migration is shown to be equivalent to vertical migration, then gravity effects on flow are negligible and
oil movement is controlled completely by capillary forces.
Thus, by comparison of results from the homogeneous case to those from the random fields, it is
evident that spatial variability of permeability and constitutive relations make little difference to the final
penetration depth and the shape of the oil body. This result, coupled with knowledge of the small
range and distribution of permeability in the field, highlights the relative homogeneity of Cottesloe
Sand. Gravity effects are also shown to be negligible and that the system is governed completely by
capillary forces. Discretization of the field is also shown to have an effect on the ratio of vertical to
lateral migration.
56
5.3.3. Investigation of a single realization
To evaluate whether variable permeability had any effect on the saturation profile, generated field
number four (RF4) was examined in finer detail. This particular field was selected as it demonstrated
a fairly average penetration time (57 minutes), although any field could have been selected for the
extended study.
Figure 5.4 illustrates identical 2-D saturation profiles generated in the homogeneous domain and also
in RF4, demonstrating that spatial variability of permeability has no real overall influence on oil
distribution in Cottesloe Sand. The reason for this is that changes in permeability in the subsurface
are extremely small such that the contrast between permeability “layers” is almost negligible. The
variance of the natural logarithm of the permeabilities derived from actual measurements was used to
create the spatially variable realizations, and as this was value was extremely small (0.0676), then the
unresponsiveness of spills to permeability variations is not surprising. Close comparison between the
saturation and permeability profiles of the column directly beneath the spills (Figure 5.5) indicates that
that the existence of a single lower permeability “layer” at depth 0.6 m corresponds to a very slight
increase in saturation at this depth. Changes in soil properties are therefore demonstrated to have at
least some influence on the simulated NAPL saturation in Cottesloe Sand, even if only by a very minor
amount.
Figure 5-4 NAPL distribution for the homogeneous field in comparison to Random Field Four (RF4).This two-dimensional contour plot illustrates the identical spill shape between the two and highlightsthe immunity of NAPL saturation to the low variations in permeability.
57
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-24.2-24.1-24.0-23.9-23.8-23.7
ln k
dep
th (
m)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.1 0.11 0.12 0.13 0.14 0.15
NAPL saturation (%)
dep
th (
m)
Figure 5-5 The natural logarithm of permeability of RF4 in comparison to NAPL saturation. Only avery slight increase in saturation can be seen at depth 0.6m which can be seen to correspond to ahigher permeability layer. However, the values of the change in permeability and the increase insaturation are extremely small.
Investigations into the effect of release characteristics on oil migration are presented in the selections
below. RF4 was used in all of these simulations so that the effect of altering each spill scenario could
be studied and stochastic effects ignored, without removing the natural heterogeneity of the aquifer.
5.4 Effect of Spill Volume
Simulations were performed for NAPL releases of 10L, 20L, 50L, 100L and 200L to investigate the
sensitivity of the system to spill volume. Each simulation was in RF4 and oil entered the domain
through the same single source node as in the Monte Carlo analysis. A contour plot of these spills is
presented in Figure 5.6 which visually demonstrates increased vertical and lateral migration for greater
spill volumes. Penetration depths ranged from 0.5 m for the 10 L spill to 1.3 m for the 200 L spill. A
brief summary table of results is presented in Appendix L.
Upon examination of Figure 5.7, it is evident that the total NAPL volume in each horizontal layer is
much greater at each depth in the domain, particularly in the upper layers, for larger spills. As more
NAPL enters through the source node, the fluid pressure and saturation in pores at the perimeter of
the spill increase which consequently leads to lateral spreading. Increase in saturation also increases
the relative permeability of the migrating NAPL body. The NAPL saturation profile in the column
directly beneath the spill is identical in all simulations because the NAPL source pressure and
saturation was not altered.
58
Figure 5-6 Contour plots for the final distribution of NAPL in the y-z plane for various spill volumes.
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0 5 10 15 20 25 30
NAPL volume (L)
Dep
th (
m)
10 L
20 L
50 L
100 L
200 L
Figure 5-7 NAPL volume in each layer for different spill volumes. Due to lateral spreading, there isevidently a greater NAPL saturation at all depths for larger spills.
Figure 5.8 presents a plot of release volume against maximum penetration depth as well as the
vertical centre of mass. It is evident, and somewhat obvious, that the larger release volumes
penetrated to greater depths in the porous media than did smaller volumes. Increased lateral
spreading in larger volume releases meant that NAPL mass was effectively taken away from the main
migrating body, contributing to a non-linear relationship between volume spilled and depth penetrated.
This plot is useful as it gives a direct indication of penetration depth for any given spill volume in a
0.12m2 spill area in Cottesloe Sand.
59
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 40 80 120 160 200
Volume of oil (L)
Dep
th (
m) Maximum penetration
Centre of mass
Figure 5-8 Depth of penetration for varying volumes of oil spilled in 1 node (0.12m2). The graphexhibits a non-linear relationship due to the loss of mass through lateral spreading.
Anisotropy is detected by the plot of the second moments in the x and y directions (Figure 5.9).
Spreading increases with volume spilled and is greatest in the x direction, perhaps due to the
presence of longer permeability lenses in this direction but more likely because the shape of the
source area was rectangular (i.e. 0.4m in x and 0.3m in y), bringing about a larger spreading in this
direction. Spreading about the centre of mass also increases with volume spilled.
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0 50 100 150 200 250
Spill volume (m3)
Sec
on
d m
om
ent
(m2)
x direction
y direction
Figure 5-9 Second moments in the x and y direction for various spill volumes. It is evident thatspreading of the NAPL body is greater in the x direction and increases with volume spilled.
A fundamental factor influencing the ultimate depth of penetration of migrating oil is the spill volume.
When large volumes of NAPL enters the subsurface, the saturation of the fluid increases which
consequently increases the relative permeability of the oil. The boundary of the NAPL body is
continually pushed outwards from the source as more volume is added, but the rate of this migration
slows significantly once the driving force behind NAPL migration is removed and the injection force is
dissipated.
60
5.5 Effect of Spill Area
Spill area is known to affect NAPL migration in the subsurface, in particular penetration depth and
NAPL saturations (Poulsen and Kueper 1992). Source areas of 1 node (0.12m2), 4 nodes (0.48m2), 9
nodes (1.08m2), 16 nodes (1.92m2) and 25 nodes (3m2) were used in separate simulations. All
simulations were performed in RF4 and with a spill volume of 100L. A brief summary of results is
included in Appendix M.
Contour plots of slices of the three-dimensional NAPL bodies for various spill areas are presented in
Figure 5.10. Penetration depths varied from 0.7 m for the 3 m2 spill area to 1.1 m for the 0.12 m2 spill
area. Larger spill areas exhibited less vertical movement because of the smaller local NAPL mass
available for penetration. Average saturation of NAPL at each layer for the various spill areas is
shown in Figure 5.11. These profiles confirm that the small release area spills penetrate further and
also that the bulk saturation for these releases is smaller in the upper layers (conservation of mass). It
is important to also notice that although the bulk saturation for each simulation was different, the
saturation profile directly beneath each spill were identical due to the constant pressure head.
