Journal of Contaminant Hydrology 30 Ž1998. 79–100
Influence of fracture truncation on dispersion:
A dual permeability model
Paige Stafford a , Laura Toran
a
a,)
, Larry McKay
b
EnÕironmental Sciences DiÕision, Oak Ridge National Laboratory 1, Oak Ridge, TN 37831-6400, USA
b
Department of Geological Sciences, UniÕersity of Tennessee, KnoxÕille, TN 37996-1410, USA
Received 27 September 1996; revised 3 April 1997; accepted 3 April 1997
Abstract
Simulations with a dual permeability model show that a few discrete fractures can have a
major influence on plume geometry. A limited number of truncated fractures Ž1–4. within a
permeable matrix can create nearly circular plumes, with about the same degree of spreading in
the direction transverse to the average hydraulic gradient as in the longitudinal direction. By
comparison, continuous fractures in the direction of flow tend to produce elongated plumes,
similar to those typically seen in granular materials. Both types of plumes have been observed in
tracer experiments in fractured porous media on the Oak Ridge Reservation. Understanding the
influence of fracture geometry is important in planning field characterization and subsequent
remediation in fractured porous media. q 1998 Elsevier Science B.V.
1. Background and purpose
Shales are typically considered adequate barriers against migration of contaminants.
However, on the Oak Ridge Reservation ŽORR. the upper portion of these deposits
Žusually less than 10 m depth. are highly weathered and fractured, which substantially
increases the hydraulic conductivity and potential for contaminant migration ŽSolomon
et al., 1991.. For example, tritium migration from shallow low-level radioactive waste
)
Corresponding author. Current address: Dept. of Geology, Temple University, Philadelphia, PA 19022,
USA. Tel.: q1-215-2048227; fax: q1-215-2043496.
1
Oak Ridge National Laboratory is managed by Lockheed Martin Energy Research Corp. for the U.S.
Department of Energy under contract No. DE-AC05-96OR22464.
0169-7722r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved.
PII S 0 1 6 9 - 7 7 2 2 Ž 9 7 . 0 0 0 3 7 - 5
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P. Stafford et al.r Journal of Contaminant Hydrology 30 (1998) 79–100
trenches within the weathered shales has been observed at a number of sites on the ORR
ŽOlsen et al., 1986; Wickliff et al., 1989; Solomon et al., 1991; Shevenell et al., 1994;
Sanford and Solomon, 1995; McKay et al., in press.. Investigations in fractured
clay-rich glacial deposits ŽKeller et al., 1986; D’Astous et al., 1989; Thompson, 1990;
Balfour, 1991, Ruland et al., 1991; McKay et al., 1993a., which are similar to the
weathered shales, have also shown that contaminant migration can occur at environmentally significant rates.
Numerical modeling of groundwater flow and solute migration in the weathered and
fractured shale poses special challenges because it is not clear whether the material can
be considered as a continuum or equivalent porous media ŽEPM., or whether it must be
modeled on the scale of individual fractures Ždiscrete fracture or DF approach.. The
EPM approach defines a fractured system as a single continuum, or series of continua,
where the parameter values are affected by the presence of fractures, but the fractures
are not modeled explicitly. The advantage of this approach is that just a few parameters,
such as hydraulic conductivity, hydraulic gradient, effective porosity and dispersivity,
are necessary for simulations. They are either measured in the field or laboratory, or are
obtained from fitting simulations to data from tracer experiments. This approach can still
have a high degree of uncertainty because of problems with ‘fitting’ parameters, such as
dispersivity and effective porosity, that may vary with time and scale. Many studies
exist that examine the applicability of EPM Žor continuum. models to idealized fractured
systems Že.g., Long et al., 1982; Berkowitz et al., 1988; Maloszewski and Zuber, 1993..
