&EPA
United Stat.t
Environmental Protection
Agency
Environment*! Monitoring
Sveterra Laboratory
P.O. Box 93478
Lee VegeeNV 89193-3478
EPA/HXV4-90/029
October 1980
Re«eefch and D«v»lopm»nt
Evaluation of Selected
Borehole Geophysical
Methods for Hazardous
Waste Site Investigations
and Monitoring
EJBD
ARCHIVE
EPA
600-
4-
90-
029
'//Si
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M- US EPA
^ 6 - Headquarters and Chemical Libraries
EPA West Bldg Room 3340
Mailcode 3404T
1301 Constitution Ave NW
Washington DC 20004
202-566-0556
- FINAL REPORT -
EVALUATION OF SELECTED BOREHOLE GEOPHYSICAL METHODS
FOR HAZARDOUS WASTE SITE INVESTIGATIONS AND MONITORING
by
Kendnck Taylor
John Hess
Steve Wheatcraft
t
Water Resources Center
Desert Research Institute
Las Vegas and Reno, Nevada 89S06
Cooperative Agreement No. CR812713
Repository Material
Permanent Collection
Aldo Mazzella
Environmental Monitoring Systems Laboratory
Las Vegas, NV 89193-3478
ENVIRONMENTAL MONITORING SYSTEMS LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
LAS VEGAS, NEVADA 89193-3478
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NOTICE
The information in this document has been funded wholly or in part by the United States Environmen-
tal Protection Agency under Cooperative Agreement #CR812713 to the Desert Research Institute, Universi-
ty of Nevada System. It has been subject to the Agency's peer and administrative review, and it has been
approved for publication as an EPA document. Mendon of trade names or commercial products does not
constitute endorsement or recommendation for use.
ABSTRACT
Borehole geophysical methods can be used to provide valuable information about the hydrogeology of
hazardous waste sites. This information enables remedial action programs to be designed in a more cost and
time efficient manner. Borehole geophysical methods lend themselves to addressing two classes of problems
which were addressed in this project: 1) characterizing the hydraulic properties of the subsurface; and 2)
locating electrically anomalous contaminants. Three methods were tried to determine the vertical distribu-
tion of hydraulic conductivity with depth: 1) Stoneley wave attenuation: 2) a method based on natural flow
through a well; and 3) a single-well electrical tracer test. Only the single-well electrical tracer-test method
proved effective in the unconsolidated formations typical of hazardous waste sites. Contaminants that alter
the electrical conductivity of the formation can be detected with electrical conducuvity logs, however, the
influence of clays on the logs needs to be taken into consideration during the interpretation process.
This report $as submitted in fulfillment of Cooperative Agreement No. CR812713 by Desert Research
Institute. Water Resources' Center under the partial sponsorship of the U.S. Environmental Protection
Agency.
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CONTENTS
ABSTRACT
M
FIGURES
TABLES ... u,
ACKNOWLEDGMENTS
1. INTRODUCTION ,
2. METHODS TO DETERMINE FORMATION HYDRAULIC PROPERTIES 2
Background 2
Sonic Methods 2
Overview - Stoneiey Wave Attenuation 4
Previous Work - Stoneiey Wave Attenuation 4
Field Evaluation - Stoneiey Wave Attenuation 5
Discussion - Stoneiey Wave Attenuation 8
Overview - Natural Flow Methods 5
Theoretical Development '. . . 3
Sensitivity of Hydraulic Conductivity Equations to Kr II
Measurement of Thermal Pulse Advective Velocity in a Saturated
Porous Medium ! 4
Modified Thermal Flowmeter Experiments 16
Modified Borehole-Dilution Technique for Measuring Flow Velocity
Through Porous Media 18
Factors That Influence Pore-Water Flow Within Packed Borehole
Measuring Volume ? 1
Borehole Packer Porous Materials 22
Flowchamber Construction and Characteristics . .23
Vormal and Modified Borehole-Dilution Experiments ' 25
Experimental Apparatus 25
Discussion - Natural Flow Methods 35
Single-Well Electrical Tracer (SWET) Method 38
Field Application 38
Theory of Analysis 39
Assumptions 39
Porosity Calculation 41
Calculation of Radius of Invasion ... ... -12
in
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Calculation of Hydraulic Conductivity . . 43
Checks on the Analysis Method 44
Discussion of Results 45
Well E-3 '.'.'.'."".'.'.. .... " 45
Well E-6 45
Well E-7 '..'..'..''. '..50
General Comments - Single-Well Electrical Tracer Method 50
3. METHODS TO LOCATE CONTAMINANTS ... 5!
Background 5 j
Evaluation of a Slim Hole Induction Logger 51
Background < 1
Theory of Operation 52
Calibration 52
Time Constant 53
Temperature Effects 53
Vertical Response 55
Borehole Influence 55
Comparison of Units . . 57
Discussion - Evaluation of Induction Tool 58
_
4. APPLICATION TO DETECTION OF CONTAMINANTS 63
Background 53
Method 1 - Borehole Geophysical Logging 63
Method 2 - Pumping of Discrete Intervals 67
Method 3 - Dilution Sampling 69
5. INDUCED POLARIZATION 72
Background 72
Instrumentation 73
Field Effort 73
Discussion ' 73
6. CONCLUSIONS 79
Notice 79
REFERENCES so
IV
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FIGURES
1. Sonic Logging Tool 3
2. Sonic Waveform in 10-cm Diameter Hole 6
3 Sonic Waveform in 15-cm Diameter Hole 6
4. Full Waveform Log in 15-cm Diameter Hole 7
5. Response of a Uniform Flow Field to the Presence of a Permeable Cylinder.
Shown is Map View, Flow in X-Direction. Cylinder Radius = rp 10
6. Sensitivity of Hydraulic Conductivity Equations to the Parameter Kr. The
Parameter can be thought of as Dimensionless Borehole Pore- Water Speed. ... .. 13
7. K-V Associates Thermal Flowmeter Downhole Probe Geometry 15
8. Thermal Flowmeter Experimental Configuration 17
9 Results of Thermal Flowmeter Experiments Showing Conductive Heat
Breakthrough Curves at Varied Flow Velocities, with Predicted Advective
Heat-Pulse Arrival Times Indicated . ... . 13
10. Explanation of Modified Borehole-Dilution Geometry 20
11 Idealized Diagram of the Aquifer-Simulating Flowchamber .... . 24
12. Diagram of Laboratory Apparatus. Showing Location of Mixing Chamber . . .... 26
13. Diagram of Downhole Tool used in Hydraulic Conductivity Experiments 27
14. Results of Repeatability Experiments. Laboratory Apparatus Sensitivity to
Varied Flowchamber Pore-Water Velocity is Clearly Illustrated 28
15. Theoretical Output of Laboratory Apparatus for Flowchamber Pore-Water
Velocity = 3.72 m/day . . 29
16. Theoretical and Experimental Response for the First Vaned-Kr Experiments,
Plotted at Same Scale for Comparison 30
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17. Theoretical Versus Experimental Change in Semiloganthmic Slope as a Function
of Kr, for the First Vaned-Kr Experiments. Note the Lack of Systematic Change
in the Experimental Results 31
18 Least-Squares Plot of Second Vaned-K, Experimental Results. Flowchamber
Pore-Water Velocity = 1 84 m/day . . 33
19 Theoretical Versus Experimental Change in Semiloganthmic Slope as a Function
of Kr. for the Second Vaned-Kr Experiments. Apparent Random Fluctuation in
Experimental Results is Illustrated 34
20. Idealized Representation of Flow Field Distribution Due to Packed Borehole Section 35
21. Idealized Representation of Flow Field after Increasing Packed Borehole Section. 36
22. Theoretical Versus Experimental Change in Semiloganthmic Slope as a Function
of Kr. for the Third Vaned-Kr Experiments Apparent Random Fluctuation in
Experimental Results is Illustrated . 37
23. Experimental Setup for Single-Well Electrical Tracer Test 40
24. Radial Response of EM-39 43
25. Induction Logs of Well E-3 at Different Times After Injection 46
26. Induction Logs of Well E-6 at Different Times After Injection . . 46
27. Porosity Log of Well E-6 ... 47
28. Matrix Conductivity and Natural Gamma Log of Well E-6. . . . 47
29 H\draulic Conductivity Logs of Well E-6 . ... 49
30. Hydraulic Conductivity Logs and Packer Slug Test Results in Well E-6. 49
31. Induction Logs of Well E-7 ... . 50
32 Calibration of EM-39 . . 53
33. Logging Speed-Induced Shifts on Induction Logs 54
34. Vertical Shift as a Function of Logging Speed for EM-39 55
35 Temperature Drift of EM-39 56
4
36. Vertical Averaging Function of EM-39 57
37. Response of EM-39 to Abrupt Contact. . 53
3S Response of EM-39 to Layers of Varying Thickness. Layer Thickness in Meiers
is Indicated . . 59
39. Response Versus La\er Thickness for EM-39 . . . 60
VI
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40. Example of Ambiguous Interpretations of Induction Logs . f>\
41. Comparison of Logs from Two Different EM-39 Units . . . 52
42. Induction Logs at Henderson, Nevada 55
43 Natural Gamma Logs at Henderson, Nevada 66
44 Experimental Setup for Tracer Test gg
45 Tracer Concentration Versus Time 69
46. Dilution Curves Versus Time for Various Depths for Dilution Sampling Method 70
47. Comparison of Electrical Conductivity of the Pore Fluid and Formation in Well 635 . . 71
48. Log Suite for Well 633A 75
49 Log Suite for Well 633D 76
50. Induction Logs Before and After Injection 77
51. Induced Polarization Logs Before and After Injection 77
TABLES
1. Theoretical and Experimental Glass Bead Hydraulic Conductivity Values . . . . .23
2. Induced Polarization Time Windows . . 74
Vll
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ACKNOWLEDGMENTS
Special thanks goes to Les McMillion who saw the need for this project and took the initiative to start
it. Joel Hayworth, Tom Morris, and Scott Lewis also deserve recognition for the long hours of field work.
Thanks also goes to Barbara Nauroth and Deborah Wilson who contributed their electronic publishing skills.
vin
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SECTION 1
INTRODUCTION
Ground-water contamination is a serious and widespread environmental problem. As such, the
United States Environmental Protection Agency (EPA) has identified a need to develop advanced methods
to detect and remediate ground-water contamination. Borehole geophysical methods hold considerable
promise for providing needed information about the location of contaminants and the properties of the.
subsurface through which the contaminants move. The purpose of this report is to present the results of a
cooperative agreement between the EPA and the Desert Research Institute to evaluate borehole geophysical
methods that can be used to obtain needed information about the subsurface. Development of these meth--
ods makes possible a more detailed characterization of the subsurface which permits remedial action pro-
grams to be conducted in a more efficient manner.
Borehole geophysical methods are well suited for two applications of interest in ground-water contami-
nate investigations which were addressed in this project: 1) detection of contaminants which alter the electri-
cal properties of the ground water; and 2) characterization of formation hydraulic properties which control
the movement of the pore fluids. Although borehole geophysical methods have been used by the petroleum
industry for many decades, their application in shallow ground-water monitoring investigations of small sites
is not as well developed. Borehole geophysical logging operations for ground-water contamination investiga-
tions are commonly conducted in conditions that are sufficiently different from what is encountered in the
petroleum industry, that many of the borehole geophysical methods developed by the petroleum industry
need to be modified for use in ground-water contamination investigations. For example, in contrast to
petroleum investigations, ground-water contamination investigations are frequently in unconsolidated and
shallow formations. These formations tend to collapse quickly, requiring that the borehole be cased immedi-
ately after drilling. In addition, the study sites frequently have an abundance of existing cased boreholes in
which it is desirable to conduct logging operations. Legal restriction severely restricts the use of radioactive
sources in water wells. Hence, non-radioactive borehole geophysical methods that can be used in cased
wells in unconsolidated formations are of particular interest in ground-water contamination investigations
and were the focus of this cooperative agreement.