Figure 5-10 Contour plots for the final distribution of NAPL in the y-z plane for various spill areas
61
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.0 0.4 0.8 1.2 1.6 2.0
NAPL saturation (% of bulk volume)D
epth
(m
)
1 node
4 nodes
9 nodes
16 nodes
25 nodes
Figure 5-11 NAPL saturation profile for each entire layer . The profiles at shallow depths demonstrateincreased lateral presence of NAPL for larger spill areas. At greater depths, the profiles show that oilpenetrated deeper for small release areas.
0
20
40
60
80
100
120
0 1000 2000 3000 4000
Time (seconds)
Vo
lum
e o
f o
il in
th
e d
om
ain
(L
)
1 node
4 nodes
9nodes
16 nodes
25 nodes
Figure 5-12 Volume of oil in the domain plotted against time. Larger spill areas exhibit a much sloweroverall penetration rate due to smaller fluid pressure which is the driving force behind NAPL migration.
Total NAPL volume was found to penetrate much faster through larger source areas (Figure 5.12).
The reason for this is simply due to the subsequent decrease in volume of NAPL per unit area.
62
Therefore, as the oil volume was dispersed over a larger area for multiple source node simulations,
the overall time for infiltration was greatly reduced.
Overall, it is shown that with a constant pressure head, a specified volume of oil takes longer to
penetrate when entering the domain through a smaller area. More importantly is the influence of spill
area on the ultimate penetration depth due to the spreading of NAPL mass in upper layers for larger
surface spill areas. Poulsen and Kueper (1992) showed that the penetration of 6 L of NAPL through
an area of 1cm2 migrated 1.2 m deeper than 6 L through an area of just over 1000cm2. The
implication of this is that drips of oil from transformer leaks will penetrate further than if released over a
large volume. Oil stain sizes beneath transformers are measurable and give some indication of the
spill area, although oil release patterns within this area is expected to be quite variable.
5.6 Effect of Infiltration Rate
To examine the effect of infiltration rate on oil penetration, the NAPL pressure of 2602 Pa at the
source node was abandoned, and a constant flux was employed. Infiltration rates of 1mL/s, 10mL/s
and 100mL/s were incorporated in three independent simulations using RF4 and a single source node.
The difference between the infiltration or ‘drip release’ approach and the constant NAPL head
approach is the physical nature in which the oil enters the subsurface. Contour plots of the middle
slice of the final NAPL body are presented in Figure 5.13.
Figure 5-13 Contour plots for the final distribution of NAPL in the y-z plane for various infiltration rates
All the infiltration rate simulations exhibited a maximum penetration of 1.0 m. The centre of mass for
the 1mL/s, 10mL/s and 100mL/s infiltration rates were 33.5 cm, 34.7cm and 35.0cm, respectively.
These results demonstrate that faster infiltration rates of oil lead to a greater overall increase in
vertical oil migration. An equivalent simulation using the constant NAPL head approach for infiltration
63
exhibited a vertical centre of mass of 35.3cm which was an even greater depth than all infiltration
simulations. Therefore, as we are interested in the penetration depth of transformer oil and the
likeliness that the body will reach the water table, then spill migration should be modelled with a
constant NAPL pressure head at the source node for a ‘worst case scenario’ approach.
Kueper and Frind (1991b) remarked that “slow, dripping releases of non-wetting phase contaminants
will tend to migrate further laterally than a catastrophic, high capillary pressure release.” This
comment is evident in the results presented in Figure 5.14. The highest infiltration rate release was
found to have the lowest centre of mass and thus slightly lower saturation at shallow depths. The
difference between the saturations for each infiltration simulation in the upper layers is very marginal.
This is not surprising because the variation in the vertical centre of mass is also very small.
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 0.2 0.4 0.6 0.8 1 1.2 1.4
NAPL saturation (% of bulk volume)
Dep
th (
m)
1 mL/s
10 mL/s
100 mL/s
Figure 5-14 NAPL saturation in each depth layer for varying infiltration rates. It can be seen that thehighest infiltration rate of 100mL/s exhibits slightly lower saturations in lower depths as the overallNAPL mass penetrates deeper. Variations in saturations of each layer are relatively minor.
Transformer oil is most often spilled onto the ground through slow steady drips of oil from gaskets and
flanges on the transformer. Even the slowest simulated infiltration release of 1 mL/s (equivalent to
86.4 L/day) is a much higher drip release rate than would be expected in reality. The implication of
this that it is more appropriate to overestimate the release rate of transformer oil so that the maximum
total vertical migration of oil is calculated and the ‘worst case scenario’ approach is adopted. Further
still, a constant pressure head was shown to produce the overall deepest penetration of oil which
validates the decision for selecting a constant inject pressure in modeling the movement of
transformer oil.
5.7 Effect of Rain
Rain introduces additional water into the subsurface and therefore has an effect on the movement of
transformer oil. As the water percolates through the porous media, it takes the place of oil held in
smaller pores by capillary forces. This reason for this is that the increased water pressure, due to its
64
greater saturation at the surface, creates drainage conditions of the non-wetting fluid. In particular, the
water is preferentially wetting to the soil particles than the oil, and so oil is forced out of the smaller
pores and into larger pores. In these larger pores, the NAPL may reconnect to form a continuos
phase and become more mobile.
Attempting to simulate rain in a realistic manner is difficult and so was modelled by the introduction of
constant water infiltration at the surface. Before the rain, 100 L of oil was released into RF4 through a
single source node, identical to the conditions imposed in the Monte Carlo analysis. After all the oil
had entered the domain, rain was simulated for 24 hours with a constant water infiltration rate of 1.782
x 10-5 m3m-2s-1 (equivalent to 1.54 cm day-1).
As can be seen in Figure 5.15, the “rain” caused a decrease in NAPL saturation in the top 0.3 m of the
domain and a corresponding slight increase in saturation in lower layers. The shift in oil distribution
can be attributed to an increase in water pressure from the surface and the replacement of oil with
water in pores in the upper layers.
The inevitable presence of rain in real spill scenarios causes complications when attempting to predict
movement oil in the subsurface. If interested in the ultimate depth of penetration, such as in this
study, excluding the effects of rain in simulations may underestimate vertical migration. In the case
presented above, the simulation of rain did not affect the maximum depth of the NAPL body and
shifted the vertical centre of mass of the NAPL body only 1.5cm down. The downward movement of
oil in upper layers does demonstrate that in certain conditions the centre of mass of the NAPL body
may be pushed to greater depths. Situations that may impose such conditions include multiple or
heavy rainfall events and alternative initial NAPL saturation profiles before the simulation of rain.
It also important to notice that if the simulated rainfall is assumed to be the average daily rainfall, then
this would be equivalent to 5.62 m year-1 which is much over 6 times greater than the average annual
rainfall at Cottesloe of 0.85 m year-1 (Bureau of Meteorology 2001). Therefore, it is not expected that
rain would have a large influence on the maximum NAPL penetration.
Perhaps a more significant consequence of rain is the slow dissolution of NAPL components into
slowly passing water. Contaminated water may then percolate right down to the water table, even if
the depth of the main NAPL body is meters above. As interphase mass transfer was not incorporated
in the numerical model, transport of constituents could not be examined.
65
6.0 Implications
6.1 Comparison to Field Data
Confidence in numerical modelling is enhanced when solutions are compared to actual
measurements. The primary difficulty in attempting to compare simulation results from the numerical
model to actual measurements of NAPL concentration in the field, was that the volume of spilled oil
was completely unknown and could not be estimated even to the correct order of magnitude.
