vvEPA
                            United States
                            Environmental Protection
                            Agency
                         Robert S. Kerr Environmental
                         Research Laboratory
                         Ada, OK 74820
                           Research and Development
                                              EPA/600//M-91/005 Jan. 1991
ENVIRONMENTAL
RESEARCH  BRIEF
  Macrodispersion and Spatial Variability of Hydraulic Conductivity in a Sand
                    and Gravel Aquifer, Cape Cod, Massachusetts

        Kathryn M. Hessa, Steven H. Wolfbc, Michael A. Celiabd and Stephen P. Garabedian*
Introduction

Macrodispersion is the field-scale hydrodynamic spreading of
solutes in an aquifer caused by local variations in ground-water
velocity. These variations are caused, in large part, by small-
scale variations in the hydraulic properties within the aquifer.
Several stochastic transport equations have been developed
that relate macrodispersion to aquifer heterogeneity, particularly
spatial variations of hydraulic conductivity  (K) (Dagan, 1982;
Gelhar and Axness, 1983; Neuman et al., 1987). These equations
have been field-tested to a limited degree by comparing the
macrodispersion observed in field tracer tests to that predicted
using a statistical analysis of the variability in K. The tracer test
conducted in a sandy aquifer at Base Borden, Ontario (Sudicky,
1986; Freyberg, 1986) was a pioneering effort in such studies.

The link between macrodispersion and aquifer heterogeneity
has been further investigated in experiments conducted by the
U.S. Geological Survey (USGS) on Cape Cod, Massachusetts.
As part of the USGS studies, a natural-gradient tracer test was
conducted  in which the transport of  bromide, a nonreactive
tracer, was monitored in the sand and gravel aquifer for two
years (LeBlanc et al., in press).  From analyses of spatial
moments of the distribution of bromide at 16 times during the
test, a dispersivity tensor was calculated for the field transport
experiment (Garabedian et al., in press).  As a complementary
effort, detailed investigations of the variability of K in the aquifer
were made at the tracer-test site, and the stochastic transport
'U.S. Geological Survey, Marlborough, MA 01752; bDept. of Civil
Eng., Massachusetts Institute of Technology, Cambridge, MA 02139;
°Now at ENSR Consulting and Eng., Acton, MA 01720; "Now at Dept.
of Civil Eng., Princeton University, Princeton, NJ 08540.
                      equations developed by Gelhar and Axness (1983) were used in
                      conjunction with the statistical analysis of the K data to estimate
                      macrodispersion forthe aquifer. This Research Brief summarizes
                      these investigations of the variability in K at the Cape Cod site and
                      the relation of that variability to macrodispersion. This research
                      was supported by the  USGS Toxic-Substances Hydrology
                      Program and the R. S. Kerr Environmental Research Laboratory
                      of the U.S. Environmental Protection Agency.

                      Two methods of measuring K were evaluated: permeameter
                      analyses of cores and f lowmeter tests in wells. More than 1900
                      estimates of K were obtained from the permeameter and f lowmeter
                      tests. Geostatistical analyses of these data yielded estimates of
                      the mean, variance, and correlations scales forthe K distribution
                      in the aquifer.

                      Estimates of macrodispersivities based on the statistical analysis
                      of the K distribution agreed well  with the macrodispersivities
                      calculated fromthetracertest. The range in asymptotic longitudinal
                      dispersivities that was estimated from the statistical properties of
                      the f lowmeter K data, using the equations of Gelhar and Axness
                      (1983) and assuming horizontal isotropy, was 0.23 to 1.2 meters;
                      this range brackets the value of 0.96 meters calculated from the
                      tracer test. The theory also correctly predicted the tracer-test
                      result that longitudinal dispersion greatly exceeds transverse
                      dispersion. The components of transverse dispersivity were
                      underestimated by the  transport theory, however, probably
                      because temporal variations in the direction of flow caused
                      additional dispersion of the tracer during the field experiment that
                      was not accounted for in the theory of Gelhar and Axness (1983).
                      Estimation of the transverse horizontal dispersivity was greatly
                      improved after the effects of transient flow were incorporated
                      using Rehfeldt's (1988) modification of the transport theory.