Long et al. Ž1982. determined which characteristics of a fractured system increase the
likelihood of the EPM approach being appropriate. Some of these characteristics are: Ži.
high fracture density, which creates connected fractures and therefore connected flow
paths, Žii. relatively constant fracture aperture, to prevent only a few fractures from
controlling most of the flow and Žiii. random orientation of fractures so that flow is not
unidirectional. In addition, it must be possible to define a representative elemental
volume ŽREV. where: Ži. heterogeneity is negligible, Žii. the REV is large relative to the
fracture lengths to represent complete flow paths and Žiii. the REV is small compared to
the system being modeled. These factors, particularly fracture density and orientation,
can be used to provide a preliminary indication of whether an aquifer will behave as an
EPM, but there are insufficient well-documented field examples to say in which settings
an EPM approach should be effective. The limited number of field studies available has
provided important information to help conceptualize these systems Že.g. Bibby, 1981;
Pankow et al., 1986; Cacas et al., 1990; McKay et al., 1993a,b; Sanford et al., 1996;
Cook et al., 1996..
On the other hand, a discrete fracture approach requires information about both the
fractures and the blocks of soil or rock between fractures. Some of these parameters,
particularly fracture aperture and degree of fracture interconnection, are difficult to
measure and may contain a high degree of uncertainty. Discrete fracture models
typically require considerably more computer memory than an EPM model; computer
memory is often a limitation on the size and detail of the region modeled.
The matrix between discrete fractures is treated differently depending on the modeling approach. Modeling studies conducted in the 1980’s ŽLong et al., 1982; Schwartz et
al., 1983; Endo et al., 1984; Long and Witherspoon, 1985. described the importance of
P. Stafford et al.r Journal of Contaminant Hydrology 30 (1998) 79–100
81
effective porosity Žwhich they define as the porosity contributed by fractures alone. and
fracture orientation, but matrix transport parameters were considered insignificant and
were not included in these models. Other studies ŽFoster, 1975; Day, 1977; Sudicky and
Frind, 1982; Maloszewski and Zuber, 1985, 1993; Harrison et al., 1992; Sudicky and
McLaren, 1992; Zuber and Motyka, 1994. established the importance of matrix diffusion in fractured, high porosity materials by indicating its effect on delaying solute
breakthrough. Sudicky and Frind Ž1982., in simulating solute migration Žtritium. in a
fractured porous material, showed that matrix diffusion acts as a dynamic storage
mechanism. The process was sufficient to retard the overall migration rate of the plume
by several orders of magnitude, as compared to advective transport rates in fractures
alone, where no diffusion is assumed.
An alternate approach to selecting either EPM or a discrete fracture approach is to
consider a dual permeability approach. In this model, there is an EPM, resulting from
intergranular flow or from flow through a network of closely-spaced fractures, and a few
interconnected larger aperture fractures within it. This scenario is likely to be common
in fractured deposits, with the larger aperture fracture sets resulting from later tectonic
activity, or intersecting fracture sets. The importance of considering hydraulically
connected fractures as an important subset of fractures has been noted by a number of
researchers using field and modeling data Že.g., Cacas et al., 1990; Clemo and Smith,
1989, cited in Smith and Schwartz, 1993; Renshaw, 1996; Therrien and Sudicky, 1996;
Parney and Smith, 1995.. The fractures within a system that are hydraulically connected
can influence flow directions and flow rates, but be part of a limited network. Parney
and Smith Ž1995. used particle tracking in network models Žfractures only. to show that
particles tend to have longer flow paths in higher aperture pathways, and that these
select pathways need to be incorporated into EPM approaches. Rubin et al. Ž1996. found
that in fractured permeable formations, longer injection times lead to closer approximations with EPM.