Numerical simulations performed in this study gave evidence that the ultimate oil distribution and
maximum vertical penetration is mostly dependant on the spill volume. In this sense, there is no way
of evaluating exactly how well the multiphase model captured NAPL migration in Cottesloe Sand,
although qualitative comparisons are shown to be useful.
Other problems involved in attempting to compare simulation results to field data is the variable water
saturation. The saturation profile used in the model was assumed to follow hydrostatic pressure.
Daily and seasonal variations in rainfall and temperature would also play a role in dictating the water
saturation distribution. The significance of this role could be determined by performing a sensitivity
analysis to examine the effect of variations in the water saturation profile on simulated results which is
recommended. Another influence on the spatial subsurface distribution of transformer oil that was not
incorporated in the model is the presence of unnatural construction sand directly beneath the
transformer. During the construction of each transformer foundation, approximately 1m of sand is
excavated and then returned after the insertion of a concrete slab. Due to construction standards, the
sand is replaced in layers which are compacted at regular depth intervals. The presence of these
layers may promote significant amounts of lateral spreading not accommodated for in the model.
As fluid properties are well established and the effect of heterogeneity in Cottesloe Sand is shown to
be almost negligible, then the estimation capability of transformer oil migration is limited by knowledge
on the nature of the spills. Most prominently is the absence of information involving the volumes of oil
lost from transformers.
Nonetheless, core samples were taken from around the spill beneath Transformer One at Cottesloe
Substation in order to gain some insight into actual oil distribution in the subsurface. Dye infiltration
tests were also conducted in the sample trenches and provided a visual assessment of the migration
of a solute and the subsequent homogeneity of Cottesloe Sand.
6.1.1 Core Samples
6.1.1.1 Sampling Methodology
Core samples were collected at 12 different locations beneath Transformer One at Cottesloe
Substation as shown in Figure 6.1. Due to overhead electrical equipment, a 3-metre segmented
auger was used for coring which restricted the maximum depth samples could be collected . A total of
66
73 samples were acquired at half metre intervals up to 3m, or shallower in some cases of limestone
interference. A log for each core was recorded and is included in Appendix N. The colour of the sand
was observed to change colour from brown to yellow in all cores at depths ranging from 0.5m to 1.0m
deep, but usually at around 0.8m deep. This change in colour most likely indicates the interface
between disturbed sand and the natural sand, as was also observed on the walls of the sample
trenches.
Olfactory observations were recorded for each sample and classified as no smell, slight smell or
strong smell of transformer oil. These provided a qualitative indication of contamination, and as one
would expected, higher oil concentrations were detected at locations closer to the actual spill.
Each sample was retained in a glass jar and placed in dark refrigerated conditions at the earliest
convenience to ensure minimum degradation and volatilization of components due to light or
temperature. Twenty five samples were later chosen to get analysed for the total petroleum
hydrocarbon (TPH) concentration. The selected samples for analysis were distributed fairly evenly
over the sample domain and were located at 1m, 2m and 3m depths with at least one sample selected
from 11 of the 12 locations. Although more samples were available, the number selected for
laboratory testing was kept to a minimum due to the large cost of analysis.
Figure 6-1 Location of core samples taken from beneath Transformer One at Cottesloe Substation
67
6.1.1.2 Results and Discussion
From the 25 samples sent to be tested for the presence of transformer oil, only 7 were found to
contain detectable concentrations of hydrocarbons. Detected hydrocarbons were divided into groups
depending on the number of carbon atoms in the structure of the molecules. These results verify that
transformer oil is primarily composed of C15-28 and to a lesser extent C29-36, hydrocarbon molecules,
as was first presented by Bowman Bishaw Gorham (1997). Complete laboratory results are included
in Appendix O and summarized in Table 6-1 below:
Depth A C H D
1 m 8290 145 650 5830
2 m 140 3120 3380 < 0.4
3 m < 0.4 < 0.4 < 0.4 < 0.4
Table 6-1 Summary of measured concentrations of TPH ( mg oil / kg of soil) from the analysis of 25samples collected from locations around the spill beneath Transformer One.
As only samples from 4 locations and 2 depths contained oil, it was not feasible to attempt to draw any
quantitative conclusions from the measured concentrations. However, qualitative analysis of the
measured concentrations do provide some insight into NAPL distribution.
At locations C and H, NAPL concentrations were greatest at the lower depth. These measurements
would be consistent with the numerical simulations if they were located directly beneath the spills, as it
was shown from numerical simulations that the concentration of NAPL increases with depth below the
spill. However, as these were located approximately 1m from the source area, it is expected that
NAPL concentration should be greater at shallower depths. The higher NAPL concentration closer to
the surface at location A demonstrates this, although a more likely explanation for this high
concentration is presence of major cable oil spills less than a metre from this location. The migration
of cable oil interferes with expected NAPL concentrations due to transformer oil leaks, but are not
included in this study.
The maximum penetration depth for all locations were not detected beyond 2m. This depth is
comparable to the 1.5 m maximum oil penetration depth for the 200L spill in 0.12 m2 numerical
simulation. Simulated spill volumes of greater than 200L can be expected to match this 2 m depth and
are also more likely to be reflective of the total likely spill volume from the transformer over the last
several decades. Lateral spreading of NAPL in the numerical simulations were similar to the
spreading that occurred in the field. Oil was found to be present at distances of at least 1 m from the
edge of the transformer spill which was measured to be 1.5m2 in surface area. The simulations
involving the release of 100L into a 1.08 m2 and 1.92 m2 spill area were both shown to exhibit lateral
spreading of 1.4 m from the point source.
68
Actual values of oil concentrations produced from the laboratory measurements are generally two
orders of magnitude larger than the values produced from the simulated NAPL concentrations.
Possible reasons for this discrepancy are numerous and can in no way be affirmed, but may include
aspects such as the volume of release and perhaps also unnatural heterogeneity in the upper layers
of the subsurface.
6.1.2 Dye Infiltration Tests
Dye infiltration tests were performed in the sample trenches to observe the effect of subsurface
heterogeneity on solute transport. The tests endeavoured to also measure in situ hydraulic
conductivity, but lack of data precluded this.
Blue dye was injected into the sample trenches at a total of 21 different locations. A metal cylinder of
70mm internal diameter was pushed slightly into the top of the trench step and dye was allowed to
pond inside of this. A constant head of approximately 5cm was created inside the cylinder with the
use of a Marriott bottle, and after some initial time the flow became constant. Approximately 2L of dye
was allowed to infiltrate for each test before the Marriott bottle was removed. The dye bodies were
examined by digging away slices from the wall and the resulting dye shapes were subsequently
photographed. Several measurements on each shape was taken to record the shape of the dye
bodies (i.e. maximum penetration depth, maximum lateral spreading, maximum depth of lateral
spreading).
Figure 6.2 shows some examples of slices cut away from the wall where dye had been allowed to
infiltrate from the point source. They can be seen to exhibit almost perfect symmetry and the
perimeter of dye migration forms a regular circular shape. Heterogeneities were shown to affect dye
migration such as the presence of sticks, and also of limestone rocks. These pictures give evidence
of the extreme relative homogeneity of Cottesloe Sand.
Figure 6-2 Shapes of dye infiltration tests. Each body exhibits an almost perfect shape anddemonstrates the homogeneity of the sand. Notice in the middle picture how dye has migrated arounda stick.