                                              W£Q Printed on Recycled Paper

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Objectives

The objectives of this research were to:

     1.  Evaluate methods for determining the small-scale
        variability of K for a sand and gravel aquifer.

     2.  Statistically characterize the spatial distribution of
        K at the Cape Cod tracer-test site.

     3.  Assess the applicability of the stochastic transport
        equationsforestimatingmacrodispersion from the
        variance and correlation scales of the  spatial
        distribution of K.

Methods of Measuring Hydraulic Conductivity

Two methods were used to determine K over small intervals of
the aquifer:  laboratory  multi-port-permeameter tests of intact
cores (Wolf, 1988; Wolf et al., in press)  and in-situ borehole
flowmeter  tests (Hess,  1989).   For the  permeameter
measurements,  relatively  undisturbed, 4.8-cm (centimeter) -
diameter cores of the medium to coarse sand and gravel aquifer
were obtained using the method of Zapico et al. (1987). Cores
were taken at 16 locations (Figure 1) from a zone that was 6 to
7.5 meters thick and located immediately below the water table.
Lateral distances between coring locations ranged from 1 to 24
meters.  X-rays were taken of the cores and the resulting
radiographs were used to identify intervals within the cores that
had similar stratigraphy or inferred grain size.  These were the
intervals over which permeameter measurements were made.

A schematic of  the constant-head,  multi-port permeameter is
shown in Figure 2.  The liner in which the core was collected
served as the permeameter body, and manometer probes were
inserted through the liner into the core at the chosen intervals. K
was calculated  from  permeameter tests  on 825 vertical core
intervals which  averaged 7.3 cm in  length.  The K  values of
intervals which contained large gravel were not included in the
final data set because  the large gravels obstruct flow in the
permeameter, and the resulting K values were thought to be non-
representative of the aquifer (Wolf et al., in press).

Boreholeflowmetertestswereconducted in sixteen5-cmdiameter
wells screened over a 12-m interval just below the water table.
The wells were installed near  the coring locations and were
separated by distances of 1 to 24 meters (Figure 1). The borehole
flowmeter test is based on a method developed by Hufschmied
(1986) and modified by Rehfeldt et al. (1989). This procedure
involves measuring the incremental increase in discharge up the
well with a highly sensitive, impeller flowmeter, while maintaining
a constant drawdown in the well by pumping near the water table
at a steady rate (Figure 3).  The method is analogous to a
standard aquifer test, except that discharge is measured at short
intervals along the screen, instead of only  at the well head. This
method allows calculation of K for each interval.

About 70 estimates of K over vertical intervals of 15 cm were
obtained in each of the 16 wells using the flowmeter method, for
a total of 1109 measurements.  Only the 668 K values from the
zone above an altitude of 6 meters were used in the final analysis
of the spatial distribution of K. This is the vertical interval over
which  permeameter  measurements were made and through
which the bromide tracer traveled in the  natural-gradient test.
The array of wells and coring locations is offset about 25 meters
from the tracer-test site (Figure 1). The statistical characterization
of the K distribution at this location should be representative of
the tracer-test zone as well because the depositional environment
of the fluvially-derived glacial-outwash sediments is consistent
across the test area.

Results of Flowmeter and Permeameter Tests

Both methods produced detailed profiles of the variability of K
with altitude within the aquifer.  Figure 4 presents four profiles
obtained  by each method from  the central cluster (Figure 1)
where wells and coring locations are separated by only one meter
from their nearest neighbor.  A high degree of variability is
observed in the vertical direction for both types of K measurements.
Greater spatial continuity is observed in the horizontal direction;
several zones of similar K are evident in Figure 4. Some of these
zones are  horizontally continuous across the entire  area of
investigation. From these qualitative observations, the horizontal
correlation scale of the K distribution was expected to be much
greater than the vertical correlation scale.