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SECTION 2
METHODS TO DETERMINE FORMATION HYDRAULIC PROPERTIES
BACKGROUND
In ihe past, it was usually sufficient to consider that the hydraulic properties of a formation were
uniform. This assumption is usually acceptable when dealing with ground-water quantity issues in porous
media. However, in ground-water contamination issues, accurate transport models must take into account
the spatial variability of the hydraulic properties of ihe formation. As more accurate transport models are
developed, it has become clear that a major stumbling block in the development of advanced models is the
difficulty of obtaining information on the spatial variability of hydraulic conductivity and porosity
Hydraulic conductivity is a property of a porous medium which controls the rate at which water flows
through the porous medium under the influence of a given driving force. Determining the spatial variability
of hydraulic conductivity in unconsolidated formations is particularly difficult. Because it varies by more
than ten orders of magnitude in natural formations, it is the property of a formation that has the most impact
on the transport of fluids through the formation. Although many methods exist to determine the hydraulic
conductivity of a formation, they all have significant limitations. Porosity is an important hydraulic parame-
ter because it also controls the movement of fluid through the subsurface, although to a lesser degree than
hydraulic conductivity, and because it is a measure of the fluid stored in a saturated formation.
An overview of borehole methods and their associated limitations, available for determining the spatial
variability of formation hydraulic properties, was presented by Taylor (1989). In the course of this coopera-
tive agreement, two new methods of determining the spatial variability of hydraulic conductivity were consid-
ered and an effort was made to adapt an existing method to unconsolidated environments. One new method
to determine the spatial variability of porosity was also developed. Because of severe legal restrictions on the
use of active source logging tools in water wells, methods that utilize a radioactive source were not consid-
ered in the course of this study.
SONIC METHODS
Sonic methods relate the way induced acoustic waves propagate in the formation to the hydraulic
properties of the formation. Typically, sonic methods utilize a downhole tool having a desien shown in
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Figure 1. The tool has an acoustic source, which is usually a piezoelectric cylinder, and two receivers. When
the transmitter pulses, numerous different types of acoustic waves are generated. The optimal spacing be-
tween the source and between the receivers, and the frequency of the source, is dependent on the objective
of the survey being conducted.
Sonic velocity logging is commonly used in the petroleum industry to determine the porosity of consoli-
dated formations. The velocity of a refracted compressional wave is determined by measuring the time the
compressional wave requires to travel between the two receivers. To obtain the desired vertical resolution,
the method is usually performed with an acoustic source with a frequency of 20 kHz and a source and
receiver spacing of less than 1 m. Wyllie et al. (1962) has shown that the compressional wave velocity in the
formation is a function of the total porosity and the compressional wave velocity in the fluid and formation
matrix. If the lithology and the type of pore fluid are known, the compressional wave velocity in the fluid and
TRANSMITTER
RECEIVERS
FORMATION
., STONELEY WAVE PATH
REFRACTED
COMPRESSIONAL
WAVE PATH
FORMATION
FIGURE 1. Sonic Logging Tool.
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formation matrix can be adequately estimated and the total porosity determined. In unconsolidated forma-
tions, the congressional wave velocity in the matrix cannot be accurately estimated, which restricts this
method to consolidated formations. Another acoustic method which is under development by industry is the
Stoneley wave attenuation method. The applicability of this method to shallow unconsolidated formations
was investigated in this cooperative agreement.
Overview - Stoneiey Wave Attenuation
When an acoustical source emus a pulse in a fluid-filled borehole, several types of waves are pro-
duced. One of these, the Stoneley wave, is a guided wave that exists only within the borehole and along the
borehole-formation interface. Based on the theoretical model of Biot (1956a and 1956b). Rosenbaum
(1974) argued that the attenuation of the Stoneley wave is dependent on the hydraulic conductivity of the
adjacent formation. This has been verified in the field by numerous researchers: among them are Schmitt et
al. (1988); Cheng et al. (1987); Williams et al. (1984); Hardm et al (1987); and Burns et al. (1988) A
conceptual model of the phenomenon is that as the hydraulic conductivity of the formation increases, more
of the guided energy of the wave is lost from the borehole into the formation. This attenuates the Stoneley
wave and results in a decreased amplitude of the wave at nearby receivers. Attenuation of the Stoneley wavet
is usually quantified by a measure of the average amplitude or energy in a time window that contains the
wave.
Previous Work - Stoneley Wave Attenuation
The concept of determining hydraulic conductivity with acoustical logging methods is appealing be-
cause of the minimal logistics. In the references cued above, a full waveform log with the appropriate acqui-
sition parameters was run and the data were processed to obtain a log of hydraulic conductivity. The hydrau-
lic conductivity logs were usually qualitative in nature. It was not necessary to inject fluids or wait for natural
fluid movement to occur. Core samples were used to verify the results of the logging, but were not necessary
for the interpretation of the logs. Although the method has not matured to the extent that it is a standard
method in the petroleum industry, it is attracting significant attention. All work to date has been conducted
in open boreholes in consolidated formations with hydraulic conductivities less than 2 5 m/d. The adapta-
tion of the method to screened wells in unconsolidated formations, which generally have a higher hydraulic
conductivity, would be a significant development for shallow ground-water investigations. Analysis of, the
influence of a mudcake on the borehole wall (Schmitt et al.. 1988) suggests that the method may work in
screened wells.
T\pically, a sonic logging sonde similar to the one in Figure 1 is used. While the logger is raised in the
well, the transmitter produces an acoustic pulse. This generates several forms of propagating waves, one of
which is the Stoneley wave. The waves are detected at the two receivers. The separation of the receivers and
transmitter is adjustable. To provide better separation between the arrival times of the different waves, the
spacmgs are usually larger when the slower traveling Stoneley wave studies are being conducted than when
the more common faster compressional wave is being logged. The frequency content of the transmuted pulse
is important. At frequencies above a critical frequency, the Stoneley wave is not excited (Schmitt et al..
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1988) because the higher frequency wave will not resonate. Most commercially available instruments oper-
ate in the 20 to 30 kHz range. To excite the Stoneley wave, m consolidated formations, a transmitter
frequency less than 10 kHz is usually required. The critical frequency, though, is a function of formation and
fluid properties. Unfortunately, tools well suited for Stoneley wave studies are not commercially available.
This study was conducted to see how well commercially available sonic logging equipment would perform in
unconsolidated material.
Field Evaluation - Stoneley Wave Attenuation
A site near Mobile. Alabama, was chosen to investigate the influence of changes in hydraulic conduc-
tivity on Stoneley waves. The sue consists of Quaternary sands and clays. It has been used extensively for
large-scale tracer tests (Molz et al.. 1986a. 1986b. 1988) and testing of borehole methods for the determi-
nation of the spatial variability of hydraulic conductivity (Taylor et al., 1988; Molz et al., 1988). The major-
ity of these studies have been conducted in an aquifer located at a depth of 40 to 60 m. This unit has an
average porosity of 35 percent and an average hydraulic conductivity of 54 m/d (Molz et al., 1986a). Wells
are available m this interval that are completed with either a 10-cm PVC or 15-cm steel screen. Both types
of wells were drilled with the mud rotary method. The acoustic logging tool used in the study had a transmit-'"
ter frequency of 29 kHz. The distance from the transmitter to the closest receiver was selectable to either
0.91 or 3.57 m. The distance between the receivers was 0.3 m.
Figure 2 shows the waveform in a 10-cm well at a distance of 3.57 and 3.87 m from the source. At
these distances, the arrival time of the Stoneley wave is well separated from the compressional wave. The
relative amplitude of the two'arnvals is not meaningful in the plot because of different gams. The Stoneley
wave should be propagating with a velocity less than the velocity of a pressure wave in the fluid. Since the
well fluid is fresh water, this velocity is estimated to be 1.540 m/s. The wave should also be a sinusoidal
packet. The pulse in Figure 2 has a velocity of 1.720 m/s and is believed to'be a refracted pressure wave that
is observed through the well screen. Results are similar for all the 10-cm wells with either a 0 91 or 3.57 m
receiver-transmitter spacing. The Stoneley wave was poorly excited in the 10-cm diameter wells If a logging
tool with a lower pulse frequency were available, it might be possible to excite the Stoneley wave m these
holes.
Figure 3 shows the waveform in a 15-cm diameter well also at a distance of 3.57 and 3.87 m. Both the
velocity (1.493 m/s) and the shape of the wavelet are consistent with a Stoneley wave and the wave associ-
ated with the leaky P-mode. The leaky P-mode is a trapped compressional normal mode, the first energy of
which travels at the velocity of a compressional wave in the fluid. Hence, the velocity of the leaky P-mode is
not a function of the formation. Because the borehole fluid properties are constant as a function of depth.
the velocity of the leaky P-mode should also be constant as a function of depth. This is in contrast to the
Stoneley wave velocity, which is a function of formation properties and. hence, changes as a function of
depth.
Figure 4 shows the waveform logs of a 15-cm diameter well. The constant arrival time indicates the
velocity of the wave is a constant with respect to depth. This indicates that the observed wave is the leaky
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T-R SEPARATION 3.57 M
TIME (mS)
T-R SEPARATION 3.88 M
2.0
2.2
2.4
2.6
2.8
3.0
WELL DIAMETER 10 cm
FIGURE 2. Sonic Waveform in 10-cm Diameter Hole.
T-R SEPARATION 3.57 M
T-R SEPARATION 3.88 M
TIME (mS)
2.1
2.3
2.5
2.7
2.9
3.1
WELL DIAMETER 15cm
FIGURE 3. Sonic Waveform in 15-cm Diameter Hole.
6
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40
WELL 12
T-R SEPARATION 3.57M
TIME (mS)
I I ! |_
54-
FIGURE 4. Full Waveform Log in 15-cm Diameter Hole.
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P-mode. Additionally, the amplitude of the leaky P-mode should be larger in large-diameter wells than in
smaller-diameter wells; for Stoneley waves, the opposite is true (Paillet. 1988). Because this wave has a
larger amplitude in the larger well, it also indicates that the observed wave is the leaky P-mode. The fre-
quency of the sonic tool (29 kHz) is apparently too high to excite the Stoneley wave in this unconsolidated
formation. For the Stoneley wave attenuation method to be effective in soft formations, a lower frequency
sonic tool must be constructed.
Discussion - Stoneley Wave Attenuation
The results suggest that it is not possible to determine the hydraulic conductivity of unconsolidated
formations with Stoneley wave attenuation techniques in screened wells with commercially available equip-
ment. If further work is conducted, a transmitter with a lower frequency should be built. Numerical model-
ing will be required to determine what the optimal frequency is for a given set of field conditions. Even with a
low frequency tool, with a transmitter pulse frequency of 5 kHz. the radius of investigation is not likely 10
exceed 0.3 m. The issue of the influence of a well screen needs to be addressed
OVERVIEW - NATURAL FLOW METHODS
It is now widely recognized that in most field situations, the hydrodynamic dispersion of solutes is
insignificant compared to the dispersion caused by differential advection (Guven et al.. 1985; Sudicky et al ,
1985; Smith and Schwartz. 1980; Pickens and Gnsak, 1981). Hydrodynamic dispersion is caused by solute
velocity fluctuations at the microscopic level owing to the irregular geometry of the void space of the porous
medium. Differential advection is dispersion that occurs at the macroscopic level owing to the heterogeneity
of the aquifer hydraulic conductivity. As a result, it is very important to have a large amount of information
on the spatial distribution of hydraulic conductivity.
\Vheatcraft and Wmterberg (1985) developed solutions for flow around and through a cylinder of
different permeability from the surrounding medium. Wheatcraft et al. (1986) used these solutions 10
develop a technique that allows the direct measurement of both the ground-water velocity (magnitude and
direction) and the hydraulic conductivity as a function of depth in a borehole. The technique relies upon
obtaining accurate information from a borehole thermal flowmeter or a borehole point-dilution instrument.
The overall goal of this study was to determine the feasibility of using these flowmeter techniques in conjunc-
tion with the solution of Wheatcraft and Wmterberg (1985) to directly obtain velocity and hydraulic conduc-
tivity information. First, the theoretical work is summarized, and then laboratory experiments with the
thermal flowmeter and the borehole point-dilution techniques are summarized.
THEORETICAL DEVELOPMENT
The approach of this method is to obtain an accurate measurement of the horizontal pore-water
velocity through a section of a cylindrical borehole packed with a porous material of known hydraulic con-
ductivity; then the hydraulic conductivity of the aquifer material surrounding the borehole can be deter-
mined, as well as (in some cases) the ambient ground-water flow rate and direction.