The most significant conclusion resulting from the shape of the dye bodies, is that lateral spreading
exceeding vertical penetration in every case. This gives evidence of definite anisotropy due to
69
horizontal bedding as the lateral spreading cannot be explained in any other way. It has been shown
in this study that low permeability lenses do not significantly influence NAPL migration. Capillarity in
the horizontal direction will not naturally exceed capillarity in the vertical unless there is some kind of
structure in the sand. The observed dimensions of the dye are included in Appendix P and shows that
there exists a linear relationship between the maximum penetration depth of the dye and the depth to
width ratio of the shapes.. Therefore, it can be concluded from the dye tests that Cottesloe sand is
homogeneous (due to the regularity of the dye shapes) as well as anisotropic (due to large lateral
migration).
6.2 Applicability and Further Research
6.2.1 Use of average properties
This research has demonstrated that the range in permeability in Cottesloe Sand is very small (i.e.
within the same order of magnitude) such that the sand is very homogeneous. Although contrasts of
permeability do exist in every realization as well as in the field, the magnitude is shown to be too small
to significantly affect oil migration. This is reflected in the spill simulations which show that oil
migration characteristics in the homogeneous field are almost identical to those in all the realizations.
This conclusion is not drawn from the fact that the ensemble average of simulations in multiple
realizations is almost identical to the homogeneous field, but rather because releases in the
homogeneous field demonstrates similar behaviour of oil movement for all realizations.
The implication of this result is that it would be reasonable to model transformer spills in Cottesloe
Sand using the average permeability value due to its extreme homogeneity. If applying this theory to
other sites, it must be noted that as the variation in subsurface properties increase, then so does the
variation in migration characteristics so that the validity of this assumption would decrease.
6.2.2 Extension to other sites
Past research has indicated that NAPL migration in sand is sensitive to variations in permeability and
capillary characteristics (eg. Poulsen and Kueper 1991). If there is little variation in these properties
then influences on NAPL migration are limited to the average fluid and soil properties and the nature
of the release. However, although it has been demonstrated that variations in permeability do not
influence oil migration at Cottesloe Substation, this conclusion needs to be extended to other sites.
Figure 6.2 displays the distribution of substations according to their assigned soil type. Cottesloe
Sand is derived from the Tamala Limestone formation and is assigned as the underlying geological
unit for approximately 20% of the 65 Substations located within the Perth Metropolitan Area. Similar
to Cottesloe Sand is Karrakatta Sand, which is also derived from Tamala Limestone but is deeper and
older in origin. Karrakatta Sand accounts for over 30% of Substation soils. Therefore, it can be
concluded that the soil type at the study site is representative of approximately half of the Substations
in the Metropolitan Area.
70
30%
19%16%
7%
7%
21%Karrakatta
Cottesloe
Bassendean
Southern River
Vasse
Other
Figure 6-3 Soil types assigned to Western Power Metropolitan Substations. This pie chartdemonstrates that half of the Substations are located on the fairly homogeneous Cottesloe andKarrakatta Sands.
Further research must be undertaken to investigate the variation of subsurface properties between
sites of the same assigned soil type. The subsurface structure produced for Cottesloe Substation may
be reasonably indicative of the structure at other sites located on Cottesloe Sand (and perhaps also
Karrakatta Sand). Therefore, if this assumption can be made, then spatial variations of permeability
and capillary pressure-saturations may not need to be measured in great detail at these sites. This
approach is also suggested by Essaid and Hess (1993) who wrote that “improved simulations of field
spills can be obtained by using correlation structures of hydraulic properties from documented sites
with similar depositional histories, and conditioning the distributions to data from the site of interest, if
available.” Essaid and Hess also suggest that hydrogeological data (i.e. permeability and retention
curves) may be able to be obtained from particle-size data.
Elfeki et al. (1997) presented several techniques to describe formation heterogeneity using ‘hard data’
such as direct measures of permeability. Hard data was collected in this study through sample
collection, laboratory analysis and geostatistical modeling of variations in permeability. Although this
procedure was only performed for Cottesloe Sand, the methodology presented may be applied to
other common Substation sand types, in particular Karrakatta and Bassendean Sand, such that similar
hard data may be measured and used to describe the heterogeneous structure of these formations.
Due to economic limitations in obtaining hard data, there is often insufficient detailed information
known about the heterogeneity of geological formations of interest, therefore “more indirect qualitative
or subjective geological information (soft data) may be available from geological surveys such as
geological maps, well logs, bore hole data and geological expertise” (Elfeki et al. 1993, p. 65). Elfeki
et al. also propose a “practical methodology for modelling geological complexity of natural formations
71
using soft data.” The acquirement and application of soft data for individual sites is left for further
research.
The validity of extending the known structure of the sand at Cottesloe Substation to other sites
exhibiting Cottesloe Sand is also increased by the demonstrated homogeneity of the sand. It has
been shown that oil migration in multiple realizations can be represented by a homogeneous field for
the site. The implication of this is that the average hydrogeological properties for each site could be
used in assessing NAPL migration through numerical modelling.
Apart from the magnitude and spatial variation of subsurface hydrogeological properties, the migration
of transformer oil is also affected by fluid properties and characteristics of the release. Physical fluid
properties, namely density, viscosity and interfacial tensions, of transformer oil is known and identical
for all oil in Western Power transformers. Surface oil stains beneath transformers vary in area but are
visible and have already been photographed and measured at all Western Power Substation sites.
The random dripping nature of leaks means that no transformer spill enters the subsurface in an
identical manner. As mentioned previously, unknown spill volumes are the primary limiting factor
which undermines the predictive capabilities of transformer oil migration for all spills.
6.2.3 Comparison to a simple multiphase model
It is planned that results from the three-dimensional numerical model employed in this study be
compared to results for equivalent simulations using a simple, homogeneous one-dimensional model
obtained by Mullen (2002). HSSM (Hydrocarbon Spill Screening Model) is an example of such a
model and does not require detailed multi-dimensional permeability data. If the simulators are run with
matching inputs and results are found to be fairly similar between the models, then this will prove that
there is no real need to use the numerical model employed in this study for further investigations into
transformer oil migration.
Advantages of using a one-dimensional analytical model over a complex three-dimensional simulator,
is that the simpler model exhibit simple input commands, has a much faster run time and complex
three-dimensional permeability data is not needed. The main disadvantage of such models is that
they cannot accommodate lateral flow due to spatial variations in soil characteristics or initial water
saturations. This study has shown that there exists little variation in subsurface properties in Cottesloe
Sand, thus increasing the appropriateness of such a model.
6.2.4 Dye infiltration tests
Dye infiltration tests were performed in the sample trenches for a visual assessment of the migration
of a solute. These tests were relatively quick, cheap and easy to perform. Further investigation
should be made into applying data obtained from dye infiltration tests to model NAPL migration or
alternatively heterogeneity. Quantitative analysis of the dye tests may include the volume of dye
penetrated against time and measurements of maximum lateral spreading and penetration depth.
72
7.0 Conclusions
Previous research has demonstrated that variations in subsurface hydrogeological properties can
have a great influence on the migration of NAPL in porous media. This study investigated the effect of
spatial variability of permeability and pressure-saturation relationships on the movement of
transformer oil in Cottesloe Sand. A three-dimensional numerical model was employed to simulate
spills in 15 realizations generated from direct measurements of permeability. Results from these
simulations demonstrated that contrasts in permeability did not have any significant influence on
vertical or lateral spreading of the NAPL bodies and that average properties produced similar
solutions. The reason for this was that the magnitude of the variation in permeability of the generated
fields was extremely small, giving evidence that the sand was very homogeneous. Regular and
symmetrical dye migration shapes produced from the dye infiltration tests also supported this
conclusion, as well as demonstrating that the sand is anisotropic. Therefore, it can be concluded that
Cottelsoe Sand is homogeneous and can be modelled using average properties.