The borehole-f lowmeter method yielded a geometric mean K of
0.11 cm/s (centimeters per second) (Table 1), which is similar to
the horizontal mean of 0.13 cm/s estimated from a nearby aquifer
test (LeBlanc et al., 1988) and from the tracer test (LeBlanc et al.,
in press).  In contrast, the geometric mean of the permeameter
K values was 0.035 cm/s. This value represents a vertical mean
because  the permeameter tests were conducted  on vertical
cores. The ratio of the flowmeter to permeameter means (3:1) is
similarto the horizontal-to-verticalanisotropy (2:1 to 5:1) previously
reported for this aquifer (LeBlanc et al., 1988), which suggests
that measurement direction may cause the difference in means
obtained  from the two methods.  However, if K within the thin,
uniform intervals over which permeameter measurements were
made (5 to 10 cm) is isotropic, then the permeameter tests should
have yielded reasonable estimates of horizontal K. Acomparison
of measurements on  intact and homogenized, repacked cores
(Wolf, 1988) seems to support the assumption of isotropy at the
scale of the permeameter measurements. Wolf et al. (in press)
address other possible causes of the underestimation of K by the
permeameter method,  including non-representative sampling
and loss of porosity in the samples by compaction.

The variances of the natural logarithm of K (InK) for the two
measurement techniques also differed (Table 1). The flowmeter
variance  of 0.24 was  significantly higher than the permeameter
variance of 0.14, even though the averaging interval of 7.3 cm for
the permeameter measurements was half of the 15-cm averaging
interval for the flowmeter measurements.

The permeametertests were more laborious and time consuming
than the flowmeter tests. A flowmeter profile could be obtained
in half a day in the field, whereas an equivalent permeameter
profile required a half-day of field sampling and several days of
laboratory analyses. The flowmeter method was a more efficient
method for obtaining  detailed profiles of K and yielded a mean
value similarto those  estimated by other field tests conducted in
this aquifer.  The flowmeter  method  has also been used
successfully in other aquifers (Hufschmied, 1986; Rehfeldt et al.,
1989; Molz et al., 1989). In the flowmeter-test analysis, however,
induced  flow into the well and  aquifer stratification are both
assumed to be horizontal.  Significant deviation  from these
assumptions in some situations could limit the usefulness of the
f lowmetertest for determining the vertical distribution of horizontal
K.

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                                                                         71*00'
73'
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MASSACHUSETTS
0 20 40 60 MILES
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0 20 40 60 KILOMETERS
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42° 00'
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41" 30'

                                                                    STUDY AREA'
          -70
      CO
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      LU

      LU
      8"
      LU



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      CC
      LL
      LU
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      CO
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          -80
          -90
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         -110
         -120
            -20
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                             -10
                                                                        EJECTION WELLS


                                                                        F343-36
                                                                                                           P^AQNETIC
                                                                                                             NORTH
             DISTANCE FROM WELL F343-36,
                       IN METERS
                                                                —13.45-
                                                      F343-36)

                                                         F447,
                                                                   TT3
                                                                                      EXPLANATION
AREA OF TRACER CLOUD N WHOM BROMDE
 CONCENTRATIONS EXCEEDED 1 MLUQRAM
 PER LITER

WATER-TABLE CONTOUR. AUGUST 2. 1985 —
 Shows altitude of water table. Contour
 Interval .1 meters. Datum ia aea level

PREDICTED PATH OF TRACER CLOUD

OBSERVATION WELL, AND IDENTFIER

WELL USED FOR IN-STTU FLOWMETER TEST
 ANDDENTFIER

LOCATION OF CORES USED FOR  PERMEAMETER
 ANALYSIS. AND DENTFIER
Figure 1.  Tracer-test site in abandoned gravel pit, showing water-table contours, observed location of nonreactive bromide tracer cloud at various
         times after injection, location of long-screened wells used for borehole-flowmeter tests, and location of coring sites used for multi-port-
         permeameter tests. Water-table map and bromide-cloud areas (from LeBlanc et al., in press).

