vvEPA
Measurement of
Hydrauiic Conductivity
Distributions:
A Manual of Practice
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EPA/600/8-90/046
MEASUREMENT OF HYDRAULIC CONDUCTIVITY
DISTRIBUTIONS
A MANUAL OF PRACTICE
by
FRED J. MOLZ, OKTAY GttVEN, JOEL G. MELVILLE
Civil Engineering Department
Auburn University, AL 36849
With Contributions By
ALFRED E. HESS and FREDERICK L. PAILLET
United States Geological Survey
Denver Federal Center
Denver, CO 80225
CR-813647
Project Officer
Lowell E. Leach
Robert S. Kerr Environmental Research Laboratory
Ada, OK 74820
ROBERT S. KERR ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
ADA, OK 74820
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DISCLAIMER
The information in this document has been funded wholly or in part by the United States Environmental
Protection Agency under assistance agreement number CR-813647 to the Board of Trustees of Auburn University,
Auburn, Alabama, subjected to the Agency's peer and administrative review, and it has been approved for
publication as an EPA document Mention of trade names or commercial products does not constitute
endorsement or recommendation for use.
u
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FOREWORD
EPA is charged by Congress to protect the Nation's land, air and water systems. Under a mandate of
national environmental laws focused on air and water quality, solid waste management and the control of toxic
substances, pesticides, noise and radiation, the Agency strives to formulate and implement actions which lead to
a compatible balance between human activities and the ability of natural systems to support and nurture life.
The Robert S. Kerr Environmental Research Laboratory is the Agency's center of expertise for
investigation of the soil and subsurface environment Personnel at the laboratory are responsible for management
of research programs to: (a) determine the fate, transport and transformation rates of pollutants in the soil, the
unsaturated and saturated zones of the subsurface environment; (b) define the processes to be used in
characterizing die soil and subsurface environment as a receptor of pollutants; (c) develop techniques for
predicting the effect of pollutants on ground water, soil, and indigenous organisms; and (d) define and demonstrate
the applicability and limitations of using natural processes, indigenous to the soil and subsurface environment, for
the protection of this resource.
This manual of practice presents state-of-the-art techniques for field measurements of the vertical
distribution of hydraulic conductivity in contaminated ground water aquifers for more accurate characterization
of Superfund and other sites. These field techniques allow fully three-dimensional characterization of aquifer
properties which can be used in advection-dominated transport models to significantly enhance our ability to
understand and predict contaminant transport, reaction and degradation in the field. The techniques also provide
data for optimum placement of well screens for remediation and monitoring.
U
Clinton W. Hall
Director
Robert S. Kerr Environmental
Research Laboratory
ui
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ABSTRACT
The ability of hydrologists to perform field measurements of aquifer hydraulic properties must be
enhanced in order to significantly improve the capacity to solve ground water contamination problems at
Superfund and other sites. The primary purpose of this manual is to provide new methodologies for measuring
K(z), the distribution of horizontal hydraulic conductivity in the vertical direction in the vicinity of a test well.
Measurements in nearby wells can then be used to estimate three-dimensional distributions. As dispersion-
dominated models (particularly two-dimensional, vertically-averaged models) approach their limitations, it is
becoming increasingly important to develop two-dimensional vertical profile or fully three-dimensional advection-
dominated transport models in order to significantly increase the ability to understand and predict contaminant
transport, reaction, and degradation in the field. Such models require the measurement of hydraulic conductivity
distributions, K(z), rather than vertically averaged values in the form of transmissivities.
Three devices for measuring K(z) distributions (the impeller flowmeter, the heat-pulse flowmeter, and
a multi-level slug test apparatus) are described in detail, along with application and data reduction procedures.
Results of the various methods are compared with each other and with the results of tracer studies. The
flowmeter approach emerged as the best candidate for routine K(z) measurements. Impeller meters are now
available commercially, and the more sensitive flowmeters (heat pulse and electromagnetic) are expected to be
available in the near future.
IV
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CONTENTS
Foreword iii
Abstract iv
Figures vi
Tables viii
Abbreviations and Symbols ix
Executive Summary 1
1. The Impeller Meter Method for Measuring Hydraulic Conductivity
Distributions 3
2. Multilevel Slug Tests for Measuring Hydraulic Conductivity
Distributions 20
3. Characterizing Flow Paths and Permeability Distributions in
Fractured Rock Aquifers 35
Appendix I 47
References 57
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FIGURES
Number Page
1-1 Subsurface hydrologic system at the Mobile site 4
1-2 Apparatus and geometry associated with a borehole
flowmeter test 5
1-3 Assumed layered geometry within which impeller meter data
are collected and analyzed. (Q(z) is discharge measured at
elevation z) 6
1-4 Details of well construction and screen types in wells E7 and AS 9
1-5 Hydraulic conductivity distributions calculated from flowmeter data '
using two different methods 12
1-6 Comparison of hydraulic conductivity distributions for well E7 based
on tracer test data and impeller meter data 13
1-7 Plan view of the field site where small-scale pumping tests were
performed. The numbers next to the dots are weU designations, while
the values in parentheses are the average hydraulic conductivities
(m/day) assigned to the vicinity of each pumping welL Each arrow
represents a test and points from the observation well to the pumping
well. Wells with more than one arrow pointing toward them were
assigned average values 15
1-8 Results of small-scale pumping tests (m/day) wherein the pumping
wells were used as observation wells 16
1-9 Dimensionless horizontal hydraulic conductivity distributions based on
impeller meter readings taken at the various measurement intervals
indicated on the figure 17
I-10 Dimensionless hydraulic conductivity distributions at five-foot
intervals in well E7 taken 30 min., 60 min. and 120 min. after the
start of pumping. The results show good repeatability of the impeller
meter method 18
n-1 Schematic diagram of the apparatus for performing a multi-level slug
test 21
II-2 Plan view of part of the well field at the Mobile site 22
H-3 Multilevel slug test data from well E6. B=log(y,/y2)(tj-t1) =
magnitude of the slope of the log y(t)
response 23
II-4 Plot showing the reproducibility of data collected at well E6 24
II-5 Plots showing the influence of well development at two elevations
in well E6 26
VI
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Number
n-6 Diagram illustrating the geometry within which a partially
penetrating slug test is analyzed Diagram (A) is for the
confined case and diagram (B) is for the unconfined case 27
n-7 Plots of dimensiordess discharge, P = Q/2nKLy, for the
isotropic, confined aquifer problem as a function of L/tm
and H/L 31
n-8 Plots of dirnensionless discharge, P « Q/2icKLy, for the
isotropic, unconfined aquifer problem as a function of
L/rw and H/L 32
ffl-1 The U.S. Geological Survey's slow-velocity-sensitive thermal
flowmeter (modified from Hess, 1986) 37
m-2 The U.S. Geological Survey's thermal flowmeter with inflated flow-
concentrating packer (modified from Hess, 1988) 38
ffl-3 Example of a thermal flowmeter calibration in a 6-inch (1S.2 cm)
diameter calibration column 39
ffl-4 Acoustic-televiewer, caliper, single-point-resistance, and flowmeter
logs for borehole DH-14 in northeastern Illinois 40
ffl-5 Acoustic-televiewer and caliper logs for selected intervals in a
borehole in southeastern New York 42
ffl-6 Profile of vertical flow in a borehole in southeastern New York,
illustrating downflow with and without drawdown in the upper
fracture zone 43
ffl-7 Distribution of fracture permeability in boreholes URL14 and
URL1S in southeastern Manitoba determined from acoustic-waveform
and other geophysical logs; fracture permeability is expressed as
the aperture of a single planar fracture capable of transmitting
an equivalent volume of flow 44
ffl-8 Distribution of vertical flow measured in boreholes URL14 and
URL1S in southeastern Manitoba superimposed on the projection
of fracture planes identified using the acoustic
televiewer 46
AI-1 Details of an inflatable straddle packer design 49
AI-2 Schematic diagram illustrating a natural flow field in the vicinity
of a well 52
AI-3 Geometry and instrumentation associated with the dialysis cell
method for measurement of Darcy velocity S3
AI-4 Apparatus and geometry associated with the SWET
test 54
AI-S Apparatus and geometry associated with a borehole flowmeter
test 55
vii
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TABLES
Number page
1-1 Impeller meter (discrete mode) and differential head data obtained
in Wells E7, and A5 at the Mobile Site. (z=depth, CPM=counts per
minute, and AH=head difference between static and dynamic
conditions) 10
1-2 Well screen discharge as a function of vertical position in Wells
E7 and A5 at the Mobile Site. (z=depth, Q=discharge rate in well
screen) 10
1-3 Hydraulic conductivity distributions inferred from impeller meter
data using two different approaches described herein. Depth z is in
ft and K(z) is in ftymin.) 11
n-1 Dimensionless discharge, P, as a function of H/L and L/rw for the
confined case with K/K, = 1.0 33
II-2 Dimensionless discharge, P, as a function of H/L and L/t, for the
confined case with Kflf^ = 02 33
n-3 Dimensionless discharge, P, as a function of H/L and L/rw for the
confined case with K/K, = 0.1 33
n-4 Dimensionless discharge, P, as a function of H/L and L/rw for the
unconfined case with K/K, = 1.0 34
n-5 Dimensionless discharge, P, as a function of H/L and L/rw for the
unconfined case with K/K, = 0.2 34
n-6 Dimensionless discharge, P, as a function of H/L and L/rw for the
unconfined case with K/K, = 0.1 34
via
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LIST OF ABBREVIATIONS AND SYMBOLS
Abbreviations
Br
CPM
EFLOW
EPA
IGWMC
NWWA
OTA
USGS
Bromide
counts per minute
computer code name
Environmental Protection Agency
International Ground Water Modeling Center
National Water Well Association
Office of Technology Assessment
United States Geological Survey
Symbols
A
A.
B
B,b
D
H
h
h.
i
K
K,
K,
K
L
P
Q
QP
q
r
r.
R.
S
S.
T
t
U
V
v,
x,y
y(t)
y.
Z,z
O,
screen area per unit length, (L)
open cross-sectional area of casing, (L2)
slope of semi-log plot, (T1)
aquifer thickness, (L)
aquifer thickness, (L)
distance from confining layer to straddle packer, (L)
hydraulic head, (L)
initial head, (L)
counting index, (-)
hydraulic conductivity, (L/T)
hydraulic conductivity in radial direction, (L/T)
hydraulic conductivity in vertical direction, (L/T)
vertically-averaged hydraulic conductivity, (L/T)
length, (L)
dimensionless flow parameter, (-)
discharge rate, (L3/T)
pumping rate, (L'/T)
Darcy velocity, (L/T)
radius, (L)
casing radius, (L)
radius of influence, (L)
plunger radius, (L)
well radius, (L)
storage coefficient, (-)
specific storage, (L"1)
transmissivity, (L2/T)
time, (T)
Darcy velocity, (L/T)
pore or seepage velocity vector, (L/T)
radial seepage velocity, (L/T)
horizontal coordinates, (L)
head change in slug test, (L)
initial head change, (L)
vertical coordinates, (L)
radial dispersivity, (L4)
vertical dispersivity, (L"1)
* Generalized symbols for the dimensions of length, time and mass will be L, T, and M
respectively. The symbol (-) indicates a dimensionless quantity.
IX
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A prefix symbol indicating "change in", (-)
V gradient operator, ()
jc 3.14159, (-)
6 porosity, (-)
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EXECUTIVE SUMMARY
INTRODUCTION
In order to significantly improve the ability to understand ground-water contamination problems at
Superfund and other sites, it has become necessary to improve the ability to make field measurements. The single
most important parameter concerning contaminant migration is hydraulic conductivity. Conventionally, pumping
tests with fully penetrating wells are used to determine transmissivity and longitudinal dispersion coefficients to
describe contaminant spreading in the direction of flow. Models used for making these predictions are dispersion-
dominated.
Horizontal hydraulic conductivities can be defined as a function of vertical position (K(z)). When this
is done at a number of locations in the horizontal plane, the resulting data can serve as a basis for developing
two-dimensional vertical cross-section, quasi three-dimensional or fully three-dimensional flow and transport
models.
Shown in Figure 1-9 are dimensionless K(z) distributions obtained at four different scales in a single well
using an impeller meter. As the measurement interval varies from 10 ft (3.05 m) to 1 ft (0.305 m), the apparent
variability of the hydraulic conductivity increases. This is the type of information that is lost when fully-
penetrating pumping tests are used to obtain vertically-averaged hydraulic conductivities.
There are several techniques for making vertically-distributed measurements, including flowmeter and
multilevel slug tests. These serve as the basis for an improved understanding of subsurface transport pathways
which allow the application of new contaminant transport models that are advection-dominated and largely free
of the problems associated with scale-dependent dispersion coefficients.
SELECTED METHODOLOGY
Two techniques for obtaining K(z) information will be discussed These are the flowmeter and multi-
level slug test methods. Of the two, the flowmeter method is more responsive, less sensitive to near-well
disturbances due to drilling, and easier to apply. As illustrated in Figure 1-2, a flowmeter test involves measuring
the steady pumping rate, QP, and the flow rate distribution along the borehole or well screen, Q(z).