One further consideration in comparing EPM and DF approaches is whether dispersion within a fracture network can be modeled adequately. Dispersion in fracture
networks Žno block permeability. has been studied by Schwartz et al. Ž1983. and Smith
and Schwartz Ž1984.. They found that the longitudinal and transverse dispersivity of
mass varied for different realizations of fracture networks, and that both flow direction
and fracture geometry were important. Significant longitudinal dispersion and long tails
for solute breakthrough were observed in some fracture networks. Although an EPM
approach to characterizing dispersion has been formulated ŽVan der Kamp, 1992., the
information needed to calculate an equivalent dispersivity Že.g., fracture spacing.
requires characterization that could be used to better identify pathways if used explicitly,
and does not account for geometry of fracture configuration. Rubin and Buddemeier
Ž1996. evaluated the effects of fracture orientations and relative fracture permeability in
a permeable matrix, and found that transverse dispersivity may exceed longitudinal
dispersivity when fracture permeability is high and orientations approach a direction 908
to flow. They studied continuous fracture networks.
This paper examines how fracture geometry can influence dispersion in a hypothetical plume. The study of dispersion in discrete fractures presented here differs from
previous studies by examining Ž1. the effect of the geometry of fracture intersections,
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P. Stafford et al.r Journal of Contaminant Hydrology 30 (1998) 79–100
and Ž2. the influence in a dual permeability media. The dual permeability media consists
of a few larger aperture, hydraulically active fractures set within a matrix of small
fractures that act as a porous medium. The results of the modeling study are compared
with two existing plumes in fractured shale saprolite on the Oak Ridge Reservation in
Tennessee.
2. Example plumes
2.1. Broad plume: the burial ground 4 site
Although the modeling presented here is hypothetical, the problem is based on a
tritium plume observed on the Oak Ridge Reservation. The plume exhibited an
Fig. 1. Contours of tritium concentrations in log scale of pCirml at three different times after initial injection.
P. Stafford et al.r Journal of Contaminant Hydrology 30 (1998) 79–100
83
unusually large transverse spreading, with the width of the plume approximately equal to
its length ŽFig. 1.. The plume developed from a long term tritium tracer test that was
carried out in the fractured, highly weathered shale of the Conasauga group at Oak
Ridge National Laboratory ŽWebster, 1996. near burial ground 4 ŽBG4.. The experiment
is unique due to the high levels of tritium injected Ž50 curies. and the long monitoring
period Ž16 years to date.. This test is one of the few controlled field-scale tracer
experiments in a fractured media containing significant matrix porosity Ž10 to 40%. and
permeability Ž; 10y2 mrd.. The study site is adjacent to low level radioactive waste
disposal sites on the ORR, and hence should be relevant to assessing contaminant
migration and behavior at this and other waste sites in the same geologic deposits.
Seven monitoring wells were constructed in a semi-circle 3.7 m down-slope from the
injection well ŽFig. 1.. The depth of the monitoring wells ranges from 8.3 m to 9.4 m,
and the depth of the injection well is 6.3 m. Slug tests were carried out in each well at
Fig. 2. Contours of 10 ppb rhodamine from the West Bear Creek Valley tracer experiments at two different
times.
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P. Stafford et al.r Journal of Contaminant Hydrology 30 (1998) 79–100
the experiment site to determine bulk hydraulic conductivity, K b . The K b values range
from 1.2 = 10y2 to 3.0 = 10y3 mrd, with a geometric mean of 7.2 = 10y3 mrd. The
water table gradient from the injection well to monitoring well 7 Ždirectly downslope.
averages 0.15. The migration of the plume is characterized by a fast moving, low
concentration front Ž10’s of cm per day., a slower moving center of mass Ž- 1
cmrday., a very long Žup to 16 years. low concentration tail, and an unusually large
degree of transverse spreading.
2.2. Narrow plume: West Bear Creek Valley site
A second example is presented here that was not explicitly modeled, but used to
contrast plume shape and orientation. A rhodamine dye tracer experiment ŽLee et al.,
1989, 1992; Brown et al., 1992. was conducted at the West Bear Creek Valley ŽWBCV.
site on the ORR. The geologic material at this site is similar to that at the BG4 site in
terms of porosity, hydraulic conductivity, and fracture spacing and orientation. However,
the shape of the plume was very narrow ŽFig. 2. as compared to the wide shape of the
BG4 plume ŽFig. 1..