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                                                                                manometers
 Figure 2.  Schematic of multi-port, constant-head permeameter used to measure hydraulic conductivity on 5-cm-diameter cores (from
         Wolf et al., in press).
                                  DRAWDOWN
                                                                            WATER TABLE
                                                                PUMP INTAKE
                                       SCREENED
                                        INTERVAL
                                                          .INFLOW
                                                         IMPELLER FLOWMETER
                                                   V
Figure 3. Schematic of hydraulic test used to measure hydraulic conductivity in 5-cm-diameter, long-screened wells using an impeller flowmeter.

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       a
                  N
                    0.01
                               F447
                                         F446
     F445
                    0.1        0.01          0.1        0.01          0.1

                     HYDRAULIC CONDUCTIVITY, IN CENTIMETERS PER SECOND
     F444
                                                                                                             14
                                                                                                          -   12
                                                                                                          -   8
                                                                                                   0.1
                  N
                14
UJ
§
§
5
O
CD
DC
E
                          TT1
                                     TT2
TT3
TT4
                    0.01
                                0.1        00)1          0.1        0.01          0.1        0.01

                                 HYDRAULIC CONDUCTIVITY, IN CENTIMETERS PER SECOND
                                                                                                   0.1
                                                                                                             14
                                                                                                             12
Figure 4. Hydraulic-conductivity profiles from (a) borehole-flowmeter tests and (b) permeameter tests for the central cluster where sampling
        locations are separated by approximately one meter. Dotted lines indicate the respective geometric mean hydraulic-conductivity
        values. Cross-hatched shading indicates zones of hydraulic conductivity greater than the geometric mean. Slanted-line shading
        indicates zones less than the geometric mean.

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Table 1.  Results of geostatistical analysis of hydraulic-
        conductivity (K) data from permeameter and borehole-
        flowmeter tests.
is consistent with the predominant horizontal layering observed
in the stratigraphy at the site.
                             Flowmeter       Permeameter      Macrodispersion Estimates
Number of K values
Mean vertical spacing (centimeters)
Geometric mean (centimeters
per second)
Variance of natural logarithm of K
Vertical correlation scale (meters)
Minimum
Best-fit
Maximum
Horizontal correlation scale (meters)
Minimum
Best-fit
Maximum
668
15

.11
.24

.08
.19
.46

1.4
2.6
5.2
825
7.3

.035
.14

.13
.18
.39

.9
1.2
2.6
Geostatistical Analysis

Ageostatistical analysis of the spatial variability of K was performed
on the borehole-flowmeter and permeameter data to obtain
estimates of the correlation structure. A variogram (Journel and
Huijbregts, 1978) in the vertical direction for the permeameter
data is shown in Figure 5. A negative-exponential model fit this
experimental variogram well (Figure 5)  and was applied to all
other variograms during the analysis. Estimatesofthecorrelation
scales were obtai ned by fitting this model to the variogram values
using a sill value that was similar to the sample variance. Models
were initially fit by minimizing the sum of squares of the difference
between the model and variogram values.  A  visual check was
also conducted and, in some cases, the correlation scale and sill
value were adjusted slightly to provide a better fit of the rising limb
of the model to the variogram values.

The estimated vertical correlation scales were  similar for the two
data sets (Table  1). Best-fit vertical correlation scales were 0.19
and 0.18 meters for the flowmeter  and permeameter  data,
respectively.  By incorporating uncertainty  associated with the
sample variance using a method developed by Rehfeldt (1988),
a range of estimates around the best-fit value was found  to be
0.08 to 0.46 meters for the flowmeter measurements and 0.13 to
0.39 meters for the permeameter measurements.