Various types of flowmeters have been devised for measuring Q(z). Those most sensitive to low flows
are heat-pulse, electromagnetic, or tracer-release technology, but such instruments are not presently available
commercially. Impeller meters (commonly called spinners) have been used for several decades in the petroleum
industry, and a few suitable for ground-water applications are available.
IMPELLER METER TESTS
Impeller meter tests can be a relatively quick and convenient method for obtaining information about the
vertical variation of horizontal hydraulic conductivity as illustrated in Figure 1-2. A caliper log is first run to
determine the screen diameter so that variations can be taken into account when calculating discharge. A small
pump is operated at a constant flow rate, QP, until a pseudo steady-state is obtained. The flowmeter is lowered
to near the bottom of the well, and a measurement of discharge is obtained by impeller generated electrical pulses
over a selected period of time. The meter is then raised a few feet and another reading taken. This procedure
continues until the water table is reached. The result is a series of data points giving vertical discharge, Q, within
the well screen as a function of vertical position z. Just above the top of the screen the meter reading should
be equal to QP, the steady pumping rate that is measured independently at the surface with a water flowmeter.
The procedure may be repeated several times to ascertain that readings are stable.
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HEAT-PULSE FLOWMETER TESTS
The use of the impeller meter is limited when the presence of low permeability materials preclude
pumping at a rate sufficient to operate an impeller. The impeller operates with a minimum velocity from about
3 to 10 ft/min (1 to 3 m/min). The heat-pulse flowmeter can be used as an alternative to an impeller meter in
virtually any application due to its greater sensitivity. It has a measurement range from 0.1 to 20 ft/min (0.03
to 6.1 m/min).
The basic principle of the heat-pulse flowmeter is to create a thin horizontal disc of heated water within
the well screen at a known time and a known distance from two thermocouple heat sensors, one above and one
below the heating element As the heat moves with the upward or downward water flow, the time required for
the temperature peak to arrive at one of the heat sensors is recorded. The apparent velocity is then given by the
known travel distance divided by the recorded travel time. Thermal buoyancy effects are eliminated by raising
the water temperature by only a small fraction of a centigrade degree. The geometry associated with the heat-
pulse flowmeter is shown in Figure ffl-2.
Hopefully, thermal flowmeters now being developed by the U.S. Geological Survey, and other sensitive
devices, such as the electromagnetic flowmeter being developed by the Tennessee Valley Authority, will be
available commercially in die near future.
MULTILEVEL SLUG TESTS
The flowmeter testing procedure is generally superior to the multilevel slug test approach, because the
latter depends on the ability to hydraulically isolate a portion of the test aquifer using a straddle packer.
However, if reasonable isolation can be achieved, the multilevel slug test is a viable procedure for measuring
K(z). All equipment needed for such testing is available commercially, and there is an additional advantage of
not requiring an injection or withdrawal of water from the test well.
The testing apparatus used in a multilevel slug test is illustrated in Figure n-1. Two inflatable packers
separated by a length of perforated pipe comprise the straddle packer assembly. A larger packer, referred to as
the reservoir packer, is attached to the straddle packer creating a unit of fixed length which can be moved to
desired positions in the well. When inflated, the straddle packer isolates the desired test region of the aquifer
and the reservoir packer isolates a reservoir in the casing above the multilevel slug test unit and below the
potentiometric surface of the confined aquifer.
In a typical test, water is displaced in the reservoir above the packer creating a head which induces flow
through the central core of the reservoir packer to the straddle packer assembly. Water then flows from the
perforated pipe, through the slotted well screen, into the test region of the aquifer.
Typical results of a series of tests at different elevations are shown in Figure n-3. The data result from
a plunger insertion causing a sudden reservoir depth increase to approximately y.=3 ft The depth variation, y=y(t),
is a result of flow into the aquifer test section adjacent to the straddle packer. The different slopes of the straight
line approximations reflect the variability of the hydraulic conductivity in the aquifer at the different test section
elevations. From this data hydraulic conductivity distributions can be calculated.
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CHAPTER I
THE IMPELLER METER METHOD FOR MEASURING
HYDRAULIC CONDUCTIVITY DISTRIBUTIONS
I-I INTRODUCTION
One of the better existing methodologies for obtaining vertically distributed hydraulic conductivity
information is the borehole impeller meter test It may be viewed as a generalization of a fully penetrating
pumping test except that in addition to measuring the steady pumping rate, QP, the flow rate distribution along
the borehole or well screen, Q(z), is recorded as well
Various types of flowmeters have been devised for measuring Q(z), and described in the literature (Hada,
1977; Keys and Sullivan, 1978; Schimschal, 1981; Hufschmied, 1983; Hess, 1986; Morin et al., 1988a; Rehfeldt
et at, 1988; Molz et al., 1989a,b). Most low-flow-sensitive types of meters are based on heat-pulse,
electromagnetic or tracer-release technology (Keys and MacCary, 1971; Hess, 1986), but such instruments are not
presently available commercially, although several are nearing this stage of development Impeller meters
(commonly called spinners) have been used for several decades in the petroleum industry and a few are suitable
for ground-water applications. Hufschmied (1983) and Rehfeldt et al. (1988) have reported such investigations,
the latter being the most detailed to date regarding the assumptions made in using a borehole impeller meter to
measure hydraulic conductivity as a function of vertical position.
The purpose of this chapter is to describe the application of an impeller meter to measure K(z) at various
locations in the horizontal plane. The site used for this work is illustrated in Figure 1-1 and, as shown, consists
of interbedded sands and clays with the water table being about 3 m (9.84 ft) below the land surface.
1-2 PERFORMANCE AND ANALYSIS OF IMPELLER METER TESTS
1-2.1 Background Information
Impeller meter tests, illustrated in Figure 1-2, can be a relatively quick and convenient method for
obtaining information about the vertical variation of horizontal hydraulic conductivity. A caliper log is first run
to determine the screen diameter so that variations can be taken into account when calculating discharge. A small
pump is operated at a constant flow rate, QP, until a pseudo steady state is obtained. The flowmeter is lowered
to near the bottom of the well, and a measurement of discharge is obtained by counting impeller generated
electrical pulses over a selected period of time. The meter is then raised a few feet and another reading taken.
This procedure continues until the top of the water table is reached. The result is a series of data points giving
vertical discharge, Q, within the well screen as a function of vertical position z. Just above the top of the screen
the meter reading should be equal to QP, the steady pumping rate that is measured independently at the surface
with a water flowmeter. The procedure may be repeated several times to ascertain that readings are stable.
While Figure 1-2 applies explicitly to a confined aquifer, application to an unconfined aquifer is similar.
Most impeller meters are capable of measuring upward or downward flow, so if the selected pumping rate, QP,
causes excessive drawdown, one can employ an injection procedure as an alternative. In either case, there will
be unavoidable errors near the water table due to the deviation from horizontal flow. It is desirable in unconfined
aquifers to keep QP as small as possible, consistent with the stall velocity of the meter. Thus, more sensitive
meters will have an advantage for unconfined aquifers.
As shown in Figure 1-3, data analysis assumes that the aquifer is composed of a series of n horizontal
layers. The difference between two successive meter readings yields the net flow, AQ,, entering the screen
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&p
\
\
\
\
jji^t'i'img" IV- __\ _V
^^\\V^\V\VVI.SV\U\ V\\\VV\
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TO LOGGER (Q)
PUMP *
CAP ROCK^
^DISCHARGE RATE
«^»^r^r i i f*± I r~ r~l />%
[
7LL
)
i /
1
_
V
V7T:
y%
s
V
^LAND SURFACE
CASING
1 DATA ,
CREEN T
METER
ELEVATION=Z
Q
Figure 1-2. Apparatus and Geometry Associated with a Borehole Flowmeter Test
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n
n-l
n-2
n-3
M
3
2
1
0
SURFACE-p,
i
^
i
i
i
i
i
i
i
v i
^WELL
,_ '
1 -?-
/ / / /J/ / fit /// // /////(///
c MEASUREMENT INTERVALS5
0(ZH)'(FROM METER)
/ I 1 1 77-'
/ 1 ' 1 ^
X ?\ 1 A-SCREEN AREA
^ DARCY i | PER UNIT
k VELOCITY p D -] LENGTH- 0
\ (V) I |
SCREEN ' .1 *" "^f*5-OIAMETER
SEGMENT"^. i
N. I 1 I 7»/i
0(Zj)'(FROM METER)
Figure 1-3. Assumed Layered Geometry within which Impeller Meter Data are Collected and Analyzed.
Q(z) is Discharge Measured at Elevation z.
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segment between the elevations where the readings were taken. The Cooper-Jacob [1946] formula for horizon-
tal flow.to a well from a layer, i, of thickness Az,, given by:
/ A \*Hi
(1-1)
where AH = drawdown in ith layer, AQ = flow from ith layer into the well, Kj = horizontal hydraulic
conductivity of the ith layer, Azs = ith layer thickness, rw = effective well radius, t = time since pumping started,
and Sj = storage coefficient for the ith layer. Solving equation (1-1) for the K, outside of the log term yields:
(1-2)
rw S, J
which can be solved iteratively to obtain a value for K,. Further details may be found in Morin et al. [1988a]
or Rehfeldt et al. [1988].
A convenient alternative method for obtaining a K distribution is based on the study of flow in a
stratified aquifer by Javandel and Witherspoon [1969] which showed mat in idealized, layered aquifers, flow at
the well bore radius, r,, rapidly becomes horizontal even with relatively large permeability contrasts between
layers. Under such conditions, radial gradients along the well bore are constant and uniform, and flow into the
well from a given layer is proportional to the transmissivity of that layer, that is:
AQ, = oAz,K, (1-3)
where a is a constant of _proportionality. This condition occurs when the dimensionless time to = i^/S/w is £
100. In this expression K is the average horizontal aquifer hydraulic conductivity defined as iKfAzJb, where
b is aquifer thickness, S, is the aquifer specific storage, t is time since pumping started and rw is well bore radius.
To solve for oc, sum the AQ, over the aquifer thickness, to gee
Ad = QP = aAz^ (1-4)
Multiplying the right-hand side of equation (1-3) by b/b and solving for a yields:
a=<£ (1-5)
bK
Finally, substituting for a in equation (1-3) and solving for K/K gives:
K, _ AQ/Az, . . _ , 2
- ,ii,z, ... n (l-o)
K QP/b
To obtain equation (1-6) it was assumed that steady state conditions apply and therefore AQ and QP do not
change with time. This will occur when r^S^Tt <0.01, where S and T are aquifer storage coefficient and
transmissivity, respectively. Thus, from the basic data a plot of K/K can be obtained if a value of K from a
fully penetrating pumping test is available. The K/K approach has practical appeal because one does not have
to know values for rw or S,, which are impossible to specify precisely. Also, multiplicative errors in flowmeter
readings are cancelled out, and the meter does not have to be calibrated. However, a fully penetrating pumping
test or slug test must be performed along with each flowmeter test.
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While the data analysis involved in a flowmeter test is simple, care must be taken to satisfy all
assumptions so that only the flow caused by pumping is measured (Rehfeldt et al., 1988). For example, an
existing ambient flow must be measured prior to pumping so that initial flow conditions are known. Alternatively,
a two-step pumping procedure can be used (Rehfeldt et aL, 1988). In addition, data analysis procedures assume
horizontal flow and mat head loss is due only to water flow through the undisturbed formation. There are screen
and head losses within the well; however, these can be minimized by pumping at the lowest rate consistent with
the stall velocity of the impeller meter. For a much more detailed discussion of well head losses and their
possible correction see Rehfeldt et aL (1988). Local deviations from horizontal flow will exist in most aquifers,
but the effects should be of second order compared to those of the average flow field as long as the measurement
intervals are not too small. As Azj gets smaller, errors due to deviations from horizontal flow become larger
which leads to poor repeatability of flowmeter readings obtained from multiple tests performed in the same well.
1-2.2 Example Application
Data used in this example were obtained from tests at a site norm of Mobile, Alabama, which is
illustrated in Figure 1-1. Testing began with a mild redevelopment and cleaning of the test well screens (Fig.
1-4) with air followed by ambient flow measurements using a heat-pulse flow meter developed by the U.S. Geo-
logical Survey which has a measurement range of 0.1 to 20 ft/min (0.03 to 6.1 m/oiin.) (Hess, 1986). This is
about 10 times more sensitive than any impeller meter. Even at this sensitivity no ambient vertical flow within
the screen could be detected, which is consistent with the assumption that the aquifer is relatively permeable, well
confined, and the horizontal gradient is low. If a significant ambient vertical flow had existed at any level Az,,
it would have been subtracted from the impeller meter reading for that level prior to data analysis.
The test well is illustrated in Figure 1-2. It has a 4 in (10 cm) ID well screen (0.01 inch slotted plastic
or plastic wire-wrap, see Fig. 1-4) extending from about 130 ft (39.6 m) to 200 ft (61 m) below the land surface.
None of the screens are sand packed. The well screens were cleaned with air, and caliper and ambient pressure
logs were run. Caliper log data were used to verify and compute the cross-sectional area of the well, and the
pressure log served to establish a hydraulic-head distribution for use as a reference in evaluating AH, produced
by pumping. A pressure transducer and an impeller meter with centralizer were lowered into the well, followed
by a small submersible pump capable of pumping about 60 gpm (227 liter/min). After starting, the pump was
allowed to run for about an hour, prior to taking pressure and impeller meter readings, to obtain pseudo-steady-
state conditions as defined by the Cooper-Jacob criterion discussed previously. Data analysis showed that AHj
varied only slightly over the length of the screens.