Implications and recommended further research have been suggested and numerous pathways
presented for extending this work to model transformer oil migration at other sites. This includes the
possibility of using average properties as has shown to be appropriate for Cottesloe Sand; finding
ways to obtain and apply ‘soft data’; comparing results from a simple one-dimensional analytical
simulator; and exploring the feasibility of using data collected from dye infiltration tests to gain
quantitative insight into subsurface properties.
Results from numerical simulations showed that spill volume and release area had the most profound
influence on oil penetration depth in Cottesloe Sand. This shows that even with a perfect
reconstruction of subsurface properties, the predictive capabilities of any multiphase model is
undermined by the lack of information known about the nature of the release of individual transformer
oil leaks.
73
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Appendix APermeability calculations from laboratory data
Sample IDQ
(mL/s)Q
(mm^3/s)
PondedHead(mm)
Change inHead (mm)
SampleLength(mm)
K (mm/s)Intrinsic
permeability(microns^2)
P13 1.4483 1448.3 25 55 30 0.3581 36.50
CD8 0.9758 975.8 25 55 30 0.2413 24.59
CD1 0.8733 873.3 21 51 30 0.2328 23.74
KD10 0.7962 796.2 12 42 30 0.2578 26.28
D37 0.7826 782.6 9 39 30 0.2729 27.82
M9 1.1271 1127.1 20 50 30 0.3065 31.25
KD12 1.675 1675 20 50 30 0.4555 46.44
KD16 0.7606 760.6 17 47 30 0.2201 22.43
KD20 0.7531 753.1 28 58 30 0.1766 18.00
M6 0.9256 925.6 9 39 30 0.3227 32.90
KD1 1.0166 1016.6 15 45 30 0.3072 31.31
CD5 0.5318 531.8 14 44 30 0.1644 16.75
QLD2 0.6579 657.9 13 43 30 0.2081 21.21
KD28 1.074 1074 18 48 30 0.3043 31.02
KD8 1.023 1023 15 45 30 0.3091 31.51
CD7 0.918 918 15 45 30 0.2774 28.28
M4 0.934 934 14 44 30 0.2887 29.42
M11 0.944 944 28 58 30 0.2213 22.56
KD4 1.0408 1040.8 19 49 30 0.2888 29.44
KD6 0.9406 940.6 17 47 30 0.2721 27.74
KD14 0.9188 918.8 13 43 30 0.2906 29.62
KD24 1.3887 1388.7 18 48 30 0.3934 40.10
P7 1.3405 1340.5 17 47 30 0.3878 39.53
CD3 1.1847 1184.7 18 48 30 0.3356 34.21
KD26 1.0126 1012.6 26 56 30 0.2459 25.06
M8 1.1810 1181.0 13 43 30 0.3735 38.07
KD22 0.8327 832.7 13 43 30 0.2633 26.84
KD18 0.9141 914.1 26 56 30 0.2220 22.63
CD13 1.3243 1324.3 27 57 30 0.3159 32.21
CD15 1.2166 1216.6 26 56 30 0.2954 30.11
S14 1.0625 1062.5 27 57 30 0.2535 25.84
S16 0.6697 669.7 16 46 30 0.1980 20.18
S18 1.3017 1301.7 17 47 30 0.3766 38.39
S22 1.2023 1202.3 25 55 30 0.2973 30.30
S24 1.0531 1053.1 29 59 30 0.2427 24.74
S26 1.2258 1225.8 29 59 30 0.2825 28.80
S28 1.0079 1007.9 25 55 30 0.2492 25.40
S30 1.8086 1808.6 29 59 30 0.4168 42.49
S32 1.1582 1158.2 16 46 30 0.3424 34.90
C12 1.7473 1747.3 19 49 30 0.4849 49.43
C14 0.7434 743.4 27 57 30 0.1773 18.08
C18 1.4178 1417.8 17 47 30 0.4102 41.81
C20 1.349 1348.6 21 51 30 0.3596 36.65
C22 0.804 803.5 30 60 30 0.1821 18.56
C24 1.320 1320.3 21 51 30 0.3520 35.89
C26 1.401 1400.9 19 49 30 0.3888 39.63
C30 1.267 1267.4 22 52 30 0.3314 33.78
C34 1.433 1433.0 24 54 30 0.3609 36.78
C36 0.990 989.5 21 51 30 0.2638 26.90
81
C4 1.362 1362.1 21 51 30 0.3632 37.02
C6 1.213 1212.8 27 57 30 0.2893 29.49
C8 1.802 1801.6 15 45 30 0.5444 55.49
C10 1.335 1335.3 18 48 30 0.3783 38.56
C2 1.659 1658.6 17 47 30 0.4799 48.92
C28 1.723 1723.4 21 51 30 0.4595 46.84
C38 1.183 1183.1 24 54 30 0.2979 30.37
S4 1.326 1325.6 25 55 30 0.3277 33.41
Q6 1.777 1776.5 13 43 30 0.5618 57.27
W14 1.496 1495.6 16 46 30 0.4421 45.07
Q4 3.036 3035.6 26 56 30 0.7371 75.14
W18 1.653 1652.6 15 45 30 0.4994 50.91
Q34 1.416 1416.3 22 52 30 0.3704 37.75
W2 1.459 1459.1 20 50 30 0.3968 40.45
S8 0.768 767.7 19 49 30 0.2131 21.72
Q28 1.469 1468.9 21 51 30 0.3917 39.92
Q20 1.368 1368.1 23 53 30 0.3510 35.78
W22 1.343 1342.6 20 50 30 0.3651 37.22
Q18 1.534 1534.3 17 47 30 0.4439 45.25
Q8 1.606 1605.7 21 51 30 0.4281 43.64
Q38 1.382 1381.6 17 47 30 0.3997 40.75
S2 1.048 1047.9 11 41 30 0.3476 35.43
S12 1.217 1217.2 23 53 30 0.3123 31.83
W12 1.403 1402.5 24 54 30 0.3532 36.00
Q14 1.430 1429.8 16 46 30 0.4227 43.09
W6 1.191 1191.0 12 42 30 0.3856 39.31
S10 0.948 947.9 23 53 30 0.2432 24.79
W4 1.344 1343.8 25 55 30 0.3322 33.87
Q12 1.394 1393.6 18 48 30 0.3948 40.24
W30 1.229 1229.5 13 43 30 0.3888 39.63
W28 0.874 873.8 25 55 30 0.2160 22.02
Q36 1.504 1503.6 25 55 30 0.3717 37.89
W24 1.023 1022.9 14 44 30 0.3161 32.23
W20 1.078 1077.6 23 53 30 0.2765 28.18
Q29 1.190 1189.8 21 51 30 0.3172 32.34
Q10 1.429 1429.2 25 55 30 0.3534 36.02
W16 0.863 863.0 15 45 30 0.2608 26.58
Q22 1.843 1843.4 15 45 30 0.5570 56.78
W10 1.567 1567.1 28 58 30 0.3674 37.45
Q16 1.465 1464.9 19 49 30 0.4065 41.44
Q42 1.601 1600.6 17 47 30 0.4631 47.21
W32 1.329 1328.7 28 58 30 0.3115 31.76
Q2 1.888 1887.5 21 51 30 0.5033 51.30
W8 1.114 1113.8 24 54 30 0.2805 28.59
DR 1.530 1529.7 15 45 30 0.4622 47.12
Q32 1.333 1333.0 27 57 30 0.3180 32.42
W26 1.562 1562.4 28 58 30 0.3663 37.34
Q26 1.511 1511.0 18 48 30 0.4281 43.64
Appendix BLaboratory data for the air-NAPL pressure-saturation curve
Sample ID - P4
k = 3.224E-11 m2
Initial sat. = 23.6cm3Floor is datum
Time forequ.