The horizontal variogram values (Figure 6) showed moredeviation
about the fitted  model than did the vertical variogram values
(Figure 5). This may be due,  in part, to the limited number of
sampling locations in the horizontal direction;  only 16 locations,
spaced  1 to 24 meters apart, were used  for each type of
hydraulic-conductivity test.  The horizontal correlation scales
ranged from 1.4 to 5.2 and 0.9 to 2.6 meters, with best-fit values
of 2.6 and 1.2 meters, for the flowmeter  and permeameter data,
respectively (Table 1). Because of the large range in values, the
differences between the permeameter and flowmeter horizontal
correlation scales are probably not statistically significant.  In
addition, no  statistically  significant horizontal anisotropy was
observed during the analysis. Collection of data from additional
sampling locations may be necessary to detect any horizontal
anisotropy in the K  distribution.   If horizontal  anisotropy is
present, it is probably small.  The large ratio of horizontal to
vertical correlation scales (5:1 to 25:1) obtained for both data sets
Dispersivity values were estimated using the stochastic transport
theory of  Gelhar and Axness (1983) and the variance and
correlation scales determined in the geostatistical analysis (Table
2).  Isotropy in the plane of stratification was assumed in the
analysis (Case 1, Gelhar and Axness, 1983) because there was
no evidence of horizontal anisotropy. The range in asymptotic
longitudinal dispersivity estimated from the flowmeter data was
0.23 to 1.2 meters, with a best-fit value of 0.5 meters; this range
encompasses the value of 0.96 meters observed in thetracertest
(Garabedian et  al., in  press).  The dispersivities calculated
from the permeameter data were consistently tower than those
from the flowmeter data (Table 2) because  the  estimates of
variance and horizontal correlation scale from  the permeameter
data are  tower,  in  general, than those from  the flowmeter
measurements.

Application of the stochastic equations to the results of the
geostatistical analysis also indicated that longitudinal dispersivity
exceeds the transverse components, as was observed in the
tracer test.  The stochastic analysis, however, underestimated
the magnitude of the transverse components (Table 2). Shifts in
the hydraulic-gradient direction during the two-year-long tracer
test (Garabedian et al., in press) may have caused additional
lateral mixing and, thus, enhanced the transverse horizontal
dispersion observed in the tracer test. An estimate of 0.025
meters for transverse horizontal dispersivity (Table  2) was
calculated using the method of Rehfeldt (1988) that incorporates
the effects of the transient flow on dispersion. This estimated
value agrees well with the transverse horizontal dispersivity of
0.018  meters observed in the tracer test (Garabedian  et al, in
press).

Effective Hydraulic Conductivity

The correlation scales from the variogram analyses were also
used in  the stochastic transport equations to  estimate the
anisotropy in the effective K tensor. The horizontal-to-vertical
anisotropy ratio  of K, estimated by  the method of Gelhar and
Axness (1983)  using  either the  flowmeter or  permeameter
correlation scales, is about 1.2:1, which is slightly smaller than
the anisotropy of 2:1 to5:1 obtained from the nearby aquifer test
(LeBlanc  et al., 1988).  The anisotropy of the effective K tensor
is also smaller than the ratio of mean K values obtained from the
flowmeterand permeameter measurements (3:1). Thissuggests
that the difference  between the horizontal-K values from the
flowmeter and the vertical-K values from the permeameter may
be only partly explained by anisotropy and different measurement
directions.

Conclusions

The following conclusions can be made on the basis of results of
this research:

     1.   Flowmeter tests in long-screened wells provided a
          relatively fast and easy method for assessing the
          small-scale variability in K (hydraulic conductivity)
          at the  Cape Cod site. The resulting geometric

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      Table 2  Component* of macrodisperslvlty estimated from hydraulic-conductivity data using the stochastic theory
              of Gelhar and Axness (1983) and the modifications of the theory of Rehfeldt (1988).
Con-elation Scales
(meters)
Variance

Flowmeter
Minimum
Best-fit
Maximum
Permeameter
Minimum
Best-fit
Maximum
onni\
Horizontal

0.20 1.4
.24 2.6
.29 5.2

.12 .9
.13 1.2
.16 2.6
Vertical

0.08
.19
.46

.13
.18
.39
Macrodispersivity (meters)
Longitudinal

0.23
.50
1.2

.09
.12
.33
Transverse
Horizontal Vertical

10 • ia»
10 7 ia7
10 7 10 7

10 7 ia7
10 7 10*
10« 10*
      Tracer Test
           Garabedian et al.
           (in press)
.96
            .018
           .0015
      Flowmeter, accounting
          for transient flow
.96
.025
                    iu
                    O
                    cc
                          0.3
                          0.2
                          0.1
                          0.0
                              0.0
                                          0.5
                                                                                »