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Consider a saturated, homogeneous and isotropic aquifer in which a steady-state, lateral flow field
exists. It is assumed that the flow field obeys the two-dimensional Laplace Equation and that How within the
aquifer is uniform. Embedded within this aquifer is a permeable cylinder of hydraulic conductivity Kp which
differs from the aquifer hydraulic conductivity^. The condition of a homogeneous, isotropic aquifer exhib-
iting Darcian flow requires that all perturbations experienced by the flow field be due to the presence of the
permeable cylinder. For a cylinder which is more permeable than the surrounding aquifer, the flow field is
disrupted in such a way that fluid preferentially moves into the cylinder, increasing the pore-water velocity
within the cylinder relative to the aquifer. Conversely, for a cylinder which is less permeable than the sur-
rounding aquifer, the flow field is disrupted such that fluid tends to move around the cylinder, decreasing the
pore-water velocity within the cylinder relative to the aquifer. These situations are shown in Figure 5. For a
cylinder with hydraulic conductivity equal to that of the aquifer, the flow field remains undisturbed.
The response of the flow field to the presence of the permeable cylinder has been examined theoreti-
cally by Wheaicraft and Wmterberg (1985). The solution, detailed in Wheatcraft et al. (1986), is in terms of
complex stream functions. The important equations for this study are the total flow through the cylinder
n
Qf
where
Qp = volumetric discharge per unit length through the permeable borehole packer (L3/T)
la = Va^a = aquifer specific discharge (L2/T)
/c,
rp = radius of cylinder
Qp represents the volumetric discharge per unit length through the permeable cylinder, and can also be
written as the product of the cylinder diameter and the cylinder effective pore-water velocity
QP = ^P IP (2)
where
qp = vpnp = borehole packer specific discharge (L2/T)
np = borehole packer porosity
Setting Eqs. (1) and (2) equal and solving for qa gives
+ K.~\
(3)
< |_ "r J
which can also be written
The significance of Eq. (4) becomes apparent when applied to a particular problem. If it is assumed
that a cylindrical borehole, completed within a porous aquifer exhibiting Darcian flow and packed with a
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3 2 1
UNIFORM FLOW FIELDS
-1
-3
FIGURE 5. Response of a Uniform Flow Field to the Presence of a Permeable Cylinder.
Shown is a Map View, Flow in X-Direction. Cylinder Radius = rD
(modified after Wheatcraft et al.. 1986).
10
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material of known porosity and hydraulic conductivity approximates the conditions that validate Eq. (4),
then it is theoretically possible to determine the aquifer specific discharge qa and hydraulic conductivity Ka
by measuring the horizontal pore-water velocity through the packed borehole Vp. Application of this tech-
nique requires measurement of borehole pore-water velocity through two different borehole packing materi-
als. If Kp, is the hydraulic conductivity of the borehole packing material through which a specific discharge
of qp, is measured, and likewise Kp2, and qp2 are the same parameters for a different borehole packing
material, then using Eq. (4)
K.
pi
(5)
and
/C. + /C,;
If we divide both sides of Eqs. (5) and (6) by qp2 and let
(6)
if _
~
we can then equate Eqs. (5) and (6)
K,
+ 1
Solving for Ka, we have
= K,,
(7)
Hence, by making two independent measurements of the pore-water velocity through a borehole packed
with two different porous materials, each of known hydraulic conductivity, it is theoretically possible to
determine the hydraulic conductivity of the aquifer material directly surrounding the borehole
SENSITIVITY OF HYDRAULIC CONDUCTIVITY EQUATIONS TO Kr
It is important to understand the sensitivity of the equations developed in the previous section to the
value of the cylinder-aquifer hydraulic conductivity ratio Kr. Rearranging Eq. (3), let e be a dimensionless
constant such that
11
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K-
I + K,) W
The constant E can be thought of as a dimensionless borehole pore-water velocity. If the borehole is packed
with a porous material of zero permeability, then
lun e = 0
and
1r - 0
Similarly, if a borehole is packed with a porous material of "infinite" permeability (that is, an open
borehole), then
lun c = 2
which yields
1f = 2 qa (9)
This result demonstrates that the maximum pore-water velocity through a borehole packed with a porous
material of hydraulic conductivity Kp. embedded in a porous aquifer of hydraulic conductivity Ka (with
pore-water flow obeying Darcy's Law), is twice the aquifer pore-water velocity.
Note that calculation of Ka m Eq. (7) depends on two measurements of qp using two different values of
Kp. It is therefore important to examine how rapidly qp changes as a function of Kp. We can do this by
differentiating Eq. (8) with respect to Kr. This tells us how qp changes as a function of Kr. Differentiating Eq
(8) with respect to Kr, we obtain
de_ = 2 2Kr
dK,
Figure 6 is a graph of and d e.ldKT as a function of Kr. The curve representing E clearly demonstrates the
asymptotic nature of e. while the curve representing de.ldKr demonstrates the sensitivity of Eq (3) to
changes in Kr. As Figure 6 illustrates, e experiences us greatest change for values of Kr less than 1 For values
of KT greater than 1. changes in E become very small. For values of Kr greater than 5, changes m E are
insignificant.
j
The physical interpretation of the results is shown in Figure 6. The technique for determining m-situ
aquifer hydraulic conductivity in the region surrounding the borehole requires two measurements of
borehole pore-water velocity through porous packing material of differing but known hydraulic conductivi-
ties. Intuition suggests that a large value of Kr will produce a "sink effect" such that a large portion of aquifer
pore-water flow will be funnelled into the packed borehole, producing a large, measurable borehole pore-
water velocity Vp. However, Eq. (10) shows that when Kr is large, changes in e are relatively small. Converse-
ly, when Kr is small, changes in E are large. The change in e is what is measured between the two experi-
12
-------
VI
T3
0.8
0.0
0.0
Kr
FIGURE 6 Sensitivity of Hydraulic Conductivity Equations to the Parameter Kr. The Parameter
can be thought of as Dimensionless Borehole Pore-Water Speed.
ments. hence we need to make our measurements in the range where e changes the fastest, but this is also
the range where the borehole pore-water velocity is smallest, and therefore hardest to measure accurately.
Thus, for values of Kr in this range, instrument sensitivity to Vp will become a critical factor
Although theoretically correct, the experimental application of Eq. (7) requires a technique for direct-
ly measuring pore-water velocity through a borehole packed with a material of known hydraulic conductiv-
ity, a problem which until now has not been addressed. Furthermore, the technique used to measure the
borehole pore-water velocity must be sensitive enough to detect changes in the amount of flow moving
through the borehole packing material as a function of the hydraulic conductivity of this material Analysis
of the hydraulic conductivity equations presented in this section suggests that the most promising results
should be obtained for values of Kr less than about 2. This report considers these problems by investigating
two possible methods for direct borehole pore-water velocity measurement, a heat pulse advective transport
method and a modified borehole-dilution method.
13
-------
MEASUREMENT OF THERMAL PULSE ADVECTIVE VELOCITY IN A
SATURATED POROUS MEDIUM
K-V Associates, Inc.. have designed a single-well flo*meter which the manufacturer claims can de-
tect aquifer pore-water velocities in the range of 0.03 m/d to 3.0 m/d (Kerfoot. 1982). In general, the
system operates by generating a heat pulse within a borehole section packed with a saturated porous me-
dium. Temperature changes within this medium (due to the transported heat pulse) are then related to the
aquifer pore-water velocity. Unfortunately, operating procedures require a laboratory calibration of ques-
tionable reliability. Modifications to the flowmeier system were made in an attempt to directly measure the
pore-water velocity through the borehole porous packing material, thus allowing a value for the aquifer
hydraulic conductivity to be determined.
Measurement of ground-water velocity with the K-V Associates flowmeter is based upon the transport
of a thermal heat pulse within a porous medium, under the influence of interstitial fluid flow (Kerfoot.
1982). The flowmeter system consists of a downhole probe and an uphole electronics package. The
downhole probe contains a stainless steel heating probe symmetrically surrounded by heat-sensitive thermis-
tors (Figure 7). Ideally, the downhole probe is buried in an aquifer with minimal disturbance to the porous
medium. When operating the flowmeter. a transient, short-duration point-source of heat is generated at the
heating probe tip, which is then transported radially away from the heat source. If interstitial fluid flow does
not exist, then heat transport is by conduction, and the rate of heat transport is dependent on the thermal
conductance of the porous material and the stationary pore water. If interstitial fluid flow does exist, then
heat transport is by two mechanisms: conduction through the porous material, and advection by water
moving through the porous medium. Therefore, for conductive heat transport alone, a symmetric tempera-
ture field is generated about the heat probe, and opposing thermistors are exposed to the same temperature.
For conductive and advective heat transport, opposing thermistors are exposed to an asymmetric tempera-
ture field which is shifted in the direction of pore-water movement. Theoretically, the magnitude of the
as>mmetry between opposing thermistors is proportional to the thermal front advective velocity, and there-
fore the pore-water velocity.
When operated as designed, the flowmeter measures the difference in resistance between opposing
thermistor pairs at a set time after the heat pulse is emitted. Thus, the flowmeter output is a relative number
which must be convened to aquifer pore-water velocity. K-V Associates provides a small flowchamber
which is used to empirically calibrate the flowmeter. This is accomplished by filling the flowchamber with
porous material representative of the aquifer material in which field measurements will be performed, and
then embedding the flowmeter probe within this material. A constant-flow metering pump is used to gener-
ate a series of known flow rates through the flowchamber, and the instrument response is noted. Based on
these measurements, an empirical calibration curve of flowmeter output versus flow rate is produced. This
calibration curve is then used in the field to convert flowmeter response into aquifer pore-water velocity.
Wheatcraft et al. (1986) have thoroughly investigated the manufacturer's suggested calibration proce-
dures, and found them to be of limited value. Specifically, the practice of using disturbed aquifer material as
a medium through which the flowmeter is calibrated is flawed, since this material probably has hydraulic
properties much different than the m-situ values found in the field. Thus, in designing experiments utilizing
14
-------
pore-water direction
-t
f
1
S
1
uphole electronics cable
\
1
r0 = 1 60 cm
* *
downgradient thermistor
"7
U_fc.v
heat source
SIDE VIEW
pore-water direction
[Section A - A']
heat source
downgradient thermistor
TOP VIEW
FIGURE 7. K-V Associates Thermal Flowmeter Downhole Probe Geometry.
15
-------
the flowmeter in determining the pore-water velocity through a borehole packed with a porous material of
known hydraulic conductivity, it is very important to attempt to develop a method to obtain pore-water
velocities without using the empirical calibration procedure Equations (5) through (7) provide the theoreti-
cal basis for obtaining pore-water velocity and the hydraulic conductivity of the aquifer.
MODIFIED THERMAL FLOWMETER EXPERIMENTS
The purpose of the experiments using the modified K-V Associates thermal flowmeter was to deter-
mine the ability of the instrument to directly measure the advective velocity of a heat pulse generated within
a borehole packed with a porous medium. If it is assumed that the heat-pulse velocity approximates the
velocity of a conservative tracer, then this value is approximately equal to Vp, and theoretically can be used
to determine Ka in Eq (7).
The modified thermal flowmeter experiments utilized the small calibration flowchamber provided by
K-V Associates. A section of 5.08-cm diameter well screen (identical to that used in the large aquifer-simu-
latmg flowchamber) was placed within the calibration flowchamber, and #16 sieve silica sand was packed
around it. This porous medium was then saturated, and a constant-flow metering pump was used to establish!-
a known pore-water velocity through the chamber. A mesh endcap filled with uniform-diameter glass beads
(Kp = 3 93 x 10'3 m/s) was attached to the downhole probe, and then inserted into the well. The experimen-
tal configuration is shown in Figure 8.
Modifications to the flowmeter circuitry were made so that the downgradient thermistor could be
continuously monitored. This was accomplished by placing a resistor in series with the downgradient ther-
mistor, and providing this circuit with a constant voltage. One channel of a two-channel analog recorder was
used to monitor the voltage across the resistor as a function of time. Thus, a heat-pulse front is sensed by the
downgradient thermistor, producing a proportional increase in voltage, which is recorded as a breakthrouch
curve on the analog recorder. The second channel on the recorder was used to monitor the current supplied
to the heat-probe tip. allowing the starting time of an experiment to be recorded.