An impeller meter can function in either a stationary or a trolling mode. In the stationary mode the
meter is held at a series of set elevations, and readings are taken in the form of pulses per unit time with the
aid of an electronic pulse counter. In the trolling mode, the meter is raised or lowered at a constant rate, and
the reading reflects a superposition of the trolling and water flow velocities. For fine-scale ground-water
applications, the stationary mode seems better suited; however, both methods of data acquisition were used during
this study. Listed in Table 1-1 are the basic impeller meter data obtained in wells E7, and A5, along with the
corresponding head difference between static and pumping conditions derived from the pressure logs. In order
to convert impeller meter readings into discharge, the meter was calibrated by placing it in the unslotted top
extension of each well screen and pumping at three different rates which were measured independently at the
surface. In all cases the response was found to be linear. For wells E7 and A5, the calibration equation was
Q = 0.00428(CPM), where Q is in ftYmin and CPM represents impeller "counts per minute." Applying this
equation to the data listed in Table 1-1 resulted in the discharge profiles presented in Table 1-2.
1-23 Data Analysis
As discussed earlier, there are two procedures for inferring a hydraulic conductivity function, K(z), from
impeller meter data. One approach involves the application of equation (1-2) to each depth interval. This was
done for data obtained at wells A5 and E7 using a storage coefficient, Sj = 10"s Azj, and an average specific
storage of lO'ft"1 (3.05 x lO^m') determined from a previously performed pumping test (Parr et al., 1983). The
results are presented in Table 1-3 as Kl(z), with depth values corresponding to the midpoint of the assumed
layers. Also shown in Table 1-3, as K2(z), are the results of applying equation (1-6) to each measurement
interval. To obtain these results, values of the dimensionless function K/K were calculated, where K is the
average hydraulic conductivity obtained from a standard, fully penetrating pumping test in the vicinity of E7 and
-------
(E7)
(A5)
6"
Figure *K
Packers
Casing
Wire
Wrapped
Figure 1-4 Details of Screen Types in Wells E7 and A5.
-------
TABLE 1-1. IMPELLER METER (DISCRETE MODE) AND DIFFERENTIAL HEAD DATA
OBTAINED IN WELLS E7 AND AS AT THE MOBILE SITE.
(z=depth, CPM=counts per minute, and AH=head difference between static and dynamic conditions)
Well#E7
z(ft) CPM AH(ft)
130
135
140
145
150
155
160
165
170
175
180
185
190
1983
1933
1886
1764
1705
1607
1561
1468
1118
994
911
638
277
1218
1.202
1.189
1.177
1.166
1.157
1.149
1.143
1.139
1.138
1.138
1.138
1.138
z(ft)
1325
1375
1425
1475
1525
1575
1625
1675
1725
1775
182.5
1875
190.0
Well»A5
CPM AH(ft)
2024
1968
1885
1799
1652
1488
1362
1106
882
740
506
293
57
1.210
1.201
1.170
1.147
1.136
1.132
1.132
1.132
1.138
1.156
1.173
1.186
1.193
TABLE 1-2. WELL SCREEN DISCHARGE AS A FUNCTION OF VERTICAL POSITION
IN WELLS E7 and A5 AT THE MOBILE SITE.
(z=depth, Q=discharge rate in well screen)
z(ft)
130
135
140
145
150
155
160
165
170
175
180
185
190
Well#B7
Q(ftVmin)
8.49
8.27
8.07
755
7.30
6.88
6.68
6.28
4.79
4.25
3.90
2.73
1.19
2
-------
TABLE 1-3. HYDRAULIC CONDUCTIVITY DISTRIBUTIONS INFERRED FROM INFERRED FROM
IMPELLER METER DATA USING TW) DIFFERENT APPROACHES DESCRIBED HEREIN.
(Depth z is in ft. and K(z) is in ft/min.)
z
13X5
137.5
142.5
1475
1525
1575
1625
1675
17X5
1775
1825
1875
195.0
WeH#E7
Kl(z)
0.050
0.046
0.128
0.059
0.104
0.048
0.100
0.405
0.139
0.088
0.315
0.421
0.154
K2(z)
0.042
0.038
0.100
0.049
0.083
0.040
0.080
0.299
0.109
0.071
0.236
0.310
0.120
z
135
140
145
150
155
160
165
170
175
180
185
189
195
Well»A5
Kl(z)
0.055
0.083
0.091
0.163
0.184
0.140
0.297
0.257
0.156
0.263
0.237
0536
0.027
K2(z)
0.043
0.063
0.069
0.119
0.134
0.104
0.212
0.185
0.115
0.189
0.171
0371
0.022
A5. Using a K of 0.121 ft/min (3.69 x 10%i/min), the corresponding values of K2(z) are listed in Table 1-3
and the hydraulic conductivity profiles are plotted in Figure 1-5.
1-2.4 Comparison of Impeller Meter Tests With Tracer Tests
An examination of Figure 1-5 shows that the trends in the data are virtually identical for wells AS and
E7. There is also a fairly good agreement with the absolute (dimensional) values calculated for the hydraulic
conductivity.
It is of interest to compare the hydraulic conductivity distributions inferred from the impeller meter data
with those obtained previously using single well tracer tests (Molz et al., 1988). These tests involved one fully
penetrating tracer injection well and one multilevel observation well located about 20 ft (6.1 m) away. A bromide
tracer was injected at a constant rate through the injection well while water samples were collected periodically
from up to 14 different elevations in the observation well. Bromide concentrations allowed the determination of
travel times between the injection and observation wells as a function of elevation. From this information it is
possible to infer a relative hydraulic conductivity distribution (Molz et al., 1988). There is no reason to expect
a detailed agreement between the impeller meter results and the single-well tracer test results because the latter
data reflect an average hydraulic conductivity value inferred over a travel distance of approximately 20 ft (6.1
m) and the impeller meter data are averaged over 360°. However, as shown in Figure 1-6, the agreement is
reasonably good, indicating that the overall trend in K(z) persists over the 20 ft (6.1 m) travel distance of the
tracer test (Molz et al., 1988).
1-3 MEASUREMENT OF HYDRAULIC CONDUCTIVITY AT DIFFERENT SCALES USING
IMPELLER METER TESTS AND PUMPING TESTS
The main purpose of this section is to describe the application of impeller meter tests and pumping tests
so that the reader wiU develop an appreciation for the type and extent of hydraulic information that can be
assembled at a particular site. Once again, the site chosen for this detailed application was the Mobile site.
Vertical scale information was obtained using the impeller meter while fully penetrating pumping tests were
employed for obtaining information at various lateral scales. The testing procedures where those described in
previous sections. The fully penetrating pumping tests were analyzed using the Cooper-Jacob Method (Freeze
and Cherry, 1979, or most any contemporary ground-water text).
11
-------
WELL A5
200
130
140
150
160
170
180
190
0.2 0.4
K (ft/min)
WELL E7
0.6
200
0.0
0.2 0.4
K (ft/min)
0.6
Figure 1-5. Hydraulic Conductivity Distributions Calculated from Flowmeter Data Using Two Different
Methods.
12
-------
WELL E7
N
IMPELLER METER (Kl)
TRACER TEST
0.2 0.3
K (ft/min)
Figure 1-6. Comparison of Hydraulic Conductivity Distributions for Well E7 Based on Tracer Impeller Meter
Data.
13
-------
1-3.1 Results of Tests
Shown in Figure 1-7 is a plan view of the Mobile study site where the tests were performed. The
various wells are designated as 12, E6, A3, etc. The number in parentheses next to each well is the vertically-
averaged hydraulic conductivity in meters per day, K(x,y), that resulted from one or more small-scale pumping
tests. Arrows indicate the pattern of testing, pointing from the observation well towards the pumping well. Each
arrow represents a single test with a pumping rate of about 022 ms/min (58 gpm). The repeatability of any one
test was good with the drawdown data falling within 5% of each other.
A series of small-scale pumping tests were also performed in which the pumped wells were used as
observation wells. Once again the pumping rate was approximately 0.22 m'/min (58 gpm). The results of these
tests are shown in Figure 1-8.
A K/K distribution based on impeller meter tests performed in well E8 is shown in Figure 1-9. The
figure was obtained with the use of equation 1-6 applied to impeller meter data from measurement intervals of
0.3 m (1 ft), 0.91 m (3 ft), 1.52 m (5 ft), and 3.108 m (10 ft).
As with the fully penetrating pumping tests, repeatability of the impeller meter tests was good. Evidence
for this is shown in Figure I-10 which documents the results of repeated impeller meter tests in well E7.
1-3.2 Discussion of Results
The vertically-averaged hydraulic conductivity, K(x,y), shown in Figure 1-7 seems to imply that the study
aquifer is fairly homogeneous. The mean value of hydraulic conductivity is 54.9m/day with a standard deviation
of only 2.4 m/day; however, since the data are correlated, the standard deviation is not well defined in a statistical
sense and is used here only as a convenient measure of variation. The mean value agrees well with the result
of a large-scale pumping test (53.4 m/day) performed previously using 12 as the pumping well and pumping at
the rate of 1.48 m'/min (390 gpm) (Parr et al., 1983).
As one would expect, the results shown in Figure 1-8 are more variable because a pumping test using
the pumping well as an observation well will sample a smaller volume of the aquifer. Here the mean value is
only 3.5% smaller at 53.0 m/day, but the standard deviation has increased to 11.4 m/day.
No distinct pattern appears to emerge from Figure 1-7 or Figure 1-8. It is probable that K(x,y) will show
lateral trends over distances in excess of 38 m, which is the approximate distance between wells 12 and E10,
however, the variations here appear to be random.
Given the generally layered nature of geologic deposits in a fluvial environment, one would expect much
more variability of horizontal hydraulic conductivity as a function of verticaj_position, K(z), than of vertically-
averaged horizontal hydraulic conductivity as a function of lateral position, K(x,y). Examination of Figure 1-9
shows this to be the case. Note that K(z) at any particular z is still averaged over the 360° polar angle, so that
the impeller meter test gives no information about lateral heterogeneity or anisotropy around a given well.
Different degrees of heterogeneity are apparent at the various measurement scales of Figure 1-9. As the
measurement scale varies from 10 ft (3.05 m) to 1 ft (0.3 m), the measured variation in hydraulic conductivity
increases, and there is every reason to expect that it would increase further if the measurement scale were
decreased. Obviously, this type of heterogeneity is not reflected in the results of fully penetrating pumping tests.
1-4 SUMMARY AND CONCLUSIONS CONCERNING IMPELLER METER APPLICATIONS
Once the necessary equipment is obtained, impeller meter tests can be a relatively quick and convenient
method for obtaining information about the vertical variation of horizontal hydraulic conductivity K(z) in an
aquifer. This information can be used in a variety of ways including the design of monitoring wells or pump
and treat systems. It can also be used as the basis for the development of three-dimensional flow and transport
models which will be far more realistic than their vertically-averaged forerunners. (Applications to fractured rock
hydrology are described in Chapter III.)
14
-------
*IO-
^ E3
LJ £=.
0 '
co
-5-
A5(53)
A6(5I.8)
AK55.8) A7(53.9) A3(55.8)
2(5.9)
E6(52.l)
-10-
E9(57) El 0(54.9)
A2(5I.5) A8(59.I) A4
0 5 10
A9(58.8)
I I I
15 20 25
DISTANCE (M)-
30 35 40 45
Figure 1-7. Plan View of the Field Site where Small-Scale Pumping Tests were Performed.
15
-------
^ E3
LU
O
2
<
f-
C/>
Q
A6(32.0)
A5(50.7)
AK66.4) A7(47.8) A3(62.2)
H h
£7(66.5)'
£8(45.
-5-
-10-
£6(37.5)
£9(50.2) £10
A2(66.l)
A8(53.9)
A4
A9(57.2)
10 15 20 25
DISTANCE (M)-
30 35
I
40
45
Figure 1-8. Results of Small Scale Pumping Tests where Pumping Wells Were Used as Observation Wells.
16
-------
WELL E8 IMPELLER METER
T I I I
(3' INTERVAL) -
i i i
(I' INTERVAL) -
130
140
150
160
|70
180
I9O
200
O
I I i 7
(5' INTERVAL)
I i i i
,0 2.0 4.0
K/K
130
140
150
160
170
180
190
6.0
200
O.O
i i I I T
(10' INTERVAL)
J I
2.0
4.0
K/K
6.0
Figure 1-9. Dimensionless Horizontal Hydraulic Conductivity Distributions Based On Impeller Meter Readings
Taken at the Various Measurement Intervals Indicated on the Figure.
17
-------
WELL E7 IMPELLER METER
(5' DATA)
130
140
ISO
£* 160
N |70
ISO
190
200
1114
30 MIN. PUMPING
130
140
150
~ 160
M 170
ISO
190
0.0 2.0 4.0
K/K
6.0
200
130
140
150
^ 160
M 170
180
190
200
120 MIN. PUMPING
60 MIN. PUMPING
0.0 2.0 _ 4.0
K/K
O.O 2.O 4.O
K/K
6.0
6.O
Figure I-10. Dimensionless Hydraulic Conductivity Distributions at Five Foot Intervals in Well E7 Taken
30 min., 60 min., and 120 min. after the Start of Pumping. The Results Show Good
Repeatability of the Impeller Meter Method.