                                                                               X
  = 0.13

  = 0.18 meters

       i	
                                                     1.0
                                                                1.5
                                                                            2.0
                                                                                                  3.0
                                   MEAN SEPARATION DISTANCE OF LAG CLASS, h, IN METERS

Figure 5.  Vertical variogram of natural-logarithm of hydraulic conductivity from the permeameter data. Exponential model of the form
         YA = oj (1 - exp(-/yX)) was fit to the experimental variogram, where Yft = the semivariance, 
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                       0.3
                       0.2
                 UJ
                 O

                       0.1
                       0.0
                           0.0                5                10                15                20


                                 MEAN SEPARATION DISTANCE OF LAG CLASS, h, IN METERS


Figure 6. Horizontal variogram of natural-logarithm of hydraulic conductivity from the borehole-flowmeter data. Exponential model of the form
        Y/, = o? 0- exp(-/yX) was fit to the experimental variogram, where yft = the semivariance, tf, = the sill value, and X = the correlation
        scale. Vertical bar indicates 95% confidence interval about the sample variance. Horizontal bar indicates the corresponding horizontal
        correlation-scale range.
        mean of K was similar to the mean calculated from
        tracer and aquifer tests.

    2.  The permeameter method of measuring  K was
        more time consuming and produced a mean which
        was significantly less than that determined by other
        methods.  This lower mean may be the result of
        non-representative sampling, loss of porosity in
        the samples, and anisotropy  in the sediments.

    3.  The permeameter results provided an estimate of
        the vertical correlation scale which is similar to that
        from the flowmeter tests. However, estimates of
        the variance of InK and the horizontal correlation
        scale from  the permeameter tests are  lower, in
        general,  than those from  the  flowmeter
        measurements.

    4.  Horizontal  anisotropy  in  the  K field  was  not
        observed, and isotropy in the plane of stratification
        was assumed in the macrodispersion calculations.
        A large ratio of horizontal to vertical correlation
        scales was observed and ranged from 5:1 to 25:1.

    5.  The ratio of horizontal to vertical K indicated by the
        stochastic analysis (1.2:1) was less than the range
        in ratios calculated from a nearby aquifer test (2:1
        to 5:1).

    6.  Stochastic transport equations predicted a range
        of asymptotic long itudinal-macrodispersivities from
        the flowmeter measures of K variability (0.23 to 1.2
        meters) which brackets the  value observed in the
        tracer test (0.96 meters). Estimates of longitudinal
        macrodispersivity using statistical parametersfrom
        the permeameter measurements were consistently
        lower than the tracer-test value.

    7.  Transverse  horizontal and transverse vertical
        dispersivities were  underestimated,  probably
        because transient flow effects are not taken into
        account  in the stochastic transport equations of
        Gelhar and Axness (1983).

    8.  The  transverse horizontal dispersivity  (0.025
        meters)  estimated  by the modified  stochastic
        equations of Rehfeldt (1988),  which incorporate
        the effects of lateral shifts in the hydraulic-gradient
        direction, agrees well with the value observed in
        the tracer test (0.018 meters).

Literature Cited

Dagan, G. (1982) Stochastic modeling of groundwater flow by
unconditional and conditional probabilities: 2. The solute transport,
Water Resources  Research. 18, 835-848.

Freyberg, D.L. (1986) A natural gradient experiment on solute
transport in a sand aquifer: Spatial moments and the advection
and dispersion of nonreactive tracers. Water Resources Research.
22,2031-2046.

-------
Garabedian, S.P., LeBlanc, D.R., Gelhar, L.W., and Celia, M.A.
(in press) Large-scale natural-gradient tracer test in sand and
gravel, Cape Cod,  Massachusetts:   2.  Analysis of spatial
moments for a nonreactive tracer, Water Resources Research.