The question as to whether the advective pore-water velocity could be determined using the proposed
technique was answered by recording heat transport breakthrough curves at the downgradient thermistor.
using different but known pore-water velocities. If the advective portion of the heat-transport velocity was
sufficiently large, then us arrival at the downgradient thermistor would appear as a separate peak, distin-
guishable from the conductive heat-transport peak arrival. Additionally, the peak representing the advec-
ti\e component of the transported heat pulse would occur at earlier times for higher pore-water veloci-
ties,while the conductive heat-transport peak arrival would remain relatively constant. Hence, by knowing
the horizontal distance between the heating probe tip and the downgradient thermistor, the advective veloc-
ity of the heat pulse within the porous packing material could be calculated. If it is assumed that the advec-
me heat-pulse velocity approximates the advective velocity of a conservative tracer, then this method could
be used to determine Ka in Eq. (7)
Figure 9 gives the results of three experiments using the modified K-V Associates thermal flowmeter
The time at which the advective component of the heat pulse should have arrived at the downgradient
16
-------
uphole electronics cable
V
downhole probe
slotted PVC screen
static water level
j pore-water direction
pore-water direction |
#16 sieve silica
sand
input from constant-flow
metering pump
mesh endcap filled with uniform-
diameter glass beads
output to constant-flow
metering pump
FIGURE 8. Thermal Flowmeter Experimental Configuration.
thermistor, calculated from a priori knowledge of the pore-water velocity and heat-pulse travel distance, is
indicated for each experiment. As this figure illustrates, the arrival of the advective component of the trans-
ported heat cannot be differentiated from the conduction-dominated heat-transport breakthrough curves.
In effect, conduction of heat through the porous material surrounding the downhole probe is a much more
efficient heat-transport mechanism than advection by pore water.
The flowmeter was no longer considered a viable method to determine Ka because it was unable to
distinguish the advective component of the heat pulse at the downgradient thermistor. As a result, no further
experiments were conducted with the thermal flowmeter. Attention was instead focused on developing a
method to measure Ka using Eq. (7) and borehole-dilution techniques.
17
-------
2J)
O
O)
0)
0>
O)
(0
6
O
a
I
I
JO
-------
considered. This condition requires an elimination of all other flow components, or the derivation of correc-
tion factors to compensate for their influence.
Assuming an "instantaneous" mixing of an electrolytic tracer homogeneously distributed in the mea-
suring volume, the time rate of change of the tracer concentration within the measuring volume is given by
dC
or = -kc
where
C = tracer concentration within the borehole measuring volume
t = residence time of tracer in measuring volume
k = rate constant
The constant * corresponds to the fraction of the total amount of tracer that leaves the measuring
volume in one unit of time, thus
(12)
where
v
= borehole measuring volume
A = vertical cross-sectional area of measuring volume
Vb = apparent water velocity within borehole section
Substituting Eq. (12) into Eq. (11), integrating, and solving for, Vb yields
1/4 - - >£ 03)
where
C0 = initial tracer concentration at t=0
Krolikowski (1965) has suggested that Eq. (13) be corrected for any background tracer concentration with-
in the measuring volume:
where
Q, = background tracer concentration
In applying borehole-dilution theory to the problem of measuring pore-water velocity through a sec-
tion of a borehole packed with a porous material of known hydraulic conductivity, the basic borehole-dilu-
tion equations were modified to account for the presence of the porous material within the mixing volume.
Additionally, the factors that influence flow within a packed borehole were examined.
Figure 10 represents an isolated section of a cylindrical borehole embedded within a saturated porous
aquifer across which exists a significant hydraulic gradient. The borehole section is packed with a homoge-
neous porous material of known hydraulic conductivity Kp. It is further assumed that the porous material is
chemically nonreactive with both the normal borehole fluid and the electrolytic tracer Due to the presence
19
-------
borehole
saturated
aquifer
pore-water flow
packed
borehole
section hy-
draulic con-
ductivity =
Kp
Vertical cross-sectional area J_ to flow A=(x')(z')
Measuring volume V=,T I I z1
FIGURE 10. Explanation of Modified Borehole-Dilution Geometry.
20
-------
of the porous packing material, the effective mixing volume is now the volume of the pore spaces within the
borehole section
where
ve = effective mixing volume of packed borehole
v = volume of unpacked borehole section
nf = effective porosity of the borehole packing material
Assuming an "instantaneous" mixing of an electrolytic tracer homogeneously distributed within the
packed borehole section, then the general form of the point-dilution equations holds, and the apparent
velocity of the pore fluid within the packed borehole section becomes
where
Vp = pore-fluid velocity within the packed borehole
Application of Eq. (15) is similar to the normal borehole-dilution technique, with the electrical con-
ductance of the packed borehole pore fluid being measured as a function of time. By plotting the natural
logarithm of the corrected electrical conductivity versus time, a linear relationship is produced which allows
for the direct calculation of Vp
m ve
V» ~^- (16)
where
m = slope of the semilogarithmic line
Whereas, the aim of normal borehole-dilution theory is to determine the aquifer pore-water velocity
Va from the value measured m an open borehole, the aim of the modified borehole-dilution technique is to
determine at least two accurate values for the pore-water velocity using two packers of different hydraulic
conductivity. These two measurements of Vp will, through Eq. (7). allow determination of Ka, as well as Va.
Ideally, it is desirable that all components of flow within the packed borehole not related to the actual
aquifer pore-water velocity Va be negligible. This requires an understanding of the factors which influence
pore-water flow within the packed borehole measuring volume, so that these factors can be eliminated or
compensated for.
FACTORS THAT INFLUENCE PORE-WATER FLOW WITHIN PACKED
BOREHOLE MEASURING VOLUME
In general, the factors which influence the measured value of the apparent pore-water velocity \'p
within the packed borehole measuring volume ve are similar to those which influence the borehole-water
velocity Vh within an open borehole measuring volume v. These are factors due to hydraulic and
hydrogeologic conditions within the porous medium surrounding and within the packed borehole, borehole
21
-------
construction influences, instrument influences, and physical influences. The major difference between the
modified borehole-dilution theory and the normal borehole-dilution theory is the magnitude of the influ-
ence of these various factors on Vp.
The influence of hvdrauhc and hydrogeologic factors on the measured value of the packed borehole
pore-water velocity Vp are similar to their influence on the measured value of the open borehole-water
velocity Vh. For a borehole completed within a stratified aquifer, naturally occurring pressure gradients may
generate vertical currents within the borehole. As in the open borehole case, the use of inflatable packers as
a means of isolating the packed borehole measuring volume ve should sufficiently reduce the effects of
artificial tracer dilution caused by vertical borehole currents for most situations.
As in normal borehole-dilution applications, the influence on the packed borehole pore-water veloc-
ity Vp due to the presence of the borehole tool is minimal, provided the measuring volume ve can be accu-
rately determined, and provided the instrument does not obstruct the measuring volume vertical cross-sec-
tional area perpendicular to the aquifer pore-water flow direction.
Analogous to normal borehole-dilution applications, the modified borehole-dilution method requires
an instantaneous, homogeneous distribution of the tracer within the packed borehole measuring volume v
However, achieving this tracer distribution within the packed measuring volume is very difficult, because
m-situ mechanical mixing within the packed borehole section is impossible. Thus, if an electrolytic tracer
introduced into the packed borehole section is not efficiently mixed with the background pore fluid and
distributed throughout the measuring volume, then there is a strong likelihood that an unwanted borehole
velocity component due to artificial mixing will be generated. This is likely due to the nature of the move-
ment of the tracer, which may migrate from the packed borehole as a high concentration mass rather than
being continuously diluted by aquifer pore water moving through the packed borehole section.
Another unwanted borehole velocity component which may result from insufficient mixing and distri-
bution of the tracer within the packed borehole section is artificial outflow of the tracer due to density
differences between the high-concentration tracer cloud and the surrounding background pore-water fluid.
As in normal borehole-dilution theory, physical effects caused by tracer diffusion within the measur-
ing volume are minimal for aquifer pore-water velocities greater than approximately 0.3 m/day. Similarly,
ph\sical effects caused by temperature gradients resulting from temperature differences between the tracer
and the background borehole pore water are minimal for temperature differences between the tracer fluid
and background fluid of 2°C or less.
Because of the significant influence of the insufficiently mixed tracer, a method for efficiently mixing
and distributing the tracer within the packed borehole measuring volume is critical to the validity of the
modified borehole-dilution technique.
BOREHOLE PACKER POROUS MATERIALS
The borehole-dilution experiments were conducted using a laboratory-scale flowchamber (discussed
below) packed with porous media designed to be large enough to provide a uniform flow field around a well
22
-------
emplaced in ihe center of the flowchamber. Packers were designed using glass beads that covered a range of
hydraulic conductivity ratios of about 0.01 <: K, < 10. thus spanning two orders of magnitude. Actual hy-
draulic conductivity values were determined by laboratory permeameter tests, and are given in Table 1. The
permeameter tests were designed so that Reynolds numbers were kept to less than one, thus minimizing the
possibility of nonlinear head losses.
TABLE 1. THEORETICAL AND EXPERIMENTAL GLASS BEAD HYDRAULIC
CONDUCTIVITY VALUES
Bead Batch Size (mm)
2.8
2.0
1.4
1.18
0.85
0.71
0 61
0 25
0.18
0.15
- 2.
- 1.
- 1.
- 0.
- 0.
- 0.
- 0.
- 0.
- 0.
- 0.
0
4
0
85
60
50
425
180
125
106
Experimental Kp (mis)
nonlammar flow
2
1
3
2
1
3
1
9
.61
.72
.93
.31
.79
.16
.68
.59
x
x
X
X
X
X
X
X
10-2
10-2
10-3
10-3
10-3
10~4
io-4
10-5
K,
n/a
8
5
7 12
1
0
0
1.08
5.75
3.28
.94
.89
x 10-3
.34
.79
.61
x 11
D-I
x ID'2 ..
x 10-2
FLOWCHAMBER CONSTRUCTION AND CHARACTERISTICS
The aquifer-simulating flowchamber utilized in this study is designed to exhibit uniform flow through-
out us vertical cross section. Figure 11 is an idealized drawing of the flowchamber; construction details are
given in \Vheatcraft et al. (1986). The dimensions of the flowchamber are 1.2 m by 1.2 m (cross-sectional
area perpendicular to flow direction) by 2 m (length of flow path). Plexiglass (3/8 in) is used to contain the
flowchamber porous medium, which is composed of #16 sieve silica sand (1 19 mm geometric mean size).
Water chambers are constructed at opposite ends of the flowchamber. and act as constant-head reservoirs.
The height of these reservoirs can be adjusted with a precision of 0.01 cm Six fully penetrating, 2-mch
diameter (5.08 cm) screened wells are emplaced within the flowchamber in two rows of three, evenly spaced
parallel to the direction of flow. Well screen slot openings are 0 05 cm, arranged m five vertical rows
(Wheatcraft et al., 1986).
During construction of the flow chamber, care was taken to avoid stratification within the porous me-
dium; hence, the flowchamber closely models a confined, homogeneous and isotropic aquifer. Hydraulic
conductivity of the flowchamber medium was determined using Darcy's Law. written in the form
(17)
J-UJJl
where
Q = volumetric discharge through the flowchamber
A = vertical cross-sectional area of flowchamber
A/ = length of flowpath
A/I = hydraulic head across flowchamber (difference m reservoir heights)
23
-------
static water
plyboard confining
layer
2-inch diameter well
upgradient
head reservoir
downgradient
head reservoir
potentiometric
surface
4J-1-1J-3-I J J _l
JJ-J-IJ-1-iJJJ
-1JJJJJJJJJ
Jl J J.J Jj J _
potentiometric
surface
potentiometric
surface
flow direction
porous medium
clear Plexiglas*
FIGURE 11. Idealized Diagram of the Aquifer-Simulating Flowchamber.
All of the parameters in Eq. (17) can be accurately measured. Based on Eq. (17), the flowchamber hydrau-
lic conductivity Ka was calculated to be approximately 252 m/day.
Accurate knowledge of the flowchamber pore-water velocity is of primary importance in this study.
This parameter can also be calculated using Darcy's Law, here written as
(18)
where
Va =
flowchamber pore-water velocity
na = effective porosity of the flowchamber porous medium
The accuracy of Eq. (18) depends on an accurate measurement of na. This parameter was determined
through a conductive tracer experiment. In this experiment, an electrically conductive tracer (NaCl) was
introduced into the upgradient head reservoir at time t=0. Breakthrough curves of this tracer were then
24
-------
recorded at each well along the flow path. Based on the time-distance relationship for the peak arrival of the
tracer front at each well, an average effective porosity for the flowchamber was determined to be 43.6
percent.