18
-------
Over the past several years at the Mobile site, a fairly large amount of hydraulic conductivity data have
been developed based in pan on fully penetrating pumping tests, both large and small scale, and impeller meter
tests. As far as contaminant transport predictions are concerned, the pumping tests alone are of limited use
because, by their nature, they fail to show the large amount of vertically-distributed heterogeneity that is apparent
to varying degrees in the impeller meter tests. Although obvious, this fact merits emphasis because fully
penetrating tests and vertically-averaged hydraulic properties continue as the basis for dealing with contaminant
migration problems, while vertically distributed information is much more vital to successful remediation and
meaningful simulation of contaminant transport in aquifers.
Although the use of this layered approach to ground-water hydrology is less restrictive than its vertically
averaged counterpart, there are still serious limitations to the complete characterization of the three dimensional
variations that actually exist Errors will exist when analyzing any test, and discrepancies will arise when
different tests and different methods are compared.
The results of this investigation suggest that the best strategyjbr suppressing such errors and
discrepancies consists of using an impeller meter to obtain a dimensionless K/K distribution, and then a standard
pumping test, or a slug test, to compute K. Combining both types of information enables one to "fit" an impeller
meter test to a given aquifer and to obtain dimensional values for K(z). Shown in Figure 1-5 is the type of
information that results when the two testing procedures are combined.
In the flowmeter applications at Mobile, a different K(z)/K distribution was obtained at every vertical
scale of measurement at each of seven different wells. As one would expect, the smaller the vertical scale of
measurement the larger the degree of apparent heterogeneity. The results of this work suggest that a proper rule
of thumb would be to use measurement intervals of about one tenth of the aquifer thickness [Molz et al., 1989b].
However, once the equipment is in place, one foot measurement intervals would be practical in most aquifers.
In this way, combinations of data points could be used if at a later date more detailed information becomes
desireable, as in the use of some promising new approaches in geostatistics.
19
-------
CHAPTER H
MULTILEVEL SLUG TESTS FOR MEASURING
HYDRAULIC CONDUCTIVITY DISTRIBUTIONS
n-1 INTRODUCTION
As discussed in Appendix I, the impeller meter test is generally superior to the multilevel slug test
because the latter requires die hydraulic isolation of a portion of the test aquifer using a straddle packer.
However, if reasonable isolation can be achieved the multilevel slug test is a viable procedure for measuring
K(z). All equipment needed for such testing is available commercially and the procedure does not require the
addition or withdrawal of water to change the head in the well.
The testing apparatus used for the applications reported here are illustrated in Figure n-1. Two inflatable
packers separated by a length of perforated, galvanized steel pipe comprised the straddle packer assembly. The
length of aquifer sampled by the straddle packer is 1X3.63 ft (1.1 m). A larger packer, referred to as the
reservoir packer, is attached to the straddle packer with 2" (5.08 cm) Triloc PVC pipe, creating a unit of fixed
length of approximately 100 ft (30.5 m) which can be moved with an attached cable to desired positions in the
well. When inflated, the straddle packer isolates a desired test region of the aquifer and the reservoir packer
isolates a reservoir in the 6" (15.2 cm) casing above the multilevel slug test unit and below the potentiometric
surface of the confined aquifer.
An advantage of this design is that the 2 in (5.08 cm) connecting pipe, and other factors contributing
to head losses, remains unchanged regardless of packer elevation in the well. The inflatable lengths of the
straddle packers are 24.5 in. (62.2 cm) (model 36, pneumatic packer, Tigre Tierra, Inc.) and 39.0 in. for the
reservoir packer (99.1 cm) (model 610, pneumatic packer, Tigre Tierra, Inc.)
n-2 PERFORMANCE OF MULTILEVEL SLUG TESTS
Multilevel slug tests are described for three wells (E3, E6, E7) at the Mobile, Alabama site shown in
Figure H-2. The wells, formerly used as multilevel tracer sampling wells (Molz, et al. 1988), were constructed
of 130 ft of 6 in (152 cm) PVC casing to the top of the medium sand aquifer. Fully slotted 4 in (10.2 cm)
PVC pipe extended an additional 70 ft (21.3 m) through the aquifer. Well E3 was an exception, having 3 ft (0.91
m) slotted pipe sections separated by 7 ft (2.13 m) solid sections through the aquifer.
In a typical test, water is displaced in the reservoir above the packer. This head increase induces flow
through the central core of the reservoir packer and the TriLoc pipe to the straddle packer assembly, then through
the slotted well screen into the test region of the aquifer.
In a falling head slug test, an inserted plunger displaces a volume of water in the reservoir creating a
depth variation, y=y(t), relative to the initial potentiometric surface. In the same way, a plunger withdrawal is
used to create a rising head test. Head measurements are made with a manually operated recorder (Level Head
model LH10, with a 10 psig pressure transducer, In Situ, Inc.).
The results of a series of tests at different elevations in well E6 are shown in Figure n-3. The data
result from plunger insertion tests where a sudden reservoir depth increase of about y0=3 ft (0.91 m) was imposed.
Depth reduction, y=y(t), which is nearly an exponential decay, is a result of flow into the aquifer test section
adjacent to the straddle packer. The different slopes of the straight line approximations (least squares fits) express
the variability of hydraulic conductivity in the aquifer at the different test section elevations. Tests repeated at
a given elevation were generally reproducible, as shown in Figure II-4, with the maximum difference in slopes
being 10% or less.
20
-------
cable
-
XXX
130
.
/_/ 1
*
%
«
.r-r^-7 ' s
transduce
ft *"
^
/ /- ^ /"
«
D = 70ft"
*
*
%
* *
I
««
""!
X
\
ivl"
.
, ^*
_ ^
*"
^mmmm
i
/
\
t
"
» 1
H.
*
*
*
*
*
*
%
4
%
*
«
.
1
1
1
1
1
1
r»
-*
\
H1
I-7.'5V ... , .T.-T-
/^/ ^ / 7 f f * '
TV (t)
^--plunger
^-packer
^^^^" 4
'T* rr
JtZx^x^/^xX
f.; -
*
.
t
.
...
. '
*
JL ^!K: '
L
i ji i straddle packer
. i * t .^^
1 . F-MT'
« 1 }|
«
z
« «
«
*
*
*
*
»
*
*
n i
i
z
« * *
*
-*
r-n* \
V
" r .
Figure II-l. Schematic Diagram of the Apparatus for Performing a Multilevel Slug Test
21
-------
E1 E5
iDi O i
E2E3
r50 (ft)
-12 E7 E8 E9E10
i CD i i | O i i i | Oi i QI i i
150
E6
n injection wells
o multilevel observation/slug test wells
Figure II-2. Plan View of Part of the Well Field at the Mobile Site.
22
-------
100. 200.
time (sec)
300.
Figure H-3.
log(y)=-0.0280t-K>.47
log(y)=-0.0045t+0.49
log(y)=-0.0020t+0.50
log(y)=-0.0038t-K).49
log(y)=-0.0041 t-f 0.51
log(y)=-0.0034t+0.49
Iog(y)=-0.0026t4-0.47
log(y)=~0.0046t+0.48
log(y)=-0.0053t+0.48
logG')=-0.0071t+0.47
log(y)=-0.0092tt-0.50
Multilevel Slug Test Data from Well E6. B=log(yyyj)/(tj-t,)
log y(0 Response.
Z=11.2 ft
Z=17.2 ft
Z=23.2 ft
Z= 5.2 ft
Z=29.2 ft
Z=35.2 ft
Z=41.2 ft
Z=47.2 ft
Z=53.2 ft
Z=59.2 ft
Z=65.2 ft
Magnitude of the Slope of the
23
-------
I I
Z=5.2 ft June 9, 1987
8=0.0060
8=0.0063
8=0.0060
100 150 200
time (sec)
250 300
Figure n-4. Plot Showing the Reproducibility of Data Collected at Well E6.
24
-------
An exception to the general rule of reproducible behavior was observed in well E6. Shown in Figure
H-5 are the results of tests at two elevations conducted on three different days. For the July 20 tests, the well
had been undisturbed for approximately 40 days. For the July 21 tests it was developed by repeated air injection
and flushing prior to the slug testing. Noting the significant change, particularly for the curves having larger
slopes, die tests were repeated on July 30 after more extensive development Since the third set of data was in
close agreement with the second, it was concluded that the development was sufficient This behavior was not
observed at other test wells; however, all tests were done after a small amount of redevelopment The
construction of well E6, originally done for tracer observations (Molz, et al., 1986a, 1986b), was intended to
minimally disturb the aquifer close to the screen. In these cases, particularly after the passage of several months,
minor redevelopment may be required prior to hydraulic testing as clay and silt materials tend to migrate into
the well, coating the screen and often collecting at the well bottom.
Multilevel slug testing will be meaningful only if the straddle packer system hydraulically isolates a
segment of the screen and the adjacent aquifer. Channels, which will negate the packer seal, may be present
between the screen and the borehole. Similarly, backfill material of greater permeability than die formation can
allow flow to bypass the packers rather than flowing into the test section. Additional pressure monitoring above
and below the straddle packer assembly may be desirable if these types of problems are suspected (Taylor et al.,
1989).
O-3 ANALYSIS OF MULTILEVEL DATA
There are essentially three techniques for analyzing partially penetrating slug tests which account for both
radial and vertical flow in an aquifer assumed to be locally homogeneous and isotropic (Boast and Kirkham, 1971;
Bouwer and Rice, 1976; Dagan, 1978). None of these approaches are entirely satisfactory, especially for test
sections that have relatively large diameter to length ratios (Melville et al., 1989; Widdowson et al., 1989).
Therefore, there is a need for a more general approach that is reasonably accurate, free from limiting assumptions
and easy to use. In addition, it is desirable to have a procedure that includes the effect of anisotropy in the test
aquifer since this physical phenomenon is not uncommon.
The purpose of the remainder of this chapter is to present details of a procedure for analyzing slug test
data which considers radial and vertical, anisotropic, and axi-symmetric flow to or from a test interval. It is
based on a finite element model called EFLOW, licensed through the Electric Power Research Institute and
modified at Auburn University.
H-3.1 Mathematical Model Development
Equation n-1 is the mathematical model used in developing the data analysis procedure. Diagrams of
the two-dimensional geometry within which the mathematical model is applied are shown in Figure H-6. Diagram
(A) applies specifically to a confined aquifer while diagram (B) applies to the unconfined case. When analyzing
a partially penetrating slug test in an unconfined aquifer one assumes that the water table stays at a constant
elevation throughout the test (Dagan, 1978).
In a homogeneous, anisotropic aquifer, the equation governing transient axi-symmetric flow is given by:
3t
where S, is specific storage, h is hydraulic head, t is time, r is radial distance, z is vertical distance, and K and
KZ are hydraulic conductivities in the radial and vertical directions respectively. The initial and boundary
conditions for simulating a slug test within the geometry of Figure II-6 are:
25
-------
100 150 200 250
time (sec)
300
Figure 13-5. Plots Showing the Influence of Well Development at Two Elevations in Well E6.
26
-------
(AJ
y(t)
h(f)=h0-y(t)*{ }
*
z
\\v\\\\ \\\\ \\
H
\ \ \ \ \ \ \ \
(B)
y(t) +\
\ \ N
yd)
TV
MB
I
I
t , ;
h
ft,
r
v. S
H
i
\ \ \
1
^
D
^^^'v^^'xV
«e
\ \V T
k
ho
Figure n-6. Diagram Illustrating the Geometry in which a Partially Penetrating Slug Test is Analyzed.
Diagram (A) is for the Confined Case and Diagram (B) is for the Unconfined Case.
27
-------
1C.) h(r, z, 0) = h. (H-2)
B.C.) h(rw, z, t) = h. - y(t), for (D-H) <; z <. (D-H+L) (H-3)
|L(r, 0, t) = * (r, D, t) = 0, for rw < r < R. (EW)
dz dz
r,, z, t) = 0, for 0 <, z <(D-H) and (D-H+L) < z < D (H-5)
z, t) = h, , for OS z
-------
Through the use of Darcy's law the flow into the aquifer may also be expressed as:
/ D-H+L 3.
Q = 27trwK I _ (rw,z)dz (11-12)
J D-H or
A dimensionless flow parameter, P, can now be defined as:
-. _ p D-H+L -,,
2nKLy Ly I D-H
J
The parameter, P, depends only on the configuration of a particular slug test From numerical solutions of
equation (H-8) for different configurations of Figure n-lt and using equation (11-13), Figures n-7 and n-8 were
generated for confined and unconfined cases showing the dependence of P on H/L and L/rw for isotropic
conditions. Also, dimensionless data for K/K, ratios of 1, 0.2 and 0.1 are presented in Tables n-1 through n-
6.
Once the various figures or tables are developed for a given anisotropy ratio, they may be used in
combination with a semi-log plot of slug test data to calculate the hydraulic conductivity in the radial direction.