The major difference between the two sites is that the average water table gradient
direction at the WBCV site is approximately parallel to strike of the bedding plane, and
at the BG4 site it is nearly perpendicular to strike ŽFigs. 1 and 2.. The orientation of the
water table gradient with respect to the fracture planes likely contributed to the
difference in plume shapes. The hydraulic conductivity is expected to be higher in the
direction of strike at both locations due to bedding plane partings or fractures ŽSolomon
et al., 1991.. With this in mind, transverse spreading at the WBCV site, where there is a
strike-parallel gradient, would not be strongly influenced by fluctuating water table
direction and secondary fractures perpendicular to strike because of the lower hydraulic
conductivity in the transverse direction. Conversely, at the BG4 site, where the average
hydraulic gradient is in the direction of the lower hydraulic conductivity Žperpendicular
to strike. fluctuating water table direction and fractures perpendicular to bedding are
expected to have more of an influence on transverse spreading. It is likely that at other
locations, where water table slope is neither parallel or perpendicular to bedding strike,
the shape of the plumes would be intermediate between these two extremes.
3. Modeling approach
In this study, the discrete fracture approach was combined with the EPM approach
ŽDF-EPM. to investigate the influence of a few widely-spaced larger-aperture fractures
in a highly fractured matrix. These widely-spaced fractures, if present, could have a
large influence on transverse spreading of a plume. The fracture networks chosen are
hypothetical and may not be the cause of transverse spreading at the BG4 site. Other
factors, such as seasonal variations in the elevation and direction of slope of the water
table are expected to be significant at the site, but were not incorporated in the 2D
steady-state approach.
P. Stafford et al.r Journal of Contaminant Hydrology 30 (1998) 79–100
85
The highly fractured network was assumed to act as an EPM. A transverse dispersivity of zero was used with an implicit hypothesis that the transverse spreading can be
modeled using fractures. Different scenarios were then run with a few widely-spaced
fractures superimposed on the EPM to see if transverse spreading could be reproduced
by these fractures. Fracture aperture values for the widely-spaced fractures were set at
either 150 or 250 m m, based on estimates from hydraulic tests ŽMoore and Toran,
1992..
Other parameters used in the simulations are listed in Table 1. The water table
gradient from the injection well to the downgradient well averaged 0.15 at the BG4 site.
The matrix porosity in the shallow subsurface was estimated to be about 0.4. Using the
calculated velocity of 0.01 mrd from EPM modeling ŽStafford, 1996; McKay et al., in
press. resulted in a hydraulic conductivity of 0.03 mrd, which is close to the geometric
mean value measured in slug tests at the site Ž0.01 mrd.. Other combinations of
hydraulic conductivity and porosity could have been used, preserving the observed
velocity, with only minor effect on the transport calculation. The longitudinal dispersivity of 0.8 m was obtained from the EPM model fitting ŽStafford, 1996; McKay et al., in
press.. The longitudinal fracture dispersivity was based on literature derived values on
the order of 0.1 m. The duration of the input function was 40 days. This was chosen
based on the time necessary for the concentration in the injection well to decline to half
of its initial value, so that the area under the input function was approximately the same
as the area under the measured relative concentration Ž CrCo . versus time plot for the
injection well. For tritium, the half life is 12.4 y, the diffusion coefficient is 5.18 = 10y5
m2rd, and the retardation factor is 1. The EPM parameters for hydraulic conductivity,
porosity, and longitudinal dispersivity were used to describe the matrix for the DF-EPM
model. These parameters were not varied in this study because this was not a calibration
exercise.
Table 1
Parameters used for FRAC3DVS DF-EPM simulations
Parameters Used
Values
Flow velocity Žmrd.
Hydraulic gradient
Matrix porosity
Longitudinal dispersivity Žm.
Transverse dispersivity Žm.
Effective diffusion coefficient Žm2 rd.
Retardation
Solute half-life Žd.
Source concentration
Duration of source Žd.
Longitudinal fracture dispersivity Žm.
Transverse fracture dispersivity Žm.