NORMAL AND MODIFIED BOREHOLE-DILUTION EXPERIMENTS
Experiments utilizing the modified borehole-dilution technique were conducted in an attempt 10 di-
rectly measure the horizontal pore-water speed Vp through a borehole with a porous material of known
hydraulic conductivity. These experiments were conducted in the aquifer-simulating flowchamber, using a
laboratory apparatus designed and constructed for this purpose. In general, the method of investigation was
twofold. First, the laboratory apparatus was configured as a normal borehole-dilution device, and experi-
ments were carried out to determine if the device could produce results in agreement with borehole-dilution
theory. The mam reason for conducting these experiments was to verify that the laboratory apparatus could
produce accurate and repeatable dilution data. Having achieved this objective, the apparatus was reconfi-
gured, and experiments were performed in an attempt to produce results which were in agreement with the
m-situ hydraulic conductivity theory (Eq. 7). Initial reconfiguration of the laboratory apparatus consisted
mainly of introducing a porous material into the borehole measuring volume. Further modifications to the:-
apparatus were applied as experimentation proceeded. Basically, the modified borehole-dilution experi-
ments consisted of measuring a value for Vp as a function of Kr, while holding the flowchamber pore-water
velocity Va constant. From Eq. (8) it follows that these data should produce a curve which asymptotically
approaches a value of 2. as in Figure 6.
EXPERIMENTAL APPARATUS
The experimental setup is shown in Figure 12. with the downhole portion of the apparatus shown in
Figure 13. The mixing chamber shown in Figure 12 is designed to optimizethe mixing process so that it most
closely approximates the initial conditions of Eqs. (11) and (14). Without such a mixing chamber, wild
oscillations in concentration will be experienced in the system until the tracer slug has fully mixed, which can
take several residence times, thus ruining the early time results of the experiments. The optimum volume for
the mixing chamber was found through a set of experiments to be about 250 ml, which is about the volume of
the total system without a mixing chamber Because it is virtually impossible to remove all early-time oscilla-
tions, the first three minutes of the data were discarded for all experiments. Experience showed that three
minutes was sufficient for the data to plot as a straight line on semi-log graph paper.
A series of experiments were conducted to determine the repeatability of data obtained during a
dilution experiment. Three experiments were performed at two different flowchamber pore-water velocities
(3.72m/day and 7.62 m/day), while holding all other test parameters constant. Between each experiment.
the downhole tool was removed from the flowchamber well, and the glass beads were removed, dried, and
repacked. Care was taken to repack the glass beads in a systematic way, and to reposition the downhole tool
within the flouchamber well as consistently as possible. Figure 14 gives the results of the repeatability experi-
ments. Although there is an obvious separation between the two sets of experiments performed at different
flowchamber pore-water velocities, it is clear that the experiments are not perfectly repeatable. If the data
25
-------
two-way valves
peristaltic pump
FIGURE 12. Diagram of Laboratory Apparatus, Showing Location of Mixing Chamber
from these experiments uere used in Eq. (7) to calculate Ka, there would be a noticeable difference in some
cases. The issue of nonrepeatability will be addressed further in the next sections
Figure 15 is a semiloganthmic plot of the laboratory apparatus theoretical response, generated by
varying the parameter A', Figure 15 follows from Eqs (8). (15). and (16). which can be combined to give
where
26
-------
bladder inflation lines
system output
system input
mixing volume
upper inflatable bladder
mesh sock containing
uniform glass beads
mixing circuit
lower inflatable bladder
FIGURE 13. Diagram of Downhole Tool used in Hydraulic Conductivity Experiments.
27
-------
o
LLJ
T3
o
I
O)
m
c
-3-
-4-
-5-
Flowchamber P.W. Vel.
3.72 m/day
3.72 m/day
3.72 m/day
7.62 m/day
7.62 m/day
7.62 m/day
10
20
Time (minutes)
I
30
40
O
-2-
8 -'
3 -4.
O)
0
(0
CD 5-
-6-
Flowchamber P.W. Vel
- 3.72 m/day
m/day
m/day
m/day
m/day
3.72
3.72
-- 7.62
-- 7.62
-- 7.62 m/day
10
r~
20
Time (minutes)
I
30
FIGURE 14. Results of Repeatibility Experiments. Laboratory Apparatus Sensitivity to Varied
Flowchamber Pore-Water Velocity is Clearly Illustrated.
28
-------
o
OJ
O
I
O
m
5
Theoretical Response
V V > "»
xv v
10
Time (minutes)
FIGURE 15. Theoretical Output of Laboratory Apparatus for Flowchamber Pore-Water
Velocity = 3.72 m/day.
Figure 15 shows that by setting the flowchamber pore-water velocity Va constant and varying Kr, the slopes
change significantly (and therefore should be easy to detect experimentally) for Kr greater than about 0.5,
and Kr less than about 2. Note that the curves for Kr greater than about 2 get increasingly close together, as
one would expect according to Eq. (10).
A series of dilution experiments were performed in an attempt to duplicate experimentally the results
of Figure 15. For these experiments, the flowchamber pore-water velocity was held constant at 3.72 m/day,
and the parameter Kr was varied from 0.61 to 8.94 (as given in Table 1). Special care was taken to ensure
uniformity in experimental procedures, thus holding systematic error to a minimum.
Figure 16 presents the results of the varied-A:,. experiments, along with the theoretical response that
would be expected. The experimental response has been plotted with a best-fit log-linear regression equa-
tion to aid comparison with the theoretical response. The proportionality between Vp and Kp displayed by
the theoretical model (Figure 15) does not appear in the experimental data. Figure 17 is a comparison of the
29
-------
o
UJ
o
2
o
O
i
-o
o
3
o
k.
b
O
i
c
o
0
(O
CD
-3-
-5-
10
Time (minutes)
Experimental Response
Kr
0.61
0.79
- - 2.44
5.89
8.94
10
20
r~
30
Time (minutes)
FIGURE 16. Theoretical and Experimental Response for the First Varied-Kr Experiments,
Plotted at Same Scale for.Comparison.
30
-------
OJJ-
Theoretical Response
Experimental Response
-ai
c
O
a.
o
55
-0-4
Flowchamber Pore-Water Vel. = 3.72 m/day
~r
a
Kr
10
FIGURE 17. Theoretical Versus Experimental Change in Semiloganthmic Slope as a Function
of Kr, for the First Varied-Kr Experiments. Note the Lack of Systematic Change
in the Experimental Results.
theoretical verses experimental semilogarithmic slopes (determined from Figure 16) as a function of Kr. As
Figure 17 illustrates, the expected asymptotic behavior of flow through the packed borehole for increasing
Kr is not observed. On the contrary, the experimental results appear quite independent of Kr. As observed
from the theoretical portion of Figure 16, the slope of the dilution data (plotted semilogarithmically) should
become more negative as the parameter Kr increases. As indicated by the experimental plot, however, this is
not the case. Although there is a change in the experimental slope as a function Kr, this change does not
occur in a systematic way. Many factors could be responsible for this result. Systematic error could have
been introduced by nonuniformity in experimental procedure. Random error due to fluctuation in physical
parameters over the course of an experiment, or due to other unknown phenomena, could be responsible.
Additionally, these error sources could be operating together in some unknown way.
Because the proportionality between Vp and Kr is critical to the application of the modified borehole-
dilution technique in determining aquifer hydraulic conductivity Ka, a second set of varied-K, experiments
31
-------
were performed, taking great care to avoid introducing systematic error into the experiments. Furthermore.
water temperature variation was closely monitored, under the assumption that significant changes in water
temperature could affect the background electrical conductivity during the course of an experiment, and
therefore bias the results. Additionally, significant water temperature variations could affect the viscosity of
the flowchamber water, possibly changing the fluid flow characteristics in some way.
Figure 18 is a semiloganthmic plot of the second varied-*,, experiment results. For these experiments.
the flowchamber pore-water velocity was held constant at 1.84 m/day. and the parameter Kr was varied
from 1.34 to 8.94. Three experiments were performed at each value of Kr. Between each experiment, the
downhole tool glass beads were removed, dried, and repacked, as a means of determining the variability
between experiments likely due to packing arrangement. Again, the proportionality between Vp and Kr
predicted by the theoretical model is not observed in the experimental results. This condition can be seen
more clearly in Figure 19. which presents the theoretical and experimental slopes as a function of Kr. As
noted for the first varied-*, experiments, there is a definite change in the slope of these experimental data
for different Kr, however, this change appears to be random. The care with which these experiments were
performed, together with the successful normal point-dilution experiment results previously obtained, seem
to rule out systematic experimental error as the cause of the negative results. '
Four factors that most likely cause the observed nonproportionality between the tracer dilution rate
and the parameter Kr are: 1) the intrinsically random packing arrangement of the glass beads within the
laboratory apparatus downhole measuring volume; 2) the randomness associated with positioning the
downhole tool within the well; 3) the fundamental problem of obtaining an accurate measurement of the
packed borehole pore-water velocity Vp in the region of maximum sensitivity to the parameter Kr: and 4) the
probable existence of nonumform. three-dimensional flow within the flowchamber due to the presence of
the packed borehole. More than likely, these factors are operating in unison to produce the seemmcly
random fluctuations observed in the experimental results.
Of the four effects most likely responsible for the experimental results, the effect due to the problem of
obtaining an accurate value for Vp in the region of maximum sensitivity to the parameter Kr, coupled with the
effect due to nonumform, three-dimensional flow within the flowchamber, may be the most significant. The
first of these effects has previously been discussed. The second effect, that of three-dimensional flow
around and through the packed borehole, can be conceptualized as follows. The solution of Wheatcraft and
Wmterberg (1985) requires that flow within the porous medium surrounding the packed borehole be hori-
zontal and laminar, and further that flow transitioning from this porous medium into the borehole porous
medium and out again also obey these conditions. However, the presence and scale of the packed borehole
section may exert an influence on the flowchamber flow field such that a significant vertical component of
flow exists in the region surrounding the packed borehole. Figure 20 is an idealized representation of this
situation. Although this phenomenon is difficult to quantify, it is reasonable to assume that this process could
introduce significant changes in the portion of flow moving through the packed borehole section, relative to
the predicted amount of flow through this section based on the theoretical results in Wheatcraft and Winter-
berg (1985). It is possible that by increasing the volume (that is, the length) of the packed downhole tool
relative to the portion of the tool where the actual dilution process takes place, the randomness introduced
32
-------
o
LU
T3
ID
a
I
T3
O
o
(0
m
Time (minutes)
-4
Time (minutes)
FIGURE 18. Least-Squares Plot of Second Varied-Kr Experimental Results. Flow-
chamber Pore-Water Velocity =1.84 m/day.
33
-------
o.oo-
+ Theoretical Response
*- Experimental Response
-0.05-
c
C -0.10-
c7)
-0.15
Flowchamber Pore-Water Vel. = 1.84 m/day
-0.20-}-
3456789 10
Kr
FIGURE 19. Theoretical Versus Experimental Change in Semilogarithmic Slope as a Function of Kr,
for the Second Vaned-Kr Experiments. Apparent Random Fluctuation in Experimental
Results is Illustrated.
into the experimental data due to three-dimensional flow can be removed (Figure 21). Reducing this source
of random error may provide the sensitivity needed to detect proportional changes in dilution rate as a
function of Kr, for a given flowchamber pore-water velocity.
The significance of the length of the packed borehole section relative to the section where the dilution
measurement is made was investigated in the third varied-*, experiments. In these experiments, the
downhole tool was modified as in Figure 21 to reduce vertical flow components, and three sets of three
dilution experiments were performed, using glass beads of Kr=2A4, 5.89, and 8.84. The flowchamber pore-
water velocity was held constant at 1.72 m/day. All other experimental parameters were identical to the first
and second varied-AT, experiments. Figure 22 is a plot of the experimental versus theoretical slopes as a
function of Kr. As in the first and second varied-^ experiments, the experimental slopes from the third
varied-A:r experiments appear to be independent of the parameter Kr. Hence, it is likely the case that the
effect due to the problem of obtaining an accurate measurement of Vp in the range of maximum sensitivity to
34
-------
[x-section
borehole
Packed borehole section,
measuring volume.
flow lines
FIGURE 20. Idealized Representation of Flow Field Distribution Due to Packed Borehole Section.