For example, from Fig. H-7 the appropriate values of H/L, and L/rw can be used to obtain P (call it PJ. Then,
using equation (II-9) one notes that
Q = 2nKLyPn = - A^dy/dt) (11-14)
Using the relationship (l/y)dy/dt = d(ln(y))/dt and solving equation (11-14) for K yields:
K = -__ = - (2.3B) (n-15)
2nLPn dt 27tLPn
where B is the slope of a semi-log plot (base 10 logs) of y vs. t, with the y vs. t values obtained from an actual
slug test. B should always be considered a negative number regardless of whether y is above or below the
reference level during the slug test
n-3.3 Numerical Example
Multilevel slug test data from the Mobile site has been analyzed using the method presented here
(Melville et al., 1989). Data from eleven levels in a test well are shown in Figure II-3 along with straight line
representations using linear regression. The following applies specifically to the data centered at z=11.2 ft where
A,. = 0.180 ft3. The procedure by which the individual hydraulic conductivity values can be calculated is:
1. Obtain a measurement or estimate of aquifer anisotropy ratio.
K:^ = 6.7:1. (Parr et al., 1983)
2. Calculate H/L and log(L/rw) from experimental geometry.
Aquifer thickness, D = 70 ft
Packer separation length, L = 3.63 ft
Distance (H) to closest boundary = 13.01 ft
Radius of screen = 0.167 ft
29
-------
H/L=3.58
Lfrm = 21.8; loglo(IVrw) = 1.34
3. Select dimensionless discharge by interpolating between 1:5 and 1:10 anisotropy values in Tables U-2
and H-3.
Pn = 0.277
4. Determine slope of semi-log data plot (Figure n-3).
B « 0.028 sec'1
5. Calculate hydraulic conductivity from equation (n-15).
K = 0.00183 ft/sec = 158 ft/day
If an average hydraulic conductivity, K, is available from full aquifer pumping tests, multilevel tests like
those described here could be used to develop K(z)/K profiles. This method of obtaining K(z) profiles to assist
in the characterization of contaminant transport appears to be practical under the proper conditions.
There can be serious reservations about the reality of slug test data; however, those tests performed in
wells having slotted screens at the Mobile site appear to be reasonably accurate. It was not possible to perform
slug tests in wells having wire-wrapped screens because of vertical leakage in the screen structure that could not
be prevented with packers. As discussed in Braester and Thunvik (1984), partially-penetrating slug tests are very
sensitive to cylindrical annul! of high or low permeability surrounding a well; therefore, gravel or sand filter pack
should never be used. Tests in unscreened boreholes are questionable because the surface of the formation can
become coated with low permeability materials.
These restrictions make multilevel slug testing much more problematical than impeller meter testing.
However, if the formation permeability is sufficiently low to prevent the use of an impeller meters, because of
stall speed problems, multilevel slug testing may be a viable alternative.
30
-------
CL
O
0.55
0.50
0.45
0.40
0.35
0.30
0.25
0.2
Log (L/rw)
.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
Figure H-7. Plots of Dimensionless Discharge, P = Q/2»cKLy, for the Isotropic, Confined Aquifer Problem
as a Function of L/rw And H/L.
31
-------
Q_
CN
O
0.70
0.60
0.50
0.40
0.30
I I I I I I I I I I I I I I I I
0 2Q»t IM 111 m n 11 i M 111 it n 11 n n 11 f i
" 1.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
Log (L/rw)
Figure n-8. Plots of Dimensionless Discharge, P = QfZitKLy, for the Isotropic, Unconfined Aquifer Problem
as a Function of L/rw and H/L.
32
-------
TABLE n-1. DIMENSIONLESS DISCHARGE, P, AS A FUNCTION
OF H/L AND L/rw FOR THE CONFINED CASE WITH K/K, = 1.0.
H/L
L/r. = 8 12 18 24 36 48 72 96
1
1.25
1.5
2
4
8
16
.4117
.4448
.4617
.4805
.5029
.5155
.5243
3610
.3905
.4045
.4219
.4370
.4463
.4526
.3196
3456
3570
3725
3829
3898
3945
.2964
.3202
3303
.3402
3519
.3576
.3610
.2675
.2882
.2965
.3045
3140
.3183
3207
.2497
2685
2757
2828
2908
2945
2964
2293
2455
.2515
.2575
.2645
.2674
.2687
2147
2295
2348
2400
2459
2484
2496
TABLE H-2. DIMENSIONLESS DISCHARGE, P, AS A FUNCTION OF
H/L AND L/rw FOR THE CONFINED CASE WITH K/K^ = 02.
L/r, = 8 12 18 24 36 48 72 96
H/L
1
125
15
2
4
8
16
3205
3428
3533
3660
3771
3837
3878
2874
3076
3165
3279
3360
3411
3442
2597
2778
2852
2950
3013
3053
3076
2434
2601
.2667
2741
2806
2840
2858
.2230
.2377
.2434
.2487
.2551
.2577
.2589
2102
2238
2288
2336
2392
2415
2424
.1955
.2078
2124
.2168
.2215
.2232
.2237
.1847
.1957
.1997
2034
2076
2092
2096
TABLE H-3. DIMENSIONLESS DISCHARGE, P, AS A FUNCTION OF
H/L and L/rw FOR THE CONFINED CASE WITH K/K^ = 0.1.
L/r. = 8 12 18 24 36 48 72 96
H/L
1 2914 2634 2398 .2256 .2078 .1966 .1839 .1742
1.25 3121 .2821 2567 2410 .2207 2085 .1949 .1840
1.5 .3209 2894 2630 2457 .2255 2129 .1990 .1876
2 3295 2979 2701 .2523 .2302 2172 .2028 .1909
4 3401 .3055 2765 2588 .2357 .2219 .2068 .1945
8 .3453 .3096 2798 .2615 .2378 2238 .2081 .1958
16 3463 .3105 .2800 .2616 .2387 .2245 .2083 .1960
33
-------
TABLE H-4. DIMENSIONLESS DISCHARGE, P, AS A FUNCTION OF
H/L AND L/rw FOR THE UNCONFINED CASE WITH K/K, « 1.0.
L/r. = 8 12 18 24 36 48 72 96
H/L
1.25
1.5
2
4
8
16
.6564
.6207
.5912
.5616
.5505
.5453
.5487
.5219
.4955
.4783
.4701
.4662
.4658
.4455
.4241
.4129
.4066
.4036
.4186
.4018
3883
3748
.3697
3672
3644
3515
3410
.3305
3264
3244
3329
3220
3132
3042
3007
2990
.2973
.2887
.2813
.2736
.2707
.2695
2742
2667
2605
2540
2516
2505
TABLE n-5. DIMENSIONLESS DISCHARGE, P, AS A FUNCTION OF
H/L AND L/rw FOR THE UNCONFINED CASE WITH K/K, = 02.
L/r. = 8 12 18 24 36 48 72 96
H/L
125
1.5
2
4
8
16
.4528
.4351
.4201
.4047
3988
3960
3944
3802
3683
3564
3517
3494
3469
3356
3256
3166
3128
3110
3187
3090
3018
2926
2894
2879
.2853
.2774
2708
2639
2612
2601
2651
2582
2524
2463
2441
2431
.2423
.2362
.2311
2259
.2242
.2238
2258
2206
2162
2117
2102
2097
TABLE H-6. DIMENSIONLESS DISCHARGE, P, AS A FUNCTION OF
H/L AND L/rw FOR THE UNCONFINED CASE WITH K/B^ = 0.1.
L/r. = 8 12 18 24 36 48 72 %
H/L
125 .3960 3498 3114 2883 .2605 2434 .2237 2096
1.5 3824 3386 3023 2804 .2539 2376 .2185 2051
2 3724 3292 2946 2737 .2482 2326 2141 2012
4 3587 3195 2867 2667 .2424 2274 .2098 .1974
8 .3540 3157 2835 2640 .2402 2255 .2085 .1962
16 3517 3139 2821 2628 .2393 2248 .2083 .1960
34
-------
CHAPTER HI
CHARACTERIZING FLOW PATHS AND PERMEABILITY DISTRIBUTIONS
IN FRACTURED ROCK AQUIFERS'
m-1 INTRODUCTION
In chapters I and n, the impeller meter test and the multilevel slug test were described as a means for
measuring vertical hydraulic conductivity distributions. This chapter deals with the application of the borehole
heat-pulse flowmeter. It can be used as an alternative to an impeller flow meter in virtually any application
because of its greater sensitivity. This increased sensitivity is particularly important near the bottom of test wells
where flow velocities are small
Spinner flowmeters are limited to minimum velocities of about 3 to 10 fl/min (1 to 3 m/min) allowing
flow volumes of as much as 4 gal/min (IS 1/min) to go undetected in a 4-in (10 cm) diameter borehole.
However, impeller flowmeters are available commercially while heat-pulse flowmeters are in a developmental
stage.
Since the analysis of data obtained with a heat-pulse flowmeter in granular aquifers is identical to that
discussed for impeller meter data this chapter will be devoted to the application of flowmeters, particularly heat-
pulse flowmeters, to fractured rock aquifers. Such meters may be used to locate productive fracture zones and
to characterize apparent hydraulic conductivity distributions. Because flow from or into individual fractures is
often small, flowmeters more sensitive than impeller meters ate commonly needed.
Several thermal flow-measuring techniques have been developed for the measurement of slow flows,
including a thermal flowmeter described by Chapman and Robinson (1962) and an evaluation of hot-wire and hot-
film anemometers by Morrow and Kline (1971). Dudgeon et al. (1975) reported the development of a heat-
pulse flowmeter that uses a minimal-energy thermal pulse in a tag-trace, travel-time technique which is only 1.63
in (41 mm) in diameter and can be used in small-diameter boreholes. Although other thermal flowmeters
considered have not proved to be practical in a borehole environment, the commercial version of the Dudgeon
style heat-pulse flowmeter was determined to be viable even though it lacks important features; such as seals,
which could withstand water pressures to at least 10,000 ft (3,048 m), insensitivity to changes in logging cable
resistance and stray electrical currents, and integral centralizers (Hess, 1982).
The basic measurement principle of the USGS Meter is to create a thin horizontal disc of heated water
within the well screen at a known time and a known distance from two thermocouple heat sensors, one above
and one below the heating element As the heat pulse moves upward or downward with the water flow, the time
required for the temperature peak to arrive at one of the heat sensors is measured. The velocity is then
determined by dividing the known travel distance by the time of travel Thermal buoyancy effects are eliminated
by raising the water temperature only a small fraction of a centigrade degree.
This chapter describes three case studies where flow measurements were used to provide a quick survey
of aquifer hydraulic responses in fractured rock. They markedly reduce the time required to complete aquifer
characterizations using conventional hydraulic tests and tracer studies.
m-2 THE U.S. GEOLOGICAL SURVEY'S THERMAL FLOWMETER
The urgent need for a reliable, slow-velocity flowmeter prompted the USGS to develop a small-diameter,
sensitive, thermal flowmeter that would operate to depths of 10,000 ft (3,048 m) or more using 16,000 ft (5,000
m) or longer lengths of conventional four-conductor logging cable (Figure III-l). The thermal flowmeter
developed by the U.S.G.S. has interchangeable flow-sensors, 1.63 and 2.5 in. (41 and 64 mm) in diameters, and
* Material in this chapter was prepared by Alfred E. Hess and Frederick L. Paillet under sponsorship of the
Water Resources Division, U.S. Geological Survey, at the Denver Federal Center, Denver, CO 80225.
35
-------
has a flow sensitivity from 0.1 to 20 ft/min (0.03 to 6.1 m/min) in boreholes with diameters that range from 2
to 5 in (50 to 125 mm). The vertical velocity in a borehole is measured with the thermal flowmeter by noting
the time-of-travel of a heat pulse and using calibration charts developed in the laboratory using a tube with a
diameter similar to that of the borehole under investigation (Hess, 1986).
After the thermal flowmeter was tested at several sites, an inflatable, flow-concentrating packer was
developed to decrease measurement uncertainties caused by geothermally induced convection currents within the
borehole and to increase flow sensitivity in larger diameter holes. The flowmeter and packer have been integrated
into a single probe operating on logging lines having four or more conductors (Figure ni-2). The assembly can
be used with other borehole probes, such as spinner flowmeters and pressure transducers, whose functions are
enhanced by the use of an easily controlled packer (Hess, 1988).
The thermal flowmeter, with or without packers, has been used to measure natural or artificially induced
flow distributions in boreholes with diameters ranging from 3 to 10 in (75 to 250 mm), at temperatures from
6 to 60°C, and in a variety of lithologies including basalt, dolomite, gneiss, granite, limestone, sandstone, and
shale.
With the packer inflated, thermal travel times correlate with borehole flows, rather than vertical velocity,
and can detect flows in the range of 0.02 to 2 gal/min (0.04 to 8 L/m). A representative flow calibration chart
is shown in Figure ni-3 with curves for the packer inflated, deflated, or not installed. The inverse of the time-
of-travel is used on the calibration chart for ease and accuracy in reading the curves (Hess, 1982).