Fracture aperture Ž2 b . Ž m m.
Fracture retardation
0.01
0.15
0.40
0.8
0
5.18=10y5
1.0
4.53=10 3
1.0
40.0
0.10
0
150, 250
1.0
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86
3.1. FRAC3DVS
The model used was FRAC3DVS, a discrete fracture numerical model where
advective transport and diffusion are accounted for in the matrix ŽTherrien and Sudicky,
1996.. The matrix is represented in three dimensions, and fractures are represented by
two-dimensional planes.
The model employs a time marching Galerkin finite element technique which is used
to discretize the solute transport equation with either finite element or by mimicking a
finite difference discretization. The solution for the flow equation is solved by the
control volume finite element approach and a preconditioned ORTHOMIN solver. The
fracture elements are common to nodes comprising the porous matrix elements which
ensures the continuity of hydraulic head at the fracture-matrix interface.
The governing equation for solute transport in the matrix is
R
dc
dt
d
s
d xi
ž
Di j
dc
d xj
/
dc
y Õj
d xi
y R l c i , j s 1, 2
where Di j ŽL2 Ty1 . is dispersion defined as
q1 q 2
Di j s Ž a L y a T .
q a T < q < d i j q D )d i j
< q<
i , j s 1, 2,
Ž 1.
Ž 2.
where a L ŽL. is the longitudinal dispersivity, a T ŽL. is the transverse dispersivity, < q < is
the magnitude of the Darcy flux, defined as
d
qs
d xi
ž
Ki j
d ŽCqz .
d xj
/
i , j s 1, 2
where c ŽL. is the pressure head, z ŽL. is the elevation head.
Fig. 3. Model domain for FRAC3DVS simulations.
Ž 3.
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87
For transport in the fracture, the governing equation is
0s2 b R f
d cf
dt
d
y
d xi
ž
Df i j
d cf
d xj
/
q qf
d cf
d xj
q R f l cf
y V n < Iyq V < Iq i , j s 1, 2,
Ž 4.
where the terms V n represents the advective–dispersive loss or gain of solute mass
across the fracture-matrix interfaces Iy and Iq due to fluid leakage and hydrodynamic
dispersion and 2 b is the fracture aperture. The Darcy flux in the fracture is
d
d Ž cf q zf .
qf s
i , j s 1, 2,
Ž2 b. Kf
Ž 5.
d xi
d xj
where c f ŽL. is the pressure head in the fracture, z f ŽL. is the elevation head in the
fracture, and qf is the fluid flux in the fracture ŽLrT.. The fracture dispersivity is
defined in the same way as matrix dispersivity where dispersivity coefficients and fluxes
correspond to the fracture.
Fig. 4. Fracture effects on head distribution using an aperture of 250 m m for the domain shown in Fig. 3, with
Õ s 0.01 mrd Žbefore addition of fractures.. Direction of flow is from top to bottom.
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P. Stafford et al.r Journal of Contaminant Hydrology 30 (1998) 79–100
3.2. Model grid
The two-dimensional modeling in this study was performed with the FRAC3DVS
code for a 10 m = 10 m plan view region as shown in Fig. 3. The same model grid used
for the EPM modeling to determine matrix parameters was used for the DF-EPM model.
The flow system was assumed to be at steady-state and fully saturated, with the medium
Žbefore addition of fractures. homogeneous and isotropic. A uniform, constant head
along the top and bottom of the grid was used to establish an overall hydraulic gradient
of 0.15. The bulk hydraulic conductivity for the medium was assumed to be isotropic,
even though it may be anisotropic at the field site, because of fractures parallel to
bedding strike. However, strike-parallel fractures were represented explicitly in the
DF-EPM model. The source term used was a step-function with a relative concentration
of 1.0 for 40 days.
Fig. 5. Simulation results for two-dimensional DF-EPM model, case A, using 2 bs 250 m m.