Kr is the dominant factor responsible for the apparent random experimental results. Unfortunately, this
effect cannot be controlled experimentally. Thus, it is reasonable to conclude that the modified borehole-
dilution method, as applied in these experiments, is an inappropriate method for investigating the in-situ
saturated hydraulic conductivity theory.
DISCUSSION - NATURAL FLOW METHODS
The experiments performed to determine packed borehole pore-water velocity Vp by measuring the
arrival time of the advected portion of a heat pulse generated within a packed borehole were unsuccessful,
mainly because conduction of the heat pulse was the dominant transport mechanism. Hence, the arrival of
the advective heat front at the downgradient thermistor was completely masked by the arrival of the conduc-
tive heat front. It is possible that by utilizing a porous packing material less sensitive to heat conduction, the
advected portion of the heat pulse may be detectable, in which case the thermal-pulse technique for deter-
mining Vp may be applicable. Additionally, an effort was made to determine a method for utilizing the
measured differences in thermistor response between the upgradient and downgradient thermistors, howev-
35
-------
[x-section]
packed borehole section
flow lines
FIGURE 21. Idealized Representation of Flow Field after Increasing Packed Borehole Section.
er, this method required empirical calibration of the instrument and therefore was determined inappropri-
ate.
Results of experiments utilizing the modified borehole-dilution technique to determine Vp were incon-
clusive. Application of the technique using the laboratory apparatus has shown that first-order decay of a
continuously diluted electrolytic tracer introduced into the borehole porous medium can be measured, and
that the rate of dilution of this tracer is directly proportional to the pore-water velocity within the medium
surrounding the borehole. However, experimental investigations of the applicability of the modified bore-
hole-dilution technique required that the dilution rate of the tracer be directly proportional to the parameter
Kr (the ratio of borehole to flowchamber hydraulic conductivity), as measured at a constant flowchamher
velocity. This proportionality, the basis of the modified borehole-dilution technique, was not observed.
Many factors may be responsible for the apparent random relationship between tracer-dilution rate and Kr.
Additionally, one or more of these factors may exert a dominant influence on the data, and any of these
36
-------
-0.10
c
£
o
c/5
Theoretical Response
Experimental Response
Flowchamber Pore-Water Vel. = 1.76 m/day
-035
T
2
T~
a
Kr
10
FIGURE 22. Theoretical Versus Experimental Change in Semilogarithmic Slope as a Function of Kr,
for the Third Varied-Kr Experiments. Apparent Random Fluctuation in Experimental
Results is Illustrated.
factors may be operating in unison. Thus, understanding the cause of the randomness in the experimental
data is difficult.
The factors least likely to have influenced the experimental results are systematic errors due to exper-
imental procedure prior to and during an experiment. As previously noted, much care was taken in selling
up and conducting a dilution experiment in a systematic way; hence, any systematic error introduced in this
process should tend to influence all experimental results in a similar fashion. This argument also applies to
other potential sources of deterministic error, such as the calibration experiment performed to determine
the relationship between the laboratory apparatus electrical response and the electrical conductivity of the
circulating borehole fluid.
Influencing factors due to the introduction of random errors are the most likely cause of the nonpro-
portionality between tracer-dilution rate and Kr. Of these random errors, the least likely to affect the data
were instrument errors. All electrical equipment was checked for correct settings and sufficient charge (for
-------
battery operated devices) between each experiment, and during an experiment, these instruments uere
closely monitored for any nonumform behavior Additionally, mechanical vibrational noise and posvihle
electrical noise was monitored. Any experimental data that may have been biased by these sources of error
were rejected.
Another source of random error not likely to have influenced the experimental results is fluctuations m
the flowchamber ambient water temperature. The temperature of water entering the flowchamber was es-
sentially constant, and remained so throughout the course of an experiment. Also, water temperature unhm
the flowchamber, as measured over the course of several experiments, remained essentially constant
The results of the first, second, and third varied-*, experiments suggest that the fundamental problem
of obtaining an accurate measurement of the packed borehole pore-water velocity Vp within the region of
maximum sensitivity to the parameter K, is the dominant factor responsible for the random experimental
results. This problem cannot be controlled experimentally using the modified borehole-dilution method.
SINGLE-NELL ELECTRICAL TRACER (SWET) METHOD
The most direct way to determine the hydraulic conductivity of a formation is to observe the move- -.
ment of fluids through the formation under the influence of a known driving force. In the method developed
here, an electrically anomalous tracer (saltwater) 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. By repeatedly measuring the radius of invasion at different times, the rate of invasion can be deter-
mined. 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 of the formation. This information can be used to calculate a hydraulic conductiv-
ity log of the formation. Because multiple induction logs are run, the rate of invasion can be calculated at
several different radii of invasion. Hence, the hydraulic conductivity log of the formation can be calculated
at several different radii of invasion. A porosity log can also be calculated by using a model of formation
electrical conductivity that accounts for variations in matrix conductivity and porosity.
Field Application
The study area is located approximately 32 km north of Mobile. Alabama, and has been the site of
numerous hydrogeological studies (Molz et al., I986a and b). The surface geologic unit consists of Quater-
nary mterbedded sands and clays to a depth of 61 m. The wells used in this study are completed mm a
confined aquifer between 40 and 60 m deep. The upper 40 m of the wells are cased, the lower 20 m are
screened Cores of the aquifer show that it consists of an unconsolidated, medium to fine sand, containing 1
to 15 percent fines by weight. The potentiometnc head is 2 to 3 m below the land surface, natural vertical
and horizontal hydraulic gradients are negligible (Molz et al.. 1986a and b).
The first step m conducting the test was to establish a steady-state flow system while injecting into the
well. Injection rates varied from 2.5 to 4.4 x I0~s m3/s depending on the well. The injection fluid uas
obtained from a well completed into the same aquifer that was located 250 m away from the injection well.
38
-------
At each well, the injection was at a constant rate. When the head in the injection well stabilized for 30
minutes, the system was considered to be at steady-state. Heads were measured with a pressure transducer
to avoid errors due to turbulence from the injection stream.
After steady-state conditions had been achieved, several induction logs were run in the injection well.
These logs provide background information on the formation electrical conductivity when the formation is
saturated with native pore fluid. Logs were repeated several times to ensure that the induction tool was not
drifting. The electrical conductivity of the injection fluid was also measured. An electrical fluid conductivity
cell was secured at the top of the screened interval (40 m). This cell was used to determine the arrival time of
the tracer. To minimize the chance of instrument drift, the induction tool was not removed from the well A
Geonics EM-39 was used for the induction tool. Because the water level in the well remained below ground
level during injection, it was not necessary to use special equipment at the well head to log and inject fluid
simultaneously. Figure 23 illustrates the experimental setup.
A concentrated sodium bromide solution was pumped into the injection line with a constant rate
metering pump. The rate of the metering pump had been previously adjusted so that the electrical conduc-
tivity of the tracer solution would be three to five times greater than the 4600 jimhos/cm electrical conductiv-
ity of the native pore water. The output of the fluid conductivity cell at the top of the screened interval uas:-
recorded on an analog recorder. The time at which the electrical conductivity of the borehole fluid at the lop
of the screened interval was halfway between the conductivity of the tracer and the conductivity of the native
water was considered to be the amval time of the tracer at the top of the screened interval. The time
required for the transition from native to tracer fluid at a given depth within the well screen was on the order
of one minute. Other tests demonstrated that the tracer reached the bottom of the screened interval (60 m)
about one minute after the top of the screened interval.
Induction logs were run repeatedly while injection was continuing. In addition to digitally recording
formation electrical conductivity as a function of depth, the time at which each measurement was made was
also recorded. To complete the full quantitative analysis, the injection and logging continued until the radius
of invasion was greater than the radius of investigation of the induction tool. When this condition occurred,
repeated logs of the well were identical. Sufficient time must elapse between running the two logs to ensure
that this condition was met. One way to ensure this is to increase the interval of time between running the
logs by a factor of 2 after each log is run. With the equipment used in this study, it was necessary for the fluid
to invade 2 to 3 m into the formation to have all of the data necessary for the analysis method presenied
here. With the injection rates and wells used m this study, the time required to reach this condition was up to
three to four hours.
Theory of Analysis
Assumptions
Several assumptions are necessary for the following analysis. In general, the assumptions are realiMic
and can be tested. In some cases, it is evident from the data when an assumption is violated.
The first assumption is that well hydraulic losses are negligible compared to formation losses. Head loss
can be caused by an excessive injection rate for the well, and m this case will be evenlv distributed alonu the
39
-------
ELECTROLYTE INJECTION
LINE
TO BOREHOLE LOGGER
LAND SURFACE
HIGH PERMEABILITY
ZONES
ELECTROLYTE
FRONT
INDUCTION TOOL
FIGURE 23. Experimental Setup for Single-Well Electrical Tracer Test.
40
-------
well. It can also be limited to short intervals of the well as will happen if the screen is damaged or plugged In
a poorly completed well, drilling mud can also seal-off a portion of the formation from the well. If only a
short interval of the well is in poor hydraulic connection with the formation, it is readily apparent in the dnia.
The second assumption is that the formation is fully saturated. If air is introduced m the formation
during the injection process, the baseline logs will not be accurate and an unrealistic increase m electrical
conductivity will be observed.
The third assumption is that there are no chemical reactions between the injected fluid and the forma-
tion. The possibility exists in some formations with clay that the salt solution can react with the formation and
alter the hydraulic properties of the formation.
The fourth assumption is that the tracer is perfect and moves radially away from the well by advecuon
The now will be radial because the injection rates are sufficiently high to cause an appreciable upconmc of
the potentiometnc surface. Some dispersion takes place along the 2 to 3 m travel path of the study, but this
dispersion does not influence the results.
Porosity Calculation '-
Archie's Rule (Hearst and Nelson, 1985) can be used to calculate the electrical conductivity of a
formation due to the electrical conductivity of the pore fluid. In clay-free formations saturated with pore
fluids that have a high electrical conductivity, this will be the only significant mechanism for electrical con-
duction and is a suitable model for formation conductivity. However, if clays are present, there can be
significant electrical conduction through the matrix of the formation. This is particularly true in formations
saturated with pore fluid that has a low electrical conductivity
In many ground-water investigations, the influence of the electrical conductivity of the matrix cannot
be ignored and must be taken into account. The following is the development of a model to accomplish this
task.
The formation conductivity can be represented by:
Ofln = Om + Opf (|9)
where:
Ofln = formation electrical conductivity
om = electrical conductivity of the formation due to conduction through the matrix
Opf = electrical conductivity of the formation due to conduction through the pore fluid
From Archie's Rule we know:
Opf = (of &")/a (20)
9 = porosity (\\ hich is a function of depth)
Of = electrical conductivity of the pore fluid
a = tortuosity
41
-------
m = cementation factor
°P = electrical conductivity of the formation
Jackson et al. (1978) have shown that for unconsolidated sands an appropriate value for tortuosity and ihe
cementation factor is 1 . 0 and 1 . 4 , respectively. It is important to recognize that the use of the term tortuosn y
in connection with Archie's Rule is only indirectly related to the path traveled by a fluid in the formation.
Substituting Eq. (19) into Eq. (20) yields:
+ (ar &")/a
In the case of the single-well electrical tracer (SWET) test we know the formation electrical conductiv-
ity when it is saturated « ith pore fluid of two different electrical conductivities. The electrical conductivity of
the pore fluid, with and without the tracer, is also known because it can be measured during the injection
process. The electrical conductivity of the formation when it is not invaded by the tracer is determined by
the baseline logs that are run prior to tracer injection. The electrical conductivity of the formation when it is
invaded by the tracer is determined by the logs made after the tracer has invaded the formation a sufficient
distance that only the invaded zone is measured.
Using the following notation1
°j\ = electrical conductivity of the pore fluid without the tracer
an = electrical conductivity of the pore fluid with the tracer
°flni = formation electrical conductivity without the tracer
Ofn2 = formation electrical conductivity with the tracer
allows us to write a system of equations:
= am + (ofl &")/a
- am + (afl &")/a
which can be solved for porosity and the matrix electrical conductivity.
0 =
1/m
(21)
Calculation of Radius of Invasion
To calculate the radius of invasion of the tracer, it is necessary for us to introduce a model for ihe
measurement of electrical conductivity by the induction tool:
aa = X(R) OJM + (1 -*(*)) G>,, (22)
oa = apparent formation electrical conductivity (this is what is measured by the induction tool)
R = radius of invasion
X(R) = radial response function of the induction tool
42
-------
The radial response function (Figure 24) was calculated using a knowledge of the coil geometry of the
induction tool (McNeil, 1986) and the method described by Saito (1982).