The thermal flowmeter was used initially to define naturally occurring flows in boreholes. However, it
has been used in additional applications, such as locating fractures that produce water during aquifer tests and
identifying flows induced in adjacent boreholes during such tests. The rapid measurement provided by the thermal
flowmeter suggests that a few hours of measurements may save days or weeks in investigations using conventional
packer and tracer techniques.
m-2.1 Case Study 1-Fractured Dolomite in Northeastern Illinois
Acoustic-televiewer, caliper, single-point-resistance, and flowmeter logs were obtained in a 210 ft (64 m)
borehole in northeastern Illinois as part of a study of contaminant migration in fractured dolomite (Figure ni-
4). The acoustic-televiewer log is a magnetically orientated, pseudo-television image of the borehole wall which
is produced with a short-range sonar probe (Zemanek et al., 1970). Irregularities in the borehole wall, such as
fracture and vugular openings, absorb or scatter the incident acoustic energy resulting in dark features on the
recorded image. Such televiewer logs may be used to determine the strike and dip of observed features (Paillet
et al., 1985).
The acoustic-televiewer and caliper logs for borehole DH-14 indicate a number of nearly horizontal
fractures which seem to be associated with bedding planes. The largest of these are designated A, B, C, and D
in Figure ffl-4. The caliper log indicates that the major planar features on the televiewer log are large fractures
or solution openings associated with substantial borehole diameter enlargements. The large but irregular features
between fractures B and C also are associated with borehole enlargements but are interpreted as vugular cavities
within the dolomite rather than fractures. The single-point-resistance log indicates abrupt shifts in resistance at
depths of about 130 and 185 ft (40 and 56 m) which may reflect differences in the dissolved solids concentration
of water in the borehole.
The pattern of vertical flow determined by the flowmeter indicated the probable origin of the water
quality contrasts in the borehole (Figure ffl-4). The flowmeter log indicated downflow, which probably was
associated with naturally occurring hydraulic head differences, causing water to enter at the uppermost fracture,
A, and exit at fracture B. A much smaller flow, with the same electrical conductivity and dissolved solids
concentration, continued down the borehole to fracture C. At this fracture, the downflow increased and flow
coming into the well apparently contained a greater concentration of dissolved solids, which accounts for the
greater electrical conductivity. This increased downflow exited the borehole at fracture D where there was
another, somewhat smaller shift in single-point-resistance. Although not rigorously proven from the geophysical
logs, the second shift in resistance appears to be associated with the dissolved solids concentration of the water
entering at fracture C.
36
-------
METRE
r-1.0
-O.S
-0.7
-O.S
-0.4
-0.3
-0.2
-0.1
«0.0
ELECTRONICS
SECTION
80WSPRING
Y^CENTRALUEK
\
. FLOW SENSOR
ROW SENSOR
Figure ffl-1. The U.S. Geological Survey's Slow Velocity Sensitive Thermal Howmeter (Modified Hess,
1986).
37
-------
FHHT METERS
I-1-0
-3.0
ZS
2JJ
1.5
U)
0.3
0.0
-OS
-QJt
-0.7
-0.6
OJ
Q-2
0.1
0.0
ELECTSONC
SSCTCN
WITH INFLATED
PUMP
Figure HI-2. The U.S. Geological Survey's Thermal Flowmeter with Inflated Flow-Concentrating Packer
(Modified Hess, 1988).
38
-------
AVERAGE VERTICAL VELOCITY. IN FEET PER MINUTE
2
fll
S
o
in
m
m
I
m
:j
DOWNFLOW.IN.
GALLONS PER MINUTE
ca &
i I
I
01
UPFLOW. IN GALLONS
PER MINUTE
to
I
OOWNFLOW. IN LITERS
PER MINUTE
,_ UPFLOW. IN LITERS
' PER MINUTE
6
o>
AVERAGE VERTICAL VELOCITY. IN METERS PER MINUTE
Figure UL-3. Example of a Thermal Flowmeter Calibration in a 6-inch (15.2 cm) Diameter Calibration
Column.
39
-------
CALIPER LOG
ACOUSTIC
TELEVIEWER LOG DIAMETER. IN INCHES
10
100
cr
-------
Subsequent water sampling confirmed that there were differences in the dissolved solids concentration
of the water at different depths. Sample analysis indicated that the water entering at fracture A had a dissolved
solids concentration of about 750 mg/L and that entering at fracture C had a dissolved solids concentration of
about 1,800 mg/L. In this instance the geophysical data, especially the thermal-flowmeter data, were useful in
planning subsequent packer testing and in interpreting the results of water-quality measurements.
The identification of natural differences in background water quality was useful in modeling the transport
of conservative solutes. At the same time, measurements of vertical velocity distributions provided useful
indications of hydraulic head differences between different depth intervals. This information could not be obtained
from conventional water level measurements without the time consuming installation of packers at multiple levels
in all boreholes at the site.
ffl-2.2 Case Study 2-Fractured Gneiss in Southeastern New York
Conventional geophysical and televiewer logs were obtained in a 400 ft (123 m) borehole completed in
fractured gneiss at a contaminated ground-water site in southeastern New York, about 200 ft (70 m) from Lake
Mahopac. After a night of recovery from the effects of pumping nearby wells, the water level in the borehole
appeared to be slightly higher than the lake level, even though the lake level is generally higher during the day.
The acoustic-televiewer log indicated that fractures intersected almost every depth interval of this borehole.
Although brine-solution tracing indicated there was downflow within the borehole, the locations of entry and exit
points were uncertain.
Acoustic-televiewer and caliper logs for selected intervals of the borehole are shown in Figure ffl-5. The
caliper log indicates several borehole enlargements at point A just below the bottom of the casing and other
enlargements, B and C, near the bottom of the borehole. The televiewer log confirmed a large number of major
fractures that could be entry and exit points.
Flowmeter logs indicated both the entry and exit points of downflow (Figure ITI-6). With just a few
hours of flowmeter measurements the entry points of the downflow were isolated to the uppermost fractures with
most being from fracture A. Consistent differences in the downflow indicated that about 20 percent exited at
fracture B and the rest at fracture C.
Flowmeter measurements also indicated a series of transient fluctuations in downward flow which are
attributed to the effects of pumping in nearby water-supply wells and the resulting head differences between
shallow and deep fractures. The downward flow between fractures A and B was determined to vary from a
maximum of about 0.7 gal/min (2.7 L/min) to a minimum of 0.4 gal/min (1.5 L/min) during periods ranging from
a few minutes to an hour.
These results enabled hydrologists studying the contamination problem to infer local flow conditions in
the aquifer. The results of flowmeter measurements provide useful information about hydraulic head differences
between the upper and lower fracture zones and the extent of interconnection between individual fracture sets
within those zones. Of special interest is the small proportion of the many large fractures, indicated by the
caliper log, that actually produced or accepted flow under ambient hydraulic head conditions. This conclusion
agrees with several other recent studies of fractured-rock aquifers (Paillet et al., 1987; Paillet and Hess, 1987).
ffl-2.3 Case Study 3-Water Movement in and Around a Fracture
Zone On The Canadian Shield In Manitoba
This study describes flow in interconnected fractures for an isolated fracture zone on the southeastern
margin of the Canadian Shield in Manitoba, Canada. Two boreholes 425 ft (130 m) apart intersected a fracture
zone at about 870 ft (265 m). The depths on the logs are somewhat greater than actual vertical depths because
the boreholes had been angled deliberately by about 20 degrees. As shown in Figure HI-7, the boreholes
intersected almost no fractures except those associated with the major zone. The results indicate substantial
permeability in the main fracture zone and in several sets of fractures that appear to splay from it.
41
-------
CAUPERLOG
DIAMETER IN
INCHES
ACOUSTIC so
TELEVIEWEH
LOG
100 -
350
«OO
- /
1
"i
LL
>>f=
1
B
C
\
>
- 25
IU
&
u.
(T
Jso 3
IS
DIAMETER. IN
CENTIMETERS
Figure ni-5. Acoustic-Televiewer and Caliper Logs for Selected Intervals in a Borehole in Southeastern
New York.
42
-------
i?
S* ^i
g O
5.8,
3<
**^* \0
O K°
*» &
53
If
I5'
a p
S'W
f |
SI
%*
?!
r~ <
li
W(-j
m?
S^
-O
is
i
6
b
to
o
-*
0
o
o
k
I - .1
-
.
DEPTH, IN FEET BELOW LAND SURFACE
i i i
........ \ 1 1 111
I i ' I
, WITHOUT . «
f " " DRAWDOWN '
,_ __.. i ««
c
i
\m^m^n^m^(
P
i.
o
$
> m>
f~(BO
O C
AW?^j
o mo
OH
wO
Tn
s ^
0 SQ
2.<
8
DEPTH, IN METERS BELOW LAND SURFACE
-------
SOUTH
BOREHOLE
URL15
BOREHOLE
URL14
NORTH
ESTIMATED FRACTURE
APERATURE.IN
INCHES x10'z
0.0
1.0 2.0
0.0 1.0
800
850
UJ
o
u.
CC
CO
UJ
CD
UJ
UJ
u.
900
950
UJ
Q
1000
1.2-
1
-
F
«^j /
H
_
P .
-
-
RACTUR
ZONE
/ N
i
_
_
e
\
^'"^
3
-
-
r i
23O
240
250
UJ
0
cc
260 g
Q
5
270 3
UJ
N METERS B
X
UJ
290°
300
310
320
0.0 0.2
0.0 0.2 0.4
ESTIMATED FRACTURE
APERTURE. IN
MILLIMETERS
Figure HI-7.
Distribution of Fracture Permeability in Boreholes URL14 and UKL15. Fracture
is Expressed as the Aperture of a Single, Planar Fracture Capable of Transmitting an Equivalent
Flow.
44
-------
Flowmeter tests indicate that each borehole produced water from the vicinity of the fracture zone during
pumping, but at markedly different rates. In borehole URL14, a pumping rate of only 0.07 gal/min (025 L/min)
maintained a drawdown of more than 260 ft (80 m), while in borehole URL15 a pumping rate of 5 gal/min (19
L/min) resulted in only 5 ft (1.5 m) of drawdown. All water production in borehole URL14 came from a minor
fracture, far below the major fracture zone, whereas all of the water production in borehole URL15 came from
the lower one-half of the major fracture zone.
The hydraulic connection between the two boreholes was investigated by measuring flow in borehole
URL1S while pumping borehole URL14. It was determined that flow entered borehole URL1S at the main
fracture zone, at a depth of 880 ft (270 m), and then moved downward about SO ft (IS m) to exit at an
apparently minor fracture. Flow entered borehole URL14 at a minor fracture about 130 ft (40 m) below the main
fracture zone (Figure m-8). Outflow from borehole URL1S was equal to inflow to URL 14, within the
measurement accuracy of the thermal flowmeter.
A projection of fracture planes indicates that there is no direct connection between the exit point in
borehole URL1S and the entry point in borehole URL14. This analysis indicates that the hydraulic connection
between the boreholes occurred by means of irregular fracture intersections beneath the main fracture. Although
the major fracture zone was the primary producer when borehole URL 15 was pumped, that zone produced no
inflow in borehole URL14 when it was pumped.
Although it is difficult to understand how small fractures located away from the main fracture zone could
provide the only connection between boreholes URL14 and URL15, other geophysical logs provided additional
information. Local stress concentrations may have caused local rock mass dilatency accounting for this
permeable pathway below the main fracture zone. This is inferred from borehole-wall breakouts, identified on
acoustic-televiewer logs, and later confirmed by hydraulic fracturing stress measurements.
m-3 CONCLUSIONS
These case studies illustrate the potential application of the thermal flowmeter in investigations of slow
flow in fractured aquifers. The relative ease of making thermal-flowmeter measurements permits reconnaissance
of naturally occurring flows prior to hydraulic testing as well as the transient effects caused by pumping.
Thermal-flowmeter measurements interfere with attempts to control borehole conditions, as with packers,
because of the flowmeter and wire line. In spite of this limitation, the simplicity and rapidity of thermal-
flowmeter measurements constitute a valuable means to identify contaminant plume pathways while planning
additional investigations. The thermal flowmeter is especially useful at sites where boreholes are intersected by
permeable horizontal fractures or bedding planes.
Naturally occurring hydraulic head differences, between individual fracture zones, are altered greatly by the
presence of open boreholes at a study site. These differences can only be studied by the expensive and time
consuming use of packers to close all connections between fracture zones. The simple and direct
measurement of vertical flows, caused by these head differences, can be obtained with the thermal flowmeter in
a few hours. Additional improvements of the thermal-flowmeter, by adding a packer and refining techniques for
flowmeter interpretation, may greatly decrease the time and effort required to characterize fractured rock aquifers
using conventional hydraulic testing.
While the case studies described in this chapter did not all involve contaminated ground water, it is
believed that the potential application to such sites is obvious. Hopefully, thermal flowmeters and other sensitive
devices, such as the electromagnetic flowmeter being developed by the Tennessee Valley Authority, will be
available commercially in the near future.
45
-------
PROJECTIONS
OF FRACTURES
Figure III-8. Distribution of Vertical Flow Measured in Boreholes URL14 and URLIS Superimposed on the
Projection of Fracture Planes Identified Using the Acoustic Televiewer.
46
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APPENDIX I
OVERVIEW AND EVALUATION OF METHODS FOR DETERMINING
THE DISTRIBUTION OF HORIZONTAL HYDRAULIC
CONDUCTIVITY IN THE VERTICAL DIMENSION
AI-1 INTRODUCTION
This appendix overviews several techniques for measuring K(z), the vertical distribution of horizontal
hydraulic conductivity. It is based largely on a paper by Taylor et al. (1989) published in Ground Water and
should be consulted for a more in-depth evaluation of those techniques not emphasized in this report
As discussed in the Executive Summary the application of advection-based models requires the
measurement of hydraulic conductivity distributions. This has been done previously using forced gradient tracer
techniques (Molz et al., 1988,1989b), but the technology is expensive, time consuming, and usually not practical.