P. Stafford et al.r Journal of Contaminant Hydrology 30 (1998) 79–100
89
3.3. Discrete fracture-EPM (DF-EPM) simulation
Simulations were carried out with very simple networks typically with one to four
fractures. Isolated fractures which did not penetrate a boundary or another fracture were
not considered because they are expected to have less influence than interconnected
fractures. To create transverse spreading, fracture patterns which are truncated by a
fracture parallel to the direction of spreading are considered. Truncation of fractures
with a perpendicular fracture set is a common style of fracturing because stress relief in
an alternate direction will cause a fracture to terminate at fracture intersections ŽHancock,
1985; Pollard and Aydin, 1988..
The influence of different styles of fractures ŽFig. 4. is compared by examining both
the head and the concentration contours. Then some variations on fracture aperture,
fracture density and source location are also examined.
Fig. 6. Simulation results for two-dimensional DF-EPM model, case B, using 2 bs 250 m m.
P. Stafford et al.r Journal of Contaminant Hydrology 30 (1998) 79–100
90
4. Results
4.1. EPM modeling to determine matrix parameters
An EPM model was fit to the BG4 plume using velocity and longitudinal dispersivity
as fitting parameters ŽStafford, 1996; McKay et al., in press.. In the EPM model, a high
transverse dispersivity is needed to represent the broad shape of the plume ŽFig. 1.. The
best fit to the shape of the plume was for a transverse dispersivity of approximately 0.8
m, which contrasts with the commonly seen assumption that transverse dispersivity will
be about an order of magnitude smaller than longitudinal. Although a variety of factors
can contribute to the broad plume at BG4, the one explored here is the affect of fracture
flow on plume spreading.
Fig. 7. Simulation results for two-dimensional DF-EPM model, case C, using 2 bs 250 m m.
P. Stafford et al.r Journal of Contaminant Hydrology 30 (1998) 79–100
91
4.2. Fracture geometry
In the DF-EPM model, the transverse dispersivity is set to zero, and instead fractures
are used to spread the plume. The degree of spreading varied depending on fracture
geometry. The initial cases A through F are described first.
ŽA. A single fracture which fully penetrated the system and was perpendicular to
flow direction had no effect on the head distribution, and no effect on transport ŽFig. 5..
The simulated plume was identical to the plume generated for the case with no fractures
and no transverse dispersivity. This case represents a setting where the flow direction is
perpendicular to the dominant fracture orientation, and there is no secondary fracture set.
Fig. 8. Simulation results for two-dimensional DF-EPM model, case D, using 2 bs 250 m m.
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P. Stafford et al.r Journal of Contaminant Hydrology 30 (1998) 79–100
ŽB. A single fracture which fully penetrated the system and was aligned parallel to
the direction of flow had no influence on hydraulic head. There was relatively little
influence on transverse spreading ŽFig. 6.. There was somewhat faster transverse
spreading at early times, but about the same amount of spreading as case ŽA. at later
times. However, the fracture, which intersected the source well, caused longitudinal
transport rates to increase, as seen by the faster arrival of breakthrough at the lower
boundary Ž85 days.. This case represents a setting where the flow direction is oriented
along the dominant fracture orientation, and there is no secondary fracture set.
ŽC. Two orthogonal fractures which fully penetrate the system and intersect downgradient of the source well had no effect on head distribution, and had the same effects
Fig. 9. Simulation results for two-dimensional DF-EPM model, case E, using 2 bs 250 m m.
P. Stafford et al.r Journal of Contaminant Hydrology 30 (1998) 79–100
93
on transport ŽFig. 7. as described in ŽB. above, i.e., an increase in longitudinal transport
at early times.
This case illustrates that fractures orthogonal to a fully penetrating fracture do not
create significant transverse spreading, and why the plume at WBCV would not be
influenced by perpendicular fractures. The fully penetrating fracture oriented parallel to
the flow direction represents the dominant fracture set. Fractures perpendicular to both
the gradient and the fully penetrating fracture are not an important influence. Thus, a
relatively narrow plume develops.