The only unknown in Eq. (22) is the radius of invasion. This is solved for numerically by first solving
for the value of l-X(R), and using the radial response function to determine the value of /?.
Calculation of Hydraulic Conductivity
The rate of injection into a segment of the well will be equal to the rate that the pore volume is invaded:
Q = ^^~ <23>
B = thickness of segment
t = time since start of injection
Q = porosity
Q = rate of injection into well segment
R = radius of invasion
The rate of injection into the segment can also be described by Darcy's Law:
1.0
0.8
LU 0.6
co
Z
to
UJ
06 04
0.2
0.0
0.0
0.5
1.0 1.5 2.0
RADIUS (M)
2.5
3.0
FIGURE 24. Radial Response of EM-39.
43
-------
Q = IxrBK (24)
K = hydraulic conductivity
h = potentiometric head
r = radial coordinate
In each segment of the well, Eqs. (23) and (24) are equal and can be solved for the hydraulic conductivity of
the segment:
* = IST ln l^J <25>
h = head in the well
r, = radius of well (5 cm for this study)
/2 = radius where the head is 0 (radius of effect of the well)
The only way to measure the radius of effect is to have a large number of wells at increasing distances
from the injection well. In addition to this, the radius of effect will be different for each segment of the well.
Fortunately, the equation is very insensitive to this variable so that it is sufficient to make a knowledgeable
estimate of the value. In this study, it was known to be less than 5 m because a well 5 m away from the
injection well was not affected by the injection.
The radius of invasion (Eq. 22) and the porosity (Eq. 21) as determined by the preceding methods can
be used in conjunction with Eq. (25) to calculate the hydraulic conductivity.
Checks on the Analysis Method
The hydraulic conductivity log calculated from the above procedure (Eq. 25) can be averaged to
determine an average hydraulic conductivity for the well. This can be compared to the hydraulic conductiv-
ity calculated from the Thiem equation (Thiem, 1906, or Kruseman and De Ridder, 1983)
K =
2nBh
A close agreement between the two methods does not mean they are correct in an absolute sense
because it is necessary to assume the same radius of effect in both procedures. A wide discrepancy between
the two methods, however, indicates that there is a problem with the data or the method of analysis.
The analysis can also be done at many different times and hence, radii of invasion. Near the well, the
invasion may be influenced by the alteration of the formation during drilling and well development. In the
analysis, it is possible to only consider radii of invasion that are sufficiently far from the well that drilling
induced disturbances are negligible. This distance was chosen to be 40 cm. The error m calculating the
radius of invasion increases with increasing distance due to the shape of the response curve. To limit this
error, onlv invasions of less than 120 cm were considered.
44
-------
One check on the uniformity of this zone (40 to 120 cm) and the analysis method is to calculate the
hydraulic conductivity log at several times when the radius of invasion is within this zone. The hydraulic
conductivity logs calculated at the different times should agree closely.
The matrix electrical conductivity log should be strongly influenced by clays. Some, but not all. cla\s
will also have a response on the natural gamma log. Hence, one would expect to see a correlation between
these two logs.
Discussion of Results
Well E-3
One well (E-3) is unique at the site because it is not screened through the entire aquifer. Instead,
there are seven screened intervals each 1 m long separated by a 2 m nonperforated cased interval. When
fluid is injected into this well, it can only enter the formation adjacent to the screened intervals. Figure 25
shows the induction logs that were run in this well. The location of the screened intervals is quite apparent.
Because of the vertical averaging of the induction tool, the logs run after the tracer has invaded the forma-
tion do not exactly overlie the background log in the nonscreened intervals. The vertical averaging is onlv a -..
significant effect where there are rapid vertical changes m the radius of invasion. Fortunately, this is noi ilie
case in fully screened wells. This example does graphically illustrate that the method is capable of detecting
invaded zones. This well was not analyzed quantitatively because of the partial screening.
Well E-6
The analysis method was applied to a fully screened well referred to as E-6. The induction tool verti-
cally averages over an interval of about 2 m. To obtain an accurate induction log. the tracer must enter the
formation through the entire vertical interval measured by the induction tool. This implies the well must he
screened at least 1 m above and below the sonde. For this reason, valid data cannot be obtained in the top
and bottom 1 m of the screened interval. These sections have been omitted from the analysis. The induction
logs are shown in Figure 26.
The porosity log was calculated by the method discussed above and is shown in Figure 27. The average
value for the log is 31 percent, which agrees well with the value of 35 percent from other studies (iMolz ei al.,
1986b). Between 57 and 58 m, the porosity is in the 35 to 40 percent range which, although high, is still
realistic. Porosity values of 40 percent have been observed in cores at the site. The porosity values calculated
by this method are a radially weighted average of the formation around the well. The weighting function is
the same as the radial response of the induction tool which was shown in Figure 24.
The matrix electrical conductivity log is plotted with the natural gamma log in Figure 28. The matrix
electrical conductivity is largely a function of the clay content of the formation. The natural gamma log will
also respond to clays that contain radioisotopes such as Potassium-40. The two correlate very well, both
indicating several zones containing increased amounts of clay. The exception is at 55 to 56 m. where ihe
matrix conducuvity log indicates clay, but the natural gamma log does not. This could occur if the type of
clay in this interval does not produce detectable amounts of gamma radiation but still has a significant matrix
45
-------
FORM. ELEC. CONDUCTIVITY
WELL E3 (MMHO/M)
20 40 60 80 100 120
FORM. ELEC. CONDUCTIVITY
WELL E6 (MMHO/M)
tu
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FIGURE 25. Induction Logs of Well E-3 at
Different Times After Injection.
FIGURE 26. Induction Logs of Well E-6 at
Different Times After Injection.
-------
POROSITY
0.20 0.25 0.20 0.35 0.40 0.45
40i
42
46
48
X
h-
Q_
50
52
54
56
58
60
\
FIGURE 27. Porosity Log of Well E-6.
MATRIX ELEC. CONDUCTIVITY (MMHO/M)
NATURAL GAMMA (CPS)
40
42
0 10 20 30 40
44
46
48
X
Q.
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54
56
58
60
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t
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FIGURE 28. Matrix Conductivity and Natural
Gamma Log of Well E-6.
47
-------
electrical conductivity. Because the well was drilled with the mud rotary method, the existence of two i\pes
of clays was not noted during drilling (Molz et al., 1986b).
During injection, the head in a second well, located 6 m away, was observed. No change in head was
observed in this well. This provided an upper bound on the radius of effect of the well. Slightly arbitrariK. a
value of 4 m was assumed for the radius of effect. Because numerous induction logs were run, it is possible 10
calculate hydraulic conductivities with data collected at several different times after the start of mjecuon.
Hydraulic conductivity logs were calculated with Eq. (25) and are shown in Figure 29. The range of scatter
at each depth gives an indication of the precision of the method. The agreement is excellent except at 57 10
59 m where there is a spread between the logs. The reason for this discrepancy is not known.
The hydraulic conductivity log can be vertically averaged to calculate an average hydraulic conductiv-
ity for the well. As mentioned earlier, the data from the SWET test can also be used to calculate the hydrau-
lic conductivity of the well by the traditional Thiem method (Thiem. 1906. or Kruseman and De Ridder,
1983). The two methods should agree. The hydraulic conductivity calculated with the Thiem method is 6 7
m/d, the value from vertically averaging the SWET test is 7.9 m/d. The agreement between the SWET test.
and the traditional Thiem method reflects favorably on the former.
A possible source of the discrepancy between the vertically averaged SWET test and the Thiem
method is in the choice of values for a and m in Eq. (21). The effect of using a different choice of a and m
can be determined by using values of a and m determined by Winsauer et al. (1952) for use in friable
sandstones. These values are 0.62 and 2.15, respectively. Although these values are not wholly suitable for
the unconsolidated sands characteristic of the site, they can be used to give an insight into the effect of a and
m on the final results. From Eq. (21) we can see that substituting these values will increase the a venue
porosity from 31 percent to 37 percent. This will cause an increase m the calculated average hydraulic
conductivity (Eq. 25) from 7.9 m/d to 9.4 m/d. Hence, for both porosity and hydraulic conductsity. the
range of uncertainty caused by the uncertainty in a and m is small, even when a different lithology is as-
sumed. The only other value in the analysis that was not directly measured is the radius of effect. If a 6 m,
instead of 4 m, radius of effect had been assumed, there would still be a 20 percent difference between the
two methods, but both methods would yield values that were 10 percent higher.
Figure 30 compares the results of the SWET test to the measurements of normalized hydraulic con-
ductivity made by performing slug tests in packed intervals (Molz et al., 1989). The agreement is quite good
The hydraulic conductivities calculated by the SWET test are representative of the formation for a
radius around the well that is roughly equivalent to the radius of effect of the well. This radius is larger than
the radius of invasion because the radius of invasion is not only influenced by the hydraulic properties of the
portion of the formation that is invaded, but is also influenced by the portion of the formation into which the
displaced native fluid is forced. In this example, this was on the order of 4 m. Because most wells have a
disturbed zone around them, techniques that have a shallow radius of investigation will be inaccurate; the
SWET test minimizes these problems.
48
-------
0.0
UAX SLUG TEST
0.4 0.8 1.2
40
42
HYD. CONDUCTIVITY (M/D)
.0 5 10 15 20 25
33 WIN
+ 40 WIN
* 48 WIN
59 M!N
HYD. CONDUCTIVITY (M/D)
0 5 !0 15 20 25 30
23 MIN
+ 40 MIN
* 48 MIN
A 59 MIN
SLUG "3
FIGURE 29. Hydraulic Conductivity Logs
of Well E-6.
FIGURE 30. Hydraulic Conductivity Logs and
Packer Slug Test Results in Well E-6.
49
-------
HYDRAUjJC ^CONDUCTIVITY (M/D)
FORM. ELCC. COND. (mSAO
10 20 30 40 50 60 70 80
60
BASELINE / 31 MIN
6 MIN
FIGURE 31. Induction Logs of Well E-7.
Well E-7
Due to equipment problems, it was not possible
to run the SWET test in a third well, referred to as
E-7, for a sufficiently long time for the tracer to in-
vade the formation further than the radius of investi-
gation of the induction tool. This prevents the use of
the quantitative analysis method described here.
However, a qualitative analysis can be made from the
formation electrical conductivity logs shown in Figure
31, which compares the induction logs to the results
of straddle packer slug tests. It is clear from this fig-
ure that fluid is invading the formation slowly at 47 to
49 m and is invading rapidly at 44 to 46, 49 to 52.
and 55 to 58 m. If a qualitative interpretation such as
this is adequate, then the volume of tracer needed to
be injected can be reduced. ;
General Comments - Single-Well Electrical
Tracer Method
The SWET method yields both porosity and
hydraulic conductivity logs. The results are in good
agreement with other methods. It is significant to
note that this method is applicable in wells that have a
nonconductive casing and a disturbed annulus. No
other geophysical technique for determining hydrau-
lic conductivity has demonstrated this capability. An-
other advantage of the SWET test is that the entire
well is subjected to the same hydraulic head. Straddle
packer tests pressurize only a portion of the well and
will be in error if there is leakage around the packer.
It is quite common for this to happen because of a
poor packer seal or by leaking through the disturbed
formation/gravel pack around the well.
50
-------
SECTION 3
METHODS TO LOCATE CONTAMINANTS
BACKGROUND
As the awareness of the complexity of ground-water contamination increases, it is apparent that meth-
ods are needed to rapidly determine the vertical and horizontal distribution of ground-water contamination.
Although sampling methods are available to do this, sampling can be costly, particularly when it is necessary
to determine the vertical distribution of contaminants. One class of contaminants that lends itself to rapid'
detection is that which significantly alters the electrical conductivity of the formation. Most commonly, ilus
is the result of an increase in the concentration of dissolved ions that are associated with the contamination.
Common examples of this class of contaminants are brines and metal processing wastes. Low concentrations
of organic compounds do not alter the electrical conductivity of the ground water enough to result m a
sufficient change to be useful for detection purposes.