Therefore, tracer methodology will not be discussed further here.
An important consideration when making measurements of hydraulic conductivity is the volume over
which the measurement is averaged. This volume may range from a few tenths of a liter, for core studies, to
hundreds or thousands of cubic meters using hydraulic testing procedures. The volume over which the
measurement is made depends on the intended use of the hydraulic conductivity data. When the volume is large,
important small scale features may be ignored, and when the volume is small, there may be a tendency to
undersample, which can result in die loss of significant features. The exact definition of large or small depends
on the local variability of hydraulic properties and the intended application of the data.
Another important consideration, with respect to hydraulic conductivity, is the significant horizontal to
vertical ratio that exists in most natural formations, where anisotropy ratios on the order of 10:1 or more are
common (Freeze and Cherry, 1979]. In such situations, measurements of hydraulic conductivity made in one
direction are of limited value when modeling fluid movement in another. When hydraulic conductivity is treated
as a scalar or a diagonalized matrix, which is usually the case, it is important that the fluid movement being
modeled is consistent with the direction in which the conductivity is determined.
All borehole methods measure properties of the formation immediately surrounding the well, and the
distance into the formation for which the measurement is valid is referred to as the radius of investigation.
Depending on the method, the radius of investigation can range from about 0.05 to 5 m and it is important to
ensure that mis zone is not disturbed significantly during drilling. Morin et al. (1988b) discuss the effects of
various drilling methods on the development of the disturbed zone.
AI-2 Straddle Packer Tests
One of the most common methods of determining the vertical distribution of horizontal conductivities
is to perform hydraulic testing over short intervals of a borehole using a straddle packer (Fig. AI-1).
There are several variations of straddle packer tests. For example, it is common to pump into or out
of a packer section at a constant rate while measuring head, or inject at a constant head while measuring flow.
Another method, called the multilevel slug test, is to change the head suddenly by adding or displacing a volume
of water, then recording head vs. time as the system returns to equilibrium.
In any case, these methods are accurate only if the packer is effective in hydraulically isolating a segment
of the borehole. If channels exist around the well screen, fluid will bypass the packer instead of flowing radially
into or out of the well as planned. Channels may be present in the structure of a well screen or caused by the
failure of the formation or backfill material to fill the annulus between the casing and the borehole wall. A
similar problem may occur if a gravel pack has a greater hydraulic conductivity than the formation. Although
expensive, the ideal well is constructed with short screened intervals that are isolated from one another by
grouting.
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If leakage around the packers exists, results obtained with a straddle packer test will indicate a hydraulic
conductivity that is erroneously high. To detect such leakage it is necessary to monitor the head in zones above
and below the packed off interval using a pressure transducer. However, if the transmissivity of these two zones
is significantly larger than that of the test zone, leakage around the straddle packer will not cause a detectable
change in head outside the packed off interval. To identify this problem, it is necessary to install a second set
of packers (Fig. AI-1). The hydraulic head in the segments of the well that are between the two sets of packers
will now be sensitive to leakage around the first set of packers.
If the hydraulic head in the segments between the two sets of packers is influenced significantly by
hydraulic testing, the straddle packer is not isolating the test segment of the well and the results will not be valid.
If this situation occurs, it is usually not possible to correct and the straddle packer method cannot be used. Four
packers and three transducers can be a cumbersome arrangement to operate in the field. Nevertheless, based on
comparisons with other test results, the straddle packer technique worked well at the Mobile site and, therefore,
was selected for detailed study.
The straddle packer method can be used to measure hydraulic conductivity over well segments mat range
from centimeters to hundreds of meters in length. However, the data must be analyzed carefully for small test
intervals because the flow can have significant vertical components (Dagan, 1978; Melville et al., 1989). The
calculated hydraulic conductivity reflects that of the formation material within 25 to 35 well radii for a typical
2 in (5 cm) well (Braester and Thunvik, 1984).
AI-3 Particle Size Methods
In a formation consisting of unconsolidated particles, the hydraulic conductivity is controlled, in part, by
the size and distribution of the pores. In an effort to quantify this, Fair and Hatch (1933) and Masch and Denny
(1966) have developed analytical approaches to estimate hydraulic conductivity from a description of the formation
grains. The model proposed by Fair and Hatch requires that the distribution of grain sizes be known while mat
of Masch and Denny requires the mean and standard deviation of the grain sizes.
Both of these methods suffer from several of the fundamental problems listed below.
1. Samples must be collected during drilling. This is not always done, hence for many if not most
existing wells, these methods cannot be used.
2. To determine grain-size statistics the formation must be sieved. Obviously, features such as
small scale layering, compaction, and sorting are destroyed by this process. If these features
exist, which is usually the case, the material to be evaluated will not be representative of the
formation.
3. Bias may be introduced by the sampling method. The method may be unable to collect large
material, such as gravel, or fine particles such as silt and clay.
4. The methods are limited to clean formations with sand size particles greater than 0.06 mm.
Formations that have silt or clay-size material cannot be accurately analyzed with these methods.
Because of these problems, grain size analyses are limited and are unlikely to be suitable in
characterizing aquifers for use in contaminant transport modeling.
48
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0
INFLATION
PRESSURE
trr
B
Figure AI-1. DetaUs of an Inflatable Straddle Packer Design.
49
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AI-4 Empirical Relationships Between Electrical and Hydraulic Conductivity
The electrical conductivity of a porous medium is a measure of its ability to conduct electrical current
In natural formations, electrical conduction occurs along two paths. The first is by ionic conduction, which is
controlled by the electrical conductivity and volume of the pore fluid and the manner in which the pores are
connected. The size of individual pores does not influence the electrical conductivity of die fluid. The second
is along the surface of the formation matrix which is a function of the type and distribution of the matrix
mineralogy, particularly with respect to the clay minerals. In clay free formations, with a constant pore fluid
electrical conductivity, the electrical conductivity is usually a function of porosity. Archie's rule is a frequently
used relationship relating electrical conductivity and porosity in clay-free formations (Keller and Frischknecht,
1966).
The hydraulic conductivity of a porous medium is a function of the size of the pores and the manner
in which they are connected. Two formations with the same porosity, but different pores sizes, will have the
same electrical conductivity but different hydraulic conductivity, so there is no clear relationship between electrical
and hydraulic properties. This is further complicated when anisotropic effects are considered because the axis
of anisotropy for electrical and hydraulic conductivity may not coincide. The presence of clays will further
complicate any relationship between electrical and hydraulic conductivity.
Despite these problems, there are many examples in the literature of empirical relationships between
electrical and hydraulic properties (Mazac et al., 1985; Kwader, 1985; Huntiey, 1986; Urish, 1981). These were
developed in clay free formations where electrical conduction by the matrix was not a significant factor. It is
also necessary for the formation to have a relationship between porosity and hydraulic conductivity and to have
a pore fluid of constant and known electrical conductivity. Depending on the formation and the methods used
to measure the properties, both positive and negative correlations between the two properties have been observed.
These empirical relationships are only applicable over limited areas of a specific formation. Such restrictions,
and the need to measure the hydraulic conductivities at numerous locations to define the relationship, severely
limit the utility of this approach. However, if a relationship can be defined, electrical measurements can be made
rapidly and a large number of hydraulic conductivity determinations can be made with little additional effort.
The radius of investigation of this method is dependent on the process used to determine electrical and
hydraulic conductivities. Hydraulic conductivities are usually determined by hydraulic testing and have a radius
of investigation of several meters. The radius of investigation of the electrical measurements is controlled by the
instrumentation and should be comparable to that of hydraulic measurements.
AI-5 Measurements Based on Natural Flow Through a Well
There are several techniques for determining the hydraulic conductivity distribution surrounding a well
by measuring the natural fluid velocity distribution through the welL These are illustrated in Figure AI-2 and
are most effective when the fluid velocity is horizontal. They differ according to how the velocity measurement
is made within the packed off section of the well These include heat-pulse devices for making the measurement
(Melville et al., 1985) as well as various types of point-dilution approaches (Drost et aL, 1968; McLinn and
Palmer, 1989; Taylor et al., 1989).
In the latter approach, a tracer is injected into the segment of the well of interest where it must be kept
well mixed. The tracer is removed from the segment by diffusion and advection of the fluid moving through
the well. This movement is horizontal as vertical fluid movement is blocked by packers. If the velocity is
high, the tracer concentration, which must be recorded, will decrease more rapidly than if the velocity is low.
Since the decay is exponential, the slope of the tracer decay curve on a semi-log plot is a function of the
horizontal fluid velocity.
A new type of point-dilution apparatus, based on an arrangement of dialysis cells, is illustrated in Figure
AI-3. Glass cylinders having selected types of semipermeable membranes as their ends are mounted along a
positioning rod. Each cell, which has a flexible rubber seal above and below, is filled with water depleted of
the isotope oxygen-18, i.e. the O18/O16 ratio is different for the water within the cell compared to the natural
groundwater (Alternatively, other tracers may be used.). The entire apparatus, which may contain 20 or more
50
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dialysis cells spaced at equal intervals along the rod, is lowered into the well and positioned within the screen.
After positioning, oxygen-18 begins to diffuse into each cell with the rate of diffusion depending on the flow
velocity in the vicinity of the cell. By measuring OI$/0W ratios in each cell before and after a test, die ground
water flow velocity can be calculated for each cell position. The calculation procedure is only moderately
involved as described in Ronen et al., 1986, where the technique was developed and applied in an unconfined
aquifer. The method was also applied at the Mobile site with some success. Once the cells and cell holders
are available in large quantities, many measurements can be made rather easily.
As the title of this section implies, natural flow methods result in a velocity measurement not a hydraulic
conductivity measurement If one assumes that the head gradient is predominantly in the horizontal direction,
constant with depth and with a constant porosity, K(z) will be proportional to the fluid velocity distribution v(z).
An approach that results in a mote direct calculation of K is described by Taylor et al., 1989.
All of the natural flow methods are relatively difficult to apply and the resulting data difficult to interpret.
Due to a variety of factors, a complex flow pattern develops around a well screen that is sensitive to near-hole
disturbances. Some methods require that die packed-off section be filled with glass beads, and it is difficult or
impossible to achieve the same bead packing in all the measurement sections.
AI-6 Single Well Electrical Tracer (SWET) Test
In the single well electrical tracer (SWET) method (Taylor et al., 1988), salt water is injected under
steady state conditions into a well. While injection of the tracer continues, the radius of invasion of the tracer
is determined with a borehole induction tool (Figure AI-4). By repeatedly measuring the depth of invasion at
different times, the rate of invasion can be determined. The hydraulic head, which is a measure of the driving
force required to inject the fluid, is also noted. The tracer will invade different intervals of the formation at
different rates depending on the hydraulic properties of each interval.
Since multiple induction logs are run, the rate of invasion can be determined at several different radii which
can be converted into a hydraulic conductivity log. A porosity log can also be calculated using a model of
formation electrical conductivity which accounts for variations in matrix conductivity and porosity. The SWET
test procedure was field-tested for the first time at the Mobile site during the summer of 1987.
As a SWET test continues, the hydraulic conductivities calculated ate representative of the formation over
an increasing radius up to the radius of sensitivity of the induction tool. At the Mobile site this was on the order
of 4 m, which is a relatively deep radius of investigation.
Since most wells have a disturbed zone around them, techniques having a shallow radius of investigation
will be inaccurate, but the SWET test minimizes these problems. Another advantage of the SWET test is that
the entire well is subjected to the same hydraulic head as opposed to the straddle packer where only a portion
of the well is pressurized and errors can result if there is leakage around the packer.
A disadvantage of the SWET test is that the method requires the careful injection of a large volume of
electrolyte which may not be allowed at some locations.
AI-7 Borehole Flowmeter Tests
The borehole flowmeter test is illustrated in Figure AI-S. A small pump is placed in a well and operated
at a constant flow rate, Q. After near steady-state behavior is obtained the flowmeter, which measures vertical
flow, is placed near the bottom of the well and a reading taken. The meter is then raised a few feet where
another reading is taken. This procedure continues until the meter is above the top of the screen where the
reading should equal Q, the steady state pumping rate as measured independently at the surface. As illustrated
in the lower portion of Figure AI-5, the result is a series of data points giving vertical discharge within the well
screen as a function of depth.
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Land
Groundwater
Flow
Surface
V
Flow Velocity
Measured
Here
Straddle
Packer system I I
1 '
AI-2. Schematic Diagram Illustrating a Natural Flow Field in the Vicinity of a Well.
52
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To The
I Surface
Well Screen
Positioning Rod
Flexible Seals
is Cell
Semipermeable
Membrane
arcy
Figure AI-3.
Geometry and Instrumentation Associated with the Dialysis Cell Method for
Measurement of Darcy Velocity.
53
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ELECTROMAGNETIC
CONDUCTIVITY
TEST
ELECTROLYTE INJECTION
LINE
TO LOGGER
ELECTROLYTE
FRONT
HIGH PERMEABILITY
ZONES
CONDUCTIVITY
PROBE
Figure AI-4.