(hours)
BuretteReading
Soilfrom
datum
Burette 0from
datum
Oil levelfrom
datum
delta h(cm oil)
delta h(cm water)
Sw(cm3)
Sw Se
12 23.6 154 177.6 154 0 0.0 23.6 1.000 1.00012 21.1 154 157.6 136.5 17.5 15.5 21.1 0.894 0.88912 17 154 137.6 120.6 33.4 29.6 17 0.720 0.70812 11.3 154 117.6 106.3 47.7 42.2 11.3 0.479 0.45612 4.1 154 95.5 91.4 62.6 55.4 4.1 0.174 0.13812 2.6 154 75.5 72.9 81.1 71.8 2.6 0.110 0.07112 2 189.5 74 72 117.5 104.0 1 0.042 0.000
Appendix C
A standard sieve test, as outlined by Fetter (1994), was performed on four random samples
by Mullen (2002) to determine the particle size distribution. A grain-size distribution curve
was plotted for each sample which shows little variation in particle size distribution between
samples (Figure 1):
0
10
20
30
40
50
60
70
80
90
100
0.001 0.01 0.1 1 10 100
Particle size (mm)
Per
cen
t pas
sing
(%
)
k = 2.46E-11
k = 2.51E-11
k = 2.83E-11
k = 4.19E-11
Figure 1 Grain-size distribution curves for four random samples taken at the study site inCottesloe
According to the proportion (by weight) of sediments lying between standard particle size
ranges (Fetter 1994), the sediments at the study site can be classified as 50% fine sand and
50% medium sand (ie fine-medium sand).
The uniformity coefficient, Cu, is a parameter which indicates how well or poorly sorted the
grains are (Fetter 1994):
10
60
d
dCu =
where d60 is the grain size that is 60% finer by weight and d10 is the grain size that is 10%
finer by weight. From the particle size distributions, d60 was found to be approximately
0.50mm for all samples and d10 was shown to be 0.16mm, hence a uniformity coefficient of
3.12. According to Fetter (1994), a uniformity coefficient less than 4 (Cu < 4) indicates a well-
sorted sand. Therefore, the sand at the sample site in Cottelsoe is well-sorted, consisting of
particles of a fairly uniform size.
Appendix DObserved and fitted dimensionless capillary pressures
Fitting VG Parameters
observed observed fitted alpha 0.0600Se Pc nw Pcd nw Pcd nw
0.007 53.333 1.33E-05 1.25E-05 n 4.6000.008 53.333 1.31E-05 1.18E-05 m 0.7830.011 53.333 7.57E-06 1.08E-05 k 3.224E-110.012 53.333 1.32E-05 1.07E-05 0.021 53.333 7.89E-06 9.06E-06 r2 0.92666
0.022 53.333 7.19E-06 9.01E-060.023 40.000 9.97E-06 8.85E-060.027 40.000 9.93E-06 8.47E-060.038 40.000 9.82E-06 7.73E-060.060 40.000 5.92E-06 6.75E-060.074 40.000 5.40E-06 6.38E-060.112 26.667 6.62E-06 5.64E-060.133 26.667 6.65E-06 5.37E-060.163 26.667 6.55E-06 5.05E-060.222 40.000 5.68E-06 4.58E-060.243 26.667 3.60E-06 4.44E-060.281 26.667 3.95E-06 4.23E-060.484 13.333 3.31E-06 3.42E-060.556 26.667 3.79E-06 3.19E-060.617 13.333 3.27E-06 3.01E-060.628 13.333 3.32E-06 2.98E-060.696 13.333 1.80E-06 2.78E-060.705 13.333 1.97E-06 2.75E-060.846 13.333 1.89E-06 2.28E-06
Cell X Y Z k
KD1 102 183 135. 31.3QLD 102 183 112. 21.2D37 932 182 123. 27.8KD4 932 182 96.0 29.4KD6 824 182 120. 27.7KD8 824 183 101. 31.5KD1 747 183 116. 26.3KD1 747 185 96.0 46.4KD1 627 182 112. 29.6KD1 627 183 86.5 22.4KD1 547 182 114. 22.6KD2 547 182 90.5 18.0KD2 440 182 109. 26.8KD2 440 182 83.5 40.1KD2 323 180 105. 25.0KD2 323 182 89.5 31.0P7 102 172 184. 39.5
CD1 102 172 156. 23.7CD3 954 172 177. 34.2CD5 954 172 151. 16.7M4 828 172 152. 29.4M6 745 171 170. 32.9M8 745 172 150. 38.1CD7 632 170 167. 28.3CD8 632 170 135. 24.6P13 548 170 138. 36.5
CD1 445 168 151. 32.2CD1 445 168 131. 30.1M9 336 167 160. 31.2M11 336 168 140. 22.5C2 104 160 247. 30.4C4 104 160 227. 55.5C6 104 160 210. 38.6C8 947 160 251. 26.3C10 947 160 214. 46.8C12 947 160 197. 41.8C14 839 158 237. 36.6C18 839 158 181. 18.5C20 751 158 220. 35.9C22 751 158 177. 39.6C24 635 159 198. 33.8C26 635 159 171. 38.9C28 548 159 196. 46.8C30 548 159 165. 36.8C34 443 157 164. 37.0C36 322 157 193. 29.5C38 322 158 164. 30.4
Trench
Appendix E(i)
Cell X (cm) Y (cm) Z (cm) k (microns^2)
S2 166 812 18.0 35.4S4 166 812 6.0 33.4S8 165 715 0.0 21.7
S12 172.5 608 26.0 31.8S10 156 608 9.0 24.8S14 164.5 550 28.0 25.8S16 139 540 6.0 20.2S18 152 396 38.0 38.4S22 155 280 39.0 30.3S24 141 275 22.0 24.7S26 144 197 47.0 28.8S28 144 197 22.0 25.4S30 136 97 51.0 42.5S32 136 97 27.0 34.9W2 282 816 82.0 40.5W4 282 816 37.0 33.9W6 285 721 84.0 39.3W8 269 721 40.0 28.6