ŽD. A single fracture parallel to the direction of flow which passed through the tracer
injection well and penetrated the up-gradient constant head boundary, but did not reach
the other end of the system, influenced the hydraulic head distribution, causing radial
flow away from the terminus of the fracture ŽFig. 8.. The radial flow caused solute
Fig. 10. Simulation results for two-dimensional DF-EPM model, case F, using 2 bs 250 m m.
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P. Stafford et al.r Journal of Contaminant Hydrology 30 (1998) 79–100
spreading in the transverse direction ŽFig. 8.. At 85 days, the outer contour interval
Ž CrCo s 10y8 . is about three times wider for the case with the truncated fracture than
for the systems with continuous fractures ŽFigs. 5–7.. As the plume dissipates, the shape
remains broad. This case is an example of fracture geometry of a subdominant fracture
set that can broaden plume geometry. The truncation of the fracture makes it a
subdominant fracture set in contrast to fully penetrating, or longer fractures.
ŽE. Two fractures, one perpendicular to the direction of flow and the second parallel
to flow but terminating at the intersection with the other fracture, disrupted the head
distribution and increased the amount of transverse spreading ŽFig. 9. even more than a
single terminated fracture. This case illustrates that the presence of a second fracture set,
where a dominant fracture transverses the model domain, is an important influence on
plume development. This secondary set intersects the primary set providing connectivity.
ŽF. When the fracture orientation described in ŽE. was repeated such that there was a
regular brickwork of fractures, hydraulic heads were disrupted and a large degree of
transverse spreading of the plume occurred ŽFig. 10.. In this case, there was now a
continuous network of fractures in the direction of flow and the rate of longitudinal
migration of the plume increased. The truncated fractures represent a secondary fracture
Fig. 11. Simulation results for two-dimensional using 2 bs 250 m m and varying fracture spacing.
P. Stafford et al.r Journal of Contaminant Hydrology 30 (1998) 79–100
95
set because the fractures in the direction of the flow field are shorter than the fracture
perpendicular to the flow field.
4.3. Fracture density
Increasing the density of the fracture brickwork Ži.e., increasing the number of
fractures. further increased both the transverse and longitudinal spreading ŽFig. 11..
Although the contours are not smooth even for the dense network, the broad outline of
the contours becomes more convex, approaching an EPM appearance, as the network
density increases.
4.4. Fracture aperture
Increasing the fracture aperture from 150 m m to 250 m m increases transport in the
fracture and broadens the plume in the transverse direction for a fracture truncated by a
Fig. 12. Simulations for case E with different aperture Ž2 bs150 m m..
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P. Stafford et al.r Journal of Contaminant Hydrology 30 (1998) 79–100
perpendicular fracture ŽFig. 12.. The effects of increase transport in wide fractures is
seen even at early times Ž85 days..
4.5. Location of the source term
The location of the source term with respect to the fracture affects the symmetry of
the plume. When the fracture is located 0.4 m from the injection well, the head gradient
is offset and there is slightly less up-gradient spreading ŽFig. 13.. The asymmetry is
more pronounced at early times, then at later times the plume moves away from the
source more slowly than the case where the source intersects a fracture.
Fig. 13. Simulation results for two-dimensional DF-EPM model, case D, using 2 bs 250 m m and varying
fracture placement from source.
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97
5. Discussion
5.1. Implications for remediation
Tritium migration through the fractured porous material at the experiment site is
strongly influenced by matrix diffusion. If this was not so, tritium would have rapidly
flushed out through the fractures under natural gradient conditions, rather than persisting
for at least 16 years, as was observed. It is likely that tritium removal by pump-and-treat
or drainage methods would be a very slow process due to ‘storage’ effects created by
matrix diffusion. Thus, it is important to distinguish plume spreading which is influenced by fracture patterns rather than hydraulic affects. Furthermore, although a variety
of fracture networks could reproduce the present plume, they may behave very differently when simulated remediation efforts, such as pumping from wells, are added to the
system. If flow rates are increased by lowering the water table, such as could occur for
remediation purposes, this would affect predictions of the effectiveness and required
duration of remediation. These precautions are valid for any site with a dual permeability system or extreme variations in hydraulic conductivity.