Apparatus and Geometry Associated with the SWET Test
54
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OP-
PUMP
CAP ROCK
(QOISCHARGE RATE)
BOREHOLE FLOW
METER
ELEVAT!ON=Z
TO LOGGER (Q)
SURFACE
CASING
SCREEN
DATA
Q
Figure AI-5.
Apparatus and Geometry Associated with a Borehole Flowmeter Test
55
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The data analysis procedure is rather simple. The difference between two successive meter readings
yields the net flow entering the screen segment between the elevations where the readings were taken. This
information may be analyzed in several ways to obtain a K(z) value.
The flowmeter test suffers from the lack of readily available impeller meters designed for water well
applications. Also, other types of promising technologies for flowmeter applications, such as heat-pulse (Hess
and Paillet, 1989) and electromagnetic (Young and Waldrop, 1989) techniques, are not fully developed. However,
it does appear that some types of heat-pulse (Hess and Paillet, 1989) and electromagnetic (Young and Waldrop,
1989) water well flow meters will be available in the near future.
AI-8 The Role of Geophysical Logging
The more traditional geophysical logging methods such as gamma logs, electric logs of various types,
nuclear logs, etc., can be used to help identify the overall stratigraphy and geological setting of a site. They can
also provide information of a general nature concerning hydraulic conductivity distributions. Applicable techniques
are reviewed by Taylor (1989), while detailed descriptions of methods may be found in Keys and MacCary
(1971), and a bibliography of borehole geophysics as applied to ground-water hydrology has been developed by
Taylor and Dey (1985).
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REFERENCES
Bear, J. 1979. Hydraulics of Groundwater. McGraw-Hill, New York.
Boast, C.W., and D. Kirkham. 1971. Auger hole seepage theory. Soil Science Society of America Journal 35:
365-374.
Bouwer, H. and R.C. Rice. 1976. A slug test for determining hydraulic conductivity of unconfined aquifers with
completely or partially penetrating wells. Water Resources Research. 12:423-428.
Braester, C., and R. Thunvik. 1984. Determination of formation permeability by double-packer tests. Journal
of Hydrology. 72:375-389.
Bredehoeft, JD., and S.S. Papadopulos. 1980. A method for determining the hydraulic properties of tight
formations. Water Resources Research. 16:233-238.
Chapman, H.T., and A.E. Robinson. 1962. A thermal flowmeter for measuring velocity of flow in a well. U.S.
Geological Survey Water-Supply Paper, 1544-E, 12.
Cooper, H.H., J.D. Bredehoeft, and S.S. Papadopulos. 1967. Response of a finite diameter well to an
instantaneous charge of water. Water Resources Research. 3:263-269.
Cooper, H.H., and C.E. Jacob. 1946. A generalized graphical method for evaluating formation constants and
summarizing well-field history. Transactions American Geophysical Union. 27:526-534.
Dagan, G. 1978. A note on packer, slug, and recovery tests in unconfined aquifers. Water Resources Research.
14:929-934.
Davis, S.N., G.M. Thompson, H.W. Bentley, and G. Stiles. 1980. Groundwater tracers - a short review. Ground
Water. 18:14-23.
Drost, W., D. Klotz, A. Koch, H. Moser, F. Neumaier, and W. Rauert. 1968. Point dilution methods of
investigating groundwater flow by means of radioisotopes. Water Resources Research. 4:125-146.
Dudgeon, C.R., MJ. Green, and WJ. Smedmore. 1975. Heat-pulse flowmeter for boreholes: Medmenham,
Marlow, Bucks, England. Water Research Centre Technical Report TR-4, 69.
Fair, G.M., and LJP. Hatch. 1933. Fundamental factor governing the stream line flow of water through sands.
Journal American Water Works Association. 25:1551-1565.
Freeze, R.A., and J.A. Cherry. 1979. Groundwater. Prentice-Hall, Englewood Cliffs, New Jersey, 604.
Hada, S. 1977. Utilization and interpretation of micro flowmeter. Engineering Geology (Japan). 18:26-37.
Hess, A.E. 1982. A heat-pulse flowmeter for measuring low velocities in boreholes. U.S. Geological Survey
Open File Report 82-699:40 pp.
Hess, A.E. 1986. Identifying hydraulically conductive fractures with a slow-velocity borehole flowmeter.
Canadian Geotechnical Journal. 23:69-78.
Hess, A.E. 1988. Characterizing fractured hydrology using a sensitive borehole flowmeter with a wire-line
powered packer. International Conference on Fluid Flow in Fractured Rock, Proceedings, May, Atlanta, GA (in
press).
57
-------
Hess, A.E., and F.L. Paillet, 1989. Characterizing flow paths and permeability distribution in fractured rock
aquifers using a sensitive thermal borehole flowmeter. Proceedings of the Conference on New Field Techniques
for Quantifying the Physical and Chemical Properties of Heterogeneous Aquifers. Dallas, Texas.*
Hufschmied, P. 1983. Ermittlung der Durchlassigkeit von Lockergesteins- Grundwasserleitern, eine vergleichende
Untersuchung verschiedener Feldmethoden. Doctoral Dissertation No. 7397, ETH Zurich, Switzerland.
Huntley, D. 1986. Relations between permeability and electrical resistivity in granular aquifers. Ground Water.
24:466-474.
Hvorslev, HJ. 1951. Time lag and soil permeability in ground-water observations. Bulletin 36, Waterways
Experiment Station, Corps of Engineers, U.S. Army, Vicksburg, MS.
Javandel, I., and PA. Witherspoon. 1969. A method of analyzing transient fluid flow in multilayered aquifers.
Water Resources Research. 5:856-869.
Javandel, I., C. Doughty, and CJ7. Tsang. 1984. Groundwater Transport: Handbook of Mathematical Models.
American Geophysical Union, Washington, DC, 228 pp.
Keller, G.V., and F.C. Frischknecht. 1966. Electrical methods in geophysical prospecting. Pergamon Press, 519
pp.
Keys, W.S., and L.M. MacCary. 1971. Application of borehole geophysics to water resources investigations.
Techniques of water-resources investigations of the United States Geological Survey, NTIS, Washington, DC,
Book 2, ChapL El, 109-114.
Keys, W.S., and J.K. Sullivan. 1978. Role of borehole geophysics in defining the physical characteristics of the
Raft River geothermal reservoir. Idaho Geophysics. 44:1116-1141.
Kwader, T. 1985. Estimating aquifer permeability from formation resistivity factors. Ground Water. 23:762-
766.
Masch, F.D., and KJ. Denny. 1966. Grain size distribution and its effect on the permeability of unconsolidated
sands. Water Resources Research. 2:665-677.
Mazac, O., W.E. Kelly, and I. Landa. 1985. A hydrogeological model for relations between electrical and
hydraulic properties of aquifers. Journal of Hydrology. 79:1-19.
McLinn, E.L., and C.D. Palmer. 1989. Laboratory testing and comparison of specific conductance and electrical
resistivity borehole dilution devices. Proceedings, Conference of New Field Techniques for Quantifying the
Physical and Chemical Properties of Heterogeneous Aquifers. Dallas, Texas.
Melville, J.G., FJ. Molz, and O. Giiven. 1985. Laboratory investigation and analysis of a ground-water flow
meter. Ground Water. 23:486495.
Melville, J.G., FJ. Molz, O. Giiven and M.A. Widdowson. 1989. Multi-level slug tests with comparisons to
tracer data. Ground Water, submitted for publication.
Molz, FJ., O. Giiven, J.G. Melville, R.D. Crocker, and K.T. Matteson. 1986a. Performance, analysis, and
simulation of a two-well tracer test at the Mobile site. Water Resources Research. 22:1031-1037.
Molz, FJ., O. Giiven, J.G. Melville, and J.F. Keely. 1986b. Performance and analysis of aquifer tracer tests
with implications for contaminant transport modeling. USEPA, R.S. Kerr Environmental Research Laboratory,
Ada, OK 74820, EPA/600/2-86/062.
Molz, FJ., O. Giiven, J.G. Melville, J.S. Nohrstedt, and J.K. Overholtzer. 1988. Forced gradient tracer tests and
inferred hydraulic conductivity distributions at the Mobile site. Ground Water, 26:570-579.
58
-------
Molz, FJ., R.H. Morin, AE. Hess, J.G. Melville, and O. GQven. 1989a. The impeller meter for measuring
aquifer penneability variations: evaluation and comparison with other tests. Water Resources Research. 25:1677-
1683.
Molz, FJ., O. Guven, J.G. Melville, and C. Cardone. 1989b. Hydraulic conductivity measurement at different
scales and contaminant transport modeling. In: Dynamics of Fluids in Hierarchical Porous Media, edited by J.H.
Cushman. New York, Academic Press, in press.
Morin, RJEL, AJE. Hess, and Fi. Paillet. 1988a. Determining me distribution of hydraulic conductivity in a
fractured limestone aquifer by simultaneous injection and geophysical logging. Ground Water. 26:587-595.
Morin, R.H., D.R. LeBlanc, and W.E. Teasdale. 1988b. A statistical evaluation of formation disturbance
produced by well-casing installation methods. Ground Water. 26:207-217.
Morrow, TJ3., and SJ. Kline. 1971. The evaluation and use of hot-wire and hot-film anemometers in liquids.
Stanford University, Department of Mechanical Engineering, Thermosciences Division, Report MD-25, 187 pp.
Paillet, F.L., W.S. Keys, and A£. Hess. 1985. Effects of lithology on televiewer-log quality and fracture
interpretation. Society of Professional Well Log Analysis Logging Symposium, 26th, Dallas, TX, Transactions,
JJJ J.-JJJ jij.
Paillet, FJL., A.E. Hess, CM. Cheng, and E.L. Hardin. 1987. Characterization of fracture permeability with high-
resolution vertical flow measurements during borehole pumping. Ground Water. 25:28-40.
Paillet, F.L., and A.E. Hess. 1987. Geophysical well log analysis of fractured granitic rocks at Atikokan,
Ontario, Canada. U.S. Geological Survey Water Resources Investigations Report 87-4154, 36 pp.
Papadopulos, S.S., J.D. Bredehoeft, and H.H. Cooper, Jr. 1973. On the analysis of "slug test" data. Water
Resources Research. 9:1087-1089.
Parr, A.D., FJ. Molz, and J.G. Melville. 1983. Field determination of aquifer thermal energy storage parameters
Ground Water. 21:22-35.
Rehfeldt, KJ*., P. Hufschmied, L.W. Gelhar. and M.E. Schaefer. 1989. The borehole flowmeter technique for
measuring hydraulic conductivity variability. Report #EN-6511, Electric Power Research Institute, 3412 Hillview
Ave., Palo Alto, CA.
Ronen, D., M. Magaritz, N. Paldor, and Y. BackmaL 1986. The behavior of groundwater in the vicinity of the
watertable evidenced by specific discharge profiles. Water Resources Research. 22:1217-1224.
Schimschal, U. 1981. Flowmeter Analysis at Raft River, Idaho. Ground Water. 19:93-97.
Stallman, R.W. 1971. Aquifer-test design, observation and data analysis, Book 3, Chapter Bl of Techniques of
Water-Resources Investigations of the United States Geological Survey.
Taylor, T.A., and J.A. Dey. 1985. Bibliography of borehole geophysics as applied to ground-water hydrology.
Geological Survey Circular 926, #1985-576-049/20,029, U.S. Government Printing Office, Washington, DC.
Taylor, K., FJ. Molz, and J. Hayworth. 1988. A single well electrical tracer test for the determination of
hydraulic conductivity and porosity as a function of depth. Proceedings of the Second National Outdoor Action
Conference, Las Vegas, NV. May 23-26.
Taylor, K. 1989. Review of borehole methods for characterizing the heterogeneity, of aquifer hydraulic
properties. Proceedings of the Conference on New Field Techniques for Quantifying the Physical and Chemical
Properties of Heterogeneous Aquifers. Dallas, Texas.*
59
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Taylor, K., S.W. Wheatcraft, J. Hess, J.S. Hayworth, and FJ. Molz. 1989. Evaluation of methods for
determining the vertical distribution of hydraulic conductivity. Ground Water. 27:88-98.
Urish, D.W. 1981. Electrical resistivity-hydraulic conductivity relationships in glacial outwash aquifers. Water
Resources Research. 17:401-408.
U.S. Bureau of Reclamation. 1977. Groundwater Manual. Water resources technical publication, # 480.
Widdowson, MA., FJ. Molz, and J.G. Melville. 1989. Development and application of a model for simulating
microbial gorwth dynamics coupled to nutrient and oxygen transport in porous media. Proceedings, Solving
Ground Water Problems with Models, VoL 1, 28-51. National Water Well Assoc., Columbus, OH.
Young, S.C., and WJR. Waldrop. 1989. An electromagnetic borehole flowmeter for measuring hydraulic
conductivity variability. Proceedings of the Conference on New Field Techniques for Quantifying the Physical
and Chemical Properties of Heterogeneous Aquifers. Dallas, Texas.*
Zemanek, J., EJj. Glenn, LJ. Norton, and R.L. CaldwelL 1970. Formation evaluation by inspection with the
borehole televiewer. Geophysics. 35:254-269.
*Proceedings available from: Water Resources Research Institute, 202 Hargis Hall, Auburn University, AL 36849
U.S. GOVERNMENT PRINTING OFFICE 1990/748-159/00438
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