W10 292 608 87.0 37.5W12 292 608 48.0 36.0W14 274 502 88.0 45.1W16 274 502 51.0 26.6W18 277 393 91.0 50.9W20 261 393 54.0 28.2W22 272 391 99.0 37.2W24 255 391 66.0 32.2W26 264 192 104.0 37.3W28 264 192 69.0 22.0W30 245 104 109.0 39.6W32 233 104 60.0 31.8Q2 421 846 163.0 51.3Q6 405 846 113.0 57.3Q8 412 733 165.0 43.6
Q10 401 733 134.0 36.0Q12 401 733 107.0 40.2Q14 413 609 166.0 43.1Q16 402 609 138.0 41.4Q18 394 609 112.0 45.2Q20 420 500 164.0 35.8Q22 411 500 137.0 56.8Q26 428 416 170.0 43.6Q28 428 416 135.0 39.9Q29 428 416 119.0 32.3Q32 436 385 165.0 32.4Q34 436 385 146.0 37.8DR 430 385 127.0 47.1Q36 406 193 162.0 37.9Q38 396 193 134.0 40.7Q42 380 105 129.0 47.2
Trench Two
Appendix E(ii)
Appendix F (i)
Variogram for the major principal axis
Appendix F (ii)
Variogram for the minor principal axis
Appendix F (iii)
Variogram for the vertical direction
Appendix G
FGEN91 code used for Random Field Generation
1 1 ISEEDH, ISEEDG first seeds for H and G
128 128 128 NFULL nodal dimensions of full field
25 13 50 NTRUNC nodal dimensions of truncated field
0.4 0.3 0.1 SSTEP spatial step size (delta X, Y, Z)
-24.13 2.25 HMEAN,GMEAN mean of H,G
0.068 0.050 HVAR,GVAR variance of H,G
0.0 0.0 HNUG,GNUG nugget of H,G
2 ITYPE power spectrum type (1=gaussian, 2=exp. cov)
1 ICROSS cross spectrum type (1=lin, 2=+ X-spec, -2=- X-spec, 3=user)
1.00 COHER coherency sq (use COHER>0.0 for ICROSS=1)
3.1 1.1 0.4 HLAMDA correlation lengths H
1.0 1.0 0.30 GLAMDA ................... G (ignored if ICROSS=1)
-0.1 ASLOPE slope linear X-spectrum (ignored if ICROSS.NE.1)
0.0 0.0 0.0 DELAY delay vector for G relative to H
1 IPSCRN = 1 -> progress output to screen
0 ICAUTO = 1 -> calculate and output autocovariances
0 IWBIN = 1 -> write fields in binary format
1 IWASC = 1 -> write fields in free-format
0 IWSEC = 1 -> write 3 sections through middle of field
*** requires a LARGE amount of disk space
Sample IDPermeability (E-11 m^2)
Saturation (cm3)
Volume of Sample (cm3)
Porosity
W27 2.20 26.0 66.2 0.39S28 2.54 25.7 66.2 0.39P4 3.22 26.8 66.2 0.40
Q35 3.79 34.0 66.2 0.51KD11 4.65 28.4 66.2 0.43
Q1 5.13 27.0 66.2 0.41
Average 0.42
Appendix HPorosity calculations
Depth (m) Sw
0.0 0.0000.1 0.3380.2 0.3570.3 0.3760.4 0.3940.5 0.4130.6 0.4320.7 0.4510.8 0.4700.9 0.4891.0 0.5071.1 0.5341.2 0.5601.3 0.5861.4 0.6121.5 0.6381.6 0.6651.7 0.6911.8 0.7171.9 0.7432.0 0.7702.1 0.7882.2 0.8062.3 0.8252.4 0.8432.5 0.8612.6 0.8802.7 0.8982.8 0.9162.9 0.9353.0 0.9533.1 0.9583.2 0.9623.3 0.9673.4 0.9713.5 0.9763.6 0.9803.7 0.9853.8 0.9893.9 0.9944.0 0.9984.1 0.9984.2 0.9984.3 0.9994.4 0.9994.5 0.9994.6 0.9994.7 0.9994.8 1.0004.9 1.0005.0 1.000
Appendix IInitial water saturation profile for all simulations
0.0
1.0
2.0
3.0
4.0
5.0
0.00 0.20 0.40 0.60 0.80 1.00 1.20
Water Saturation (Sw)
Dep
th (
m)
Appendix J (i)
Input pressure-saturation-permeability curves for NAPL-water and air-NAPL which were usedin the numerical simulations.
The reference permeability for Leverett scaling was entered erroneously as 3.43 x 10-11 m2 inthe data file, and should have been 1.00 x 10-11 m2 for the NAPL-water curves (first block ofnumbers) and as 3.22 x 10-11 m2 for the Air-NAPL curves (second block of numbers).
Pcnw Sw krw krn5208.4 -0.1 0.000 1.0005208.4 0.0 0.000 1.0005208.4 0.1 0.000 1.0005208.4 0.2 0.000 1.0005208.4 0.3 0.025 0.5774191.3 0.4 0.085 0.3733624.8 0.5 0.175 0.2293207.2 0.6 0.292 0.1272846.7 0.7 0.434 0.0602489.5 0.8 0.600 0.0212060.3 0.9 0.789 0.004
1.4 1.0 1.000 0.0001.4 1.1 1.000 0.000
Pcan Sa krn kra-98000 0.8927 0.0014 0.8325-88200 0.8826 0.0026 0.7940-78400 0.8658 0.0055 0.7396-68600 0.8367 0.0127 0.6601-58800 0.7832 0.0320 0.5406-49000 0.6808 0.0887 0.3653-39200 0.4927 0.2531 0.1545-29400 0.2304 0.5972 0.0215-19600 0.0469 0.9000 0.0004-9800 0.0020 0.9000 0.0000
0 0.0000 0.9000 0.0000
Appendix J (ii)
Revised input pressure-saturation-permeability curves for NAPL-water and air-NAPL.The effect of these curves on simulation results needs to be investigated in further research.
The reference permeability for Leverett scaling is 3.22 x 10-11 m2 for both sets of curves.