5.2. Implications for field inÕestigations
Evaluation of field-scale systems is still problematic because of the cost and difficulty
in sampling fractured systems. Modeling studies, such as the one presented here, can be
used to determine the types of fracture geometry that can influence observable plume
features such as spreading and long term behavior. Although a few large aperture
fractures Žas shown in this study. can greatly affect plume behavior, they could be very
difficult to detect by hydraulic testing.
Instead, the plume geometry could be used to indicate behavior caused by major
fractures. For example, in the two field experiments presented here, there was a large
contrast in plume shape. At BG4, the plume was very broad, and transverse fractures
may have been important in spreading the plume. At the WBCV site, the plume was
narrow, and transverse fractures are not believed to be important because the dominant
fracture set was in the direction of flow, not perpendicular to flow.
The large aperture fracture set contributed not only to transverse spreading, but also
increased longitudinal spreading as seen in cases D–F with increased downgradient
plume concentrations. Because this was not a calibration exercise, the matrix EPM
dispersivity value was not adjusted to account for the influence of the discrete fractures.
However, this could be a future exercise to understand the relationship between EPM
parameters and DF-EPM parameters. The EPM parameters would need to account for all
fracture sets, and lumped fracture and ‘matrix’ dispersivity and conductivity values tend
to be higher. In contrast, the DF-EPM model the matrix parameters only describe the
small scale fractures and values tend to be lower.
Simulations show that it may not be necessary to characterize all of the minor
fractures, but instead focus on finding the major fractures, fracture orientations, and
network patterns. By understanding the influence of fracture geometry on plume shape,
modeling may assist the difficult task of detecting the influential fractures in the field.
98
P. Stafford et al.r Journal of Contaminant Hydrology 30 (1998) 79–100
6. Conclusions
The large transverse spreading observed in the tritium tracer test near Burial Ground
4 on the Oak Ridge Reservation could be reproduced with the DF-EPM approach using
a few larger aperture truncated fractures superimposed on an EPM. This does not imply
that truncated fractures are responsible for the spreading, but merely identifies them as a
possible cause. The combined discrete-fracturerequivalent porous media ŽDF-EPM.
approach is useful for looking at possible causes of features such as the observed
transverse spreading, but in the absence of detailed data on the fracture network, it is
likely that it would be no more effective than the EPM approach in predicting future
behavior of the plume.
Because this was a dual permeability model, transport occurred in both the fracture
and the matrix. This model represents a fractured field site where the matrix permeability is either due to primary permeability or due to a network of closely spaced fractures
acting an EPM. Superimposed on the closely spaced fractures are some large-aperture
fractures. When these fractures have deadends or truncate at a perpendicular fracture,
they can influence transport in the matrix by spreading the plume in the transverse
direction, followed by continuing transport in the matrix along the spread-out front.
Although the narrow plume at the WBCV site was not modeled, it provides further
evidence of the importance of fracture geometry. At this site, the flow direction is the
same as the dominant fracture orientation. Without the truncation of fractures in this
direction, the plume was not spread in the transverse direction.
A variety of fracture networks could result in similar plumes under a given set of
hydraulic boundary conditions, but might behave differently from one another when
these conditions are changed. The model is not yet valid as a predictive tool. Nonetheless, the contrast in plume geometry at the two sites discussed, and the modeling of BG4
with the broad plume, indicates the importance of fracture geometry in plume development through effects usually attributed to dispersivity. Thus, the simulations show that
studies focussed on characterizing the major fractures provide important information for
understanding plume behavior in fractured porous media.
Acknowledgements
These numerical simulations were an outgrowth of the extensive tracer test conducted
by David Webster of the U.S. Geological Survey, and we gratefully acknowledge his
efforts and willingness to share the results of his experiment. We also thank D. Kip
Solomon and Dale Huff for bringing the data to our attention and for their assistance in
the early stages of the project.
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