Gelhar, L.W., and  Axness, C.L (1983) Three-dimensional
stochastic analysis of macrodispersion in aquifers, Water
Resources Research. 19,161-180.

Hess, K.M. (1989) Use of a borehole flowmeter to determine
spatial  heterogeneity  of  hydraulic  conductivity  and
macrodispersion in a sand and gravel aquifer, Cape  Cod,
Massachusetts, Proceedings. NWWA Conference on New Field
Techniques for Quantify ing the Physical and Chemical Properties
of Heterogeneous Aquifers,  Dallas, TX, 497-508.

Hufschmied, P. (1986) Estimation of three-dimensional statistically
anisotropic hydraulic conductivity field by means of single well
pumping  tests combined  with  flowmeter measurements,
Hvdrogeoloqie.  2,163-174.

Journel, A.G., and Huijbregts, C.J. (1978) Mining Geostatistics.
Academic, New York, 600.

LeBlanc, D.R.,  Garabedian, S.P., Quadri, R.D., Morin, R.H.,
Teasdale, W.E., and Paillet,  F.L. (1988) Hydrogeologic controls
on solute transport in a plume of sewage-contaminated ground
water, U.S. Geological Survey Program on Toxic Waste-Ground-
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481.B7-B12.

LeBlanc, D.R.,  Garabedian, S.P.. Hess, K.M., Gelhar, L.W.,
Quadri, R.D., Stollenwerk, K.G.,  and  Wood, W.W. (in press)
Large-scale natural-gradient tracertest in sand and gravel, Cape
Cod, Massachusetts:  1. Experimental design and observed
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Molz, F.J., Morin, R.H., Hess, A.E., Melville, J.G.. and Guven, O.
(1989) The impeller meter for measuring aquifer permeability
variations:  Evaluation and comparison with other tests, Water
Resources Research. 25,1677-1683.

Neuman, S.P., Winter. C.L, and Newman, C.M. (1987) Stochastic
theory  of field-scale fickian dispersion in anisotropic porous
media, Water Resources Research. 23, 453-466.

Rehfeldt, K.R. (1988)  Prediction of macrodispersivity  in
heterogeneous aquifers, Ph.D. Thesis, Dept. of Civil Eng., Mass.
Inst. of Tech.

Rehfeldt, K.R.,  Hufschmied, P.,  Gelhar, L.W., and Schaefer,
M.E. (19891 Measuring hydraulic conductivity with the borehole
flowmeter. EPRI  Topical Report EN-6511,  Electric Power
Research Institute, Palo Alto, Calif.

Sudicky,  E.A. (1986) A natural gradient experiment on solute
transport in a sand aquifer:  Spatial variability of hydraulic
conductivity and its role in the  dispersion process, Water
Resources Research. 22,2069-2082.

Wolf, S.H. (1988) Spatial variability of hydraulic conductivity in a
sand and gravel aquifer, Engineer's thesis, Dept. of Civil Eng.,
Mass. Inst. of Tech.
Wolf, S.H., Celia, M.A., and Hess, K.M. (in press) Evaluation of
hydraulic conductivities calculated from multi-port permeameter
measurements, Ground Water.

Zapico, M.M., Vales, S., and Cherry, J.A. (1987) A wireline piston
core barrel for sampling cohesionless sand and gravel below the
water table, Ground Water Monitoring Review. 7, 74-82.

Disclaimer

The information in this document has been funded wholly or in
part by  the United States Environmental Protection Agency
under interagency agreement number DW14933317 with the
U.S. Geological Survey. This document has been subjected to
the Agency's peer and administrative  review  and  has been
approved for publication as an EPA document.

Quality Assurance Statement

All research projects making conclusions or recommendations
based on environmentally related measurements and funded by
the Environmental Protection Agency are required to  participate
in the Agency  Quality Assurance Program.  This project was
conducted under an approved Quality Assurance Program Plan.
The procedures specified in this plan were used without exception.
Information on the plan and documentation of the quality assurance
activities and results are available from the Principal Investigator.

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