Pcnw Sw krw krn2866.5 -0.1 0.0000 1.0000
2866.5 0.0 0.0000 1.0000
2866.5 0.1 0.0000 1.0000
2866.5 0.2 0.0000 1.0000
2866.6 0.3 0.0055 0.8534
2307.0 0.4 0.0313 0.6783
1995.3 0.5 0.0861 0.5048
1765.5 0.6 0.1768 0.3450
1567.0 0.7 0.3088 0.2075
1370.4 0.8 0.4871 0.0994
1134.2 0.9 0.7162 0.0275
5.0 1.0 1.0000 0.0000
5.0 1.1 1.0000 0.0000
Pcan Sa krn kra-49000 1.0000 0.0000 1.0000
-48000 0.9580 0.0000 1.0000
-47000 0.9580 0.0000 1.0000
-46000 0.9580 0.0000 1.0000
-45000 0.9579 0.0000 1.0000
-44000 0.9579 0.0000 0.9999
-43000 0.9579 0.0000 0.9999
-42000 0.9579 0.0000 0.9999
-41000 0.9579 0.0000 0.9999
-40000 0.9579 0.0000 0.9999
-39000 0.9578 0.0000 0.9999
-38000 0.9578 0.0000 0.9999
-37000 0.9578 0.0000 0.9999
-36000 0.9578 0.0000 0.9999
-35000 0.9578 0.0000 0.9999
-34000 0.9577 0.0000 0.9999
-33000 0.9577 0.0000 0.9998
-32000 0.9577 0.0000 0.9998
-31000 0.9576 0.0000 0.9998
-30000 0.9576 0.0000 0.9998
-29000 0.9575 0.0000 0.9997
-28000 0.9575 0.0000 0.9997
-27000 0.9574 0.0000 0.9997
-26000 0.9573 0.0000 0.9996
-25000 0.9572 0.0000 0.9995
-24000 0.9571 0.0000 0.9995
-23000 0.9569 0.0000 0.9994
-22000 0.9567 0.0000 0.9992
-21000 0.9565 0.0000 0.9991
-20000 0.9562 0.0000 0.9989
-19000 0.9558 0.0000 0.9986
-18000 0.9554 0.0000 0.9982
-17000 0.9548 0.0000 0.9978
-16000 0.9540 0.0000 0.9972
-15000 0.9529 0.0000 0.9963
-14000 0.9515 0.0000 0.9951
-13000 0.9495 0.0000 0.9933
-12000 0.9467 0.0000 0.9907
-11000 0.9426 0.0000 0.9866
-10000 0.9363 0.0001 0.9801
-9000 0.9264 0.0002 0.9691
-8000 0.9101 0.0006 0.9496
-7000 0.8816 0.0018 0.9130
-6000 0.8289 0.0067 0.8401
-5000 0.7272 0.0285 0.6912
-4000 0.5359 0.1289 0.4186
-3000 0.2577 0.4569 0.1136
-2000 0.0535 0.8661 0.0060
-1000 0.0024 0.9939 0.0000
0 0.0000 1.0000 0.0000
Appendix KSummary of results from the Monte Carlo Analysis
RFMaximum
PenetrationDepth (m)
VerticalCentre ofMass (m)
InfiltrationTime (s)
InfiltrationTime
(minutes)
1 1.0 0.345 2334 38.9
2 1.0 0.349 3388 56.5
3 1.0 0.329 3880 64.7
4 1.1 0.353 3421 57.0
5 1.0 0.342 2546 42.4
6 1.0 0.333 2887 48.1
7 1.0 0.337 2385 39.8
8 1.1 0.363 4345 72.4
9 1.0 0.345 4196 69.9
10 1.1 0.357 4495 74.9
11 1.0 0.339 2631 43.9
12 1.0 0.344 2362 39.4
13 1.1 0.357 2896 48.3
14 1.0 0.338 2558 42.6
15 1.0 0.340 3244 54.1
H 1.0 0.343 3235 53.9
Average 1.0 0.345 3175 52.9
Volume (L)Maximum
Penetration Depth (m)
Vertical Centre of Mass (m)
Infiltration Time (s)
Infiltration Time (minutes)
10 0.50.161
161 2.7
20 0.70.202
464 7.7
50 0.90.272
1501 25.0
100 1.10.353
3421 57.0
200 1.30.449
7425 123.8
Average 0.9 0.288 2594 43.2
Appendix L
Summary of results from the effect of spill volume
Source Area
(nodes)
Source Area (m2)
Penetration depth (m)
Vertical Centre of Mass (m)
Infiltration Time (s)
Infiltration Time
(minutes)
1 0.12 1.1 0.353 3421 57.0
4 0.48 0.9 0.327 885 14.8
9 1.08 0.9 0.297 295 4.9
16 1.92 0.8 0.264 99 1.7
25 3.00 0.7 0.230 20 0.3
Average 0.88 0.294 944 15.7
Appendix MSummary of results from the effect of spill area
Location Date CollectedX Coordinate
(mm)Y Coordinate
(mm)Depth of Aggregate
(mm)Depth Cored
(mm)Stratigraphy
150mm limestone chunk 90 x 60mm200mm limestone chunk
500mm color change brown to yellow2750mm bits of stick and limestone2900mm bits of crumbly limestone
900mm color change brown to yellow2000mm limestone chunk2200mm hard limestone
1000mm color change brown to yellow2000mm hard limestone
D 12/02/2002 2700 3670 200 3000
1000mm chunk of limestone1000mm unusual cavity150 x 80mm
first 100mm dry sand and rocks 60 x 50mm500mm cavity
800mm color change brown to yellow2700mm limestone chunks
G 18/02/2002 1600 1250 150 3000 800mm color change brown to yellow
first 300mm black, sticky, dense800mm color change brown to yellow
I 18/02/2002 1750 4000 150 700 400mm color change brown to yellow
100mm end of dark grey/black layer800mm color change brown to yellow3000mm crumbly limestone chunks
700mm hit black oily layer900mm color change brown to yellow
L 22/02/2002 900 2160 150 3000
Appendix N
Field data for core samples collected beneath Transformer One
C 2000
E 400 3700 150 3000
12/02/2002
12/02/2002
150
2750
250 500 150 2200
1600 2350
B
3000A 2750 320 1508/02/2002
12/02/2002
F
H 1503000 3000
-450275018/02/2002 0
3000
18/02/2002 2150
1503800150018/02/2002J
300015065018/02/2002 1950K
Sample C 6-9 C 10-14 C 15-28 C 29-36 > C36 TPH Note:
A3 4.3 83 7000 1100 100 8287.3A5 < 0.2 3.8 140 < 0.4 - 143.8A7 < 0.2 < 0.2 < 0.4 < 0.4 - -B5 < 0.2 < 0.2 < 0.4 < 0.4 - -C3 < 0.2 < 0.2 100 45 - 145 Number DepthC5 2 15 2500 450 150 3117 3 1mD3 4.5 38 4800 790 200 5832.5 5 2mD5 < 0.2 < 0.2 < 0.4 < 0.4 - - 6 2.5mD7 < 0.2 < 0.2 < 0.4 < 0.4 - - 7 3mE5 < 0.2 < 0.2 < 0.4 < 0.4 - -F5 < 0.2 < 0.2 < 0.4 < 0.4 - -G3 < 0.2 < 0.2 < 0.4 < 0.4 - -G5 < 0.2 < 0.2 < 0.4 < 0.4 - -G7 < 0.2 < 0.2 < 0.4 < 0.4 - -H3 < 0.2 < 0.2 500 150 - 650H5 < 0.2 5.7 3000 370 - 3375.7H7 < 0.2 < 0.2 < 0.4 < 0.4 - -J3 < 0.2 < 0.2 < 0.4 < 0.4 - -J5 < 0.2 < 0.2 < 0.4 < 0.4 - -J7 < 0.2 < 0.2 < 0.4 < 0.4 - -K3 < 0.2 < 0.2 < 0.4 < 0.4 - -K5 < 0.2 < 0.2 < 0.4 < 0.4 - -K7 < 0.2 < 0.2 < 0.4 < 0.4 - -L5 < 0.2 < 0.2 < 0.4 < 0.4 - -L6 < 0.2 < 0.2 < 0.4 < 0.4 - -
mg/kg
Letter indicates location.
Number indicates:
Appendix O
Measured oil concentrations from samples collected beneath Transformer One
Penetration depth
Maximum width
Depth of Max. Width
Depth/Width Ratio
25 37 7 0.68
25 32 5 0.78
26 38 7 0.68
27 35 9 0.77
28 38.5 7 0.73
29 41 8 0.71
30 35 10 0.86
30 37 8 0.81
30 40 7 0.75
31 39 7 0.79
31 36 6 0.86
31 39 13 0.79
32 38 10 0.84
32 42 7 0.76
32 38 11 0.84
32.5 39 10 0.83
35 42 12 0.83
42 42 15 1.00
Appendix PDimensions of individual dye bodies and a fitting linear relationship
* All measurements are in centimeters
y = 0.0163x + 0.3005
R2 = 0.7003
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
1.05
20 25 30 35 40 45
Depth
Dep
th/W
idth
Rat
io