Unfortunately, there are no methods available to directly measure the electrical conductivity of the
pore fluid. It is possible to measure the electrical conductivity of the fluid in the well bore, but because of
vertical mixing and the influences of well design, the fluid in a well at a particular depth may not be represen-
tative of the pore fluid at that depth. Instrumentation is available to measure the electrical conductivity of
the formation that surrounds the well which, when used in conjunction with conceptual models of the electri-
cal conduction by natural formations (see the discussion in the single-well electrical tracer method section of
this report), can be used to determine the pore-fluid electrical conductivity.
Until recently, it was not possible to measure formation electrical conductivity in small-diameier,
PVC-cased wells. Recently, instrumentation to do this has become commercially available. Because of the
opportunities this new instrumentation creates and concerns regarding the quality of the data that are pro-
duced, a portion of the cooperative agreement was spent evaluating this instrumentation. Then the applica-
tions and limitations of using measurements of formation electrical conductivity measurements to detect
ground-water contaminants were considered.
EVALUATION OF A SLIM HOLE INDUCTION LOGGER
Background
To measure the electrical conductivity of a formation surrounding a cased well, it is necessary to u<:e an
induction tool. Currently, there is only one manufacturer in North America that offers a unit which can he
51
-------
used in 2-mch diameter wells. Because of the interest this unit has generated in the ground-water commu-
nity, the performance of it was evaluated.
Theory of Operation
The induction tool has a transmitter coil that emits a continuous wave 39.2 kHz electromagnetic smnal.
This produces a primary field in the formation surrounding the borehole. The primary field, in turn, pro-
duces a secondary field that is sensed by the receiver coil. The strength of the secondary field is a function of
the formation conducmity (Hearst and Nelson, 1985). Because the measurement is made by induction
methods, the unit will operate in a slotted or unslotted PVC- or Teflon-cased well. It will also operate in an
open hole. It is adversely affected if there is any metal within approximately 3 m of the instrument
Two receiver coils are used in the EM-39 at distances of 25 and 50 cm from the transmitter coil
(McNeil, 1986). The receiver coil at 25 cm facilitates instrument design by canceling the primary field and
focusing the horizontal response. The focusing reduces the influence of the borehole fluid on the instru-
ment. The location of the coil that is 25 cm from the transmitter is considered to be the location of the
measurement. Because of minor instrument drift, the instrument must be zeroed before each use. This '
simple task is accomplished by holding the tool high in the air, which is a medium of zero conductivity, and
making an adjustment on the front panel so that the instrument indicates a conductivity of zero.
Calibration
The instrument is first-order calibrated by the manufacturer. A second-order correction is also re-
quired at conductivities above 300 mS/m (McNeil, 1986) and is explained with the documentation accom-
panying the instrument. However, if accurate absolute values are critical for a specific application, the
calibration should be checked. To do this, it is necessary to place the instrument in a medium of known
conductivity. This medium must be homogeneous for the approximately 4-m high and 3-m diameter c\lm-
dncal volume that is sensed by the instrument. This calibration can be easily accomplished in large bodies of
water such as lakes. The electrical conductivity of the lake water can be measured with a calibrated fluid
electrical conductivity meter. A vertical profile of fluid electrical conductivity should be run to ensure that
the lake is not stratified near the tool. As an example of this procedure, Figure 32 plots measured versus
actual conductivities for four different lakes in Nevada. In this example, the measured conductivities were
low by about 30 percent. The manufacturer has since corrected this problem, the unit used for the remain-
der of the work meets the manufacturers claim of +5 percent accuracy.
A secondary calibration procedure is available if only relative changes in conductivity are important.
The manufacturer can provide a calibration coil which, when held in a prescribed geometry, will produce a
predictable response from the instrument. By ensuring that the magnitude of this effect is the same before
each survey, one is assured that the instrument calibration has not changed. This procedure should be used
if the instrument will be used to monitor changes in conductivity over a period of time. It can also be used to
verify that a previous absolute calibration is still valid.
52
-------
1000
PYRAMID
LAKE. NV
LAHONTAN RESERVOIR. NV
10 30 100 300
TRUE CONDUCTIVITY (mmho/m)
1000
FIGURE 32. Calibration of EM-39. .
Time Constant
The instrument a\erages readings over about one second; hence, as a hole is logged, the measured
value at a given depth is an average over a short interval through which the tool has just passed. This causes a
displacement in the log. Figure 33 is an example of a log run up and down a well. Both directions were run at
the same logging speed of 7 m/mm. Note that the two logs are vertically shifted from the correct position.
which is halfway between the two. By repeating this measurement at several logging speeds.,the magnitude of
the shift can be determined as a function of logging speed (Figure 34). A logging speed less than 5 m/mm
results in a shift of less than 10 cm between the log and the formation. If vertical positioning is critical for a
given application and logging speeds are high, the logs should be adjusted to correct for this shift.
Temperature Effects
Induction tools are susceptible to temperature-induced errors because of thermal-induced variations
m coil geometry. To evaluate the magnitude of this error for the EM-39. the instrument was allowed to
53
-------
CONDUCTIVITY (MMHO/M)
0 100 200 300 400 500 600 700 800 900 1000 1100
I
a
FIGURE 33. Logging Speed-Induced Shifts on Induction Logs.
temperature equilibrate on the surface and was adjusted to read a conductivity of zero when held in the air.
It was then placed in a lake which was 7°C colder than the air temperature. Figure 35 shows the drift in
apparent conductivity caused by the temperature change. After 20 minutes, the instrument was returned to
the surface. After allowing 20 minutes for the temperature to equilibrate to surface temperatures, the instru-
ment reading had returned to zero. Figure 35 indicates that it takes about two minutes for the instrument to
respond to temperature changes and about 15 minutes for the instrument to stabilize at a slightly hither
value. The magnitude of this change, less than 0.3 mS/m/°C, is so small that in most situations temperature-
induced errors will be insignificant. If there is concern that temperature drift may be a problem, such as
logging extremely low conductivity formations in a hot environment, the stability of the instrument should he
checked before logging.
54
-------
SPEED SHIFT
20.0
Measured Values
Fitted Line
SPEED (M/MIN)
FIGURE 34. Vertical Shift as a Function of Logging Speed for EM-39.
Vertical Response
Like all borehole instruments, the EM-39 averages over a vertical interval. This averaging function
was calculated by the method described by Saito (1982) and is shown in Figure 36. The asymmetry in the
response is an effect of the coil geometry used to focus the instrument. When this response is convolved with
the true conductivity log, the conductivity log that is measured by the EM-39 is obtained. Figure 37 com-
pares the calculated response to an abrupt contact to field data for the same situation. The surface of a lake
was used for the contact. The agreement is good and shows that an abrupt contact will be smoothed over
about aim interval.
The response of the instrument to thin beds can be calculated in a similar way. Figure 38 shows the
response to a layer of varying thickness arbitrarily located at a depth of 20 m. The log was normalized by
55
-------
TEMPERATURE RESPONSE
7° C CHANGE AT TIME 0
10
E SH
>
^
6-
O
O 4-J
2-1
* >
24 6 8 10 12 14 16 18 20
TIME (MIN)
FIGURE 35. Temperature Drift of EM-39.
showing the percentage of maximum response to the high conductivity middle layer. When the layer is less
than 4 m thick, the instrument does not accurately measure the conductivity of the layer because adjoining
beds are also averaged into the measurement. Figure 39 shows the relation between layer thickness and
response. From this plot, it can be seen that beds less than 1 m thick are poorly defined. For example, a bed
of 0.5 m thick would have an apparent conductivity difference above the surrounding material that is only
half of the true conducm ity difference. Figure 40 demonstrates how this can lead to an ambiguous suuaiion.
Two models are considered, both of which have a background conductivity of 10 mS/m. The first case (»(ihd
line) has a 1-m thick la>er with a conductivity of 70 mS/m. The second case (dashed line) has a 0.5-m ihick
layer with a conductivity of 100 mS/m. The logs of the two different cases would be difficult to differentiate
in the presence of geologic noise. The ambiguity also exists for resistive layers. Because of the poor instru-
ment response to thin lavers, the instrument is not suitable for detecting thin layers of floating hydrocarbons.
Borehole Influence
A field test was performed to investigate the influence of the borehole fluid. A 15-cm diameter and
4-m long PVC pipe was suspended in a lake and filled with fluids that had higher conductivities than the
lake. This is analogous to a fluid-filled borehole in a saturated homogeneous formation. Even when the fluid
56
-------
VERTICAL RESPONSE
iii
2
2
0.06
0.05-
0.04-
0.03H
0.02-
0.01-
0.00
-2-101 2
VERTICAL DISTANCE (M)
FIGURE 36. Vertical Averaging Function of EM-39.
in the pipe had a conductivity 100 times the conductivity of the lake water, the difference between the lake
conductivity and the apparent conductivity of the lake measured with the EM-39 in the borehole was less
than 5 percent. This error is comparable to the overall accuracy of the instrument. The position of ihe
instrument in the pipe, either in the center or off to the side, had no effect on the apparent conductivity The
conductivity of the lake was 10 mS/m, the conductivity of fluid in the pipe ranged from 10 mS/m to 1.000
mS/m. This also demonstrates that the measurement is insensitive to drilling-induced formation distur-
bance.
Comparison of Units
To determine if differences exist between commercially available units, one well was logged with two
different units. Care was taken to ensure both units were properly zeroed and had reached thermal equilib-
rium. The logs (Figure 41) from the two units agree within the manufacturer's specifications of +5 percent
57
-------
RESPONSE TO ABRUPT CONTACT
CALCULATED
* MEASURED
23496789 10
APPARENT CONDUCTIVITY (mS/m)
FIGURE 37. Response of EM-39 to Abrupt Contact.
Discussion - Evaluation of Induction Tool
The EM-39 can effectively measure formation conductivity. When proper attention is paid to calibra-
tion, these measurements are accurate to within +5 percent. In most situations, the instrument is not af-
fected by temperature variations. The minimum bed thickness required by the instrument to accurately
measure electrical conductivity is 4 m. Thin beds can be detected if the conductivity contrast between
adjacent beds is large enough. For layers thinner than 4 m, an ambiguity exists in determining the layer
thickness and intrinsic conductivity. The effect of borehole fluid on the measurement is negligible for wells
up to at least 15 cm in diameter.
58
-------
NORMALIZED
RESPONSE
Q.
UJ
o
FIGURE 38. Response of EM-39 to Layers of Varying Thickness.
Layer Thickness in Meters is Indicated.
59
-------
THIN LAYER RESPONSE
LU
CO
CO
HI
tr
1 2
LAYER THICKNESS (M)
FIGURE 39. Response Versus Layer Thickness for EM-39.
60
-------
FORMATION
CONDUCTIVITY
(mS/m)
1 R
I O
1 7
18
19
g
T 20
CL
LLJ
Q
21
79
V\
24
0
20 4
io e
iO i
30 1
00
APPARENT
CONDUCTIVITY
(mS/m)
20 40 60 80 100
\\
\
FIGURE -JO. Example of Ambiguous Interpretations of Induction Logs
(dashed line - model 1; solid line - model 2).
61
-------
CONDUCTIVITY (mS/m)
0 100 200 300 400 500 600 700 800 900 1000
0
4
K 6
Q.
LLJ
Q
a
10
12
>
!
>
*
"i
^Hl
»,
- UN
-UN
r
IT 2
IT 1
.**
r*
^^
FIGURE 41. Comparison of Logs from Two Different EM-39 Units.
62
-------
SECTION 4
APPLICATION TO DETECTION OF CONTAMINANTS
BACKGROUND
To evaluate the usefulness of induction tools to locate contaminated intervals, a field investigation was
conducted. The Pittman Lateral in Henderson, Nevada, was used as the study site. The site has been used
by the U.S. Environmental Protection Agency and the Desert Research Institute to evaluate a wide varieu of
geophysical and ground-water sampling techniques. The source of the contamination is an industrial com-
plex located 2 km upgradient of the study area. The complex has been used intermittently for the lasi 40
years and has produced a plume of inorganic and organic contamination. The most contaminated water has
a significantly elevated electrical conductivity of 20,000 nmho/cm, compared to less contaminated water at
the site that has a conductivity of 5,800 nhmo/cm. In 1983, 24 wells were drilled at 61-m intervals along the
Pittman Lateral. The Lateral is approximately perpendicular to the local ground-water gradient. The wells
were drilled using the dual-tube reverse rotary air method. The 20-cm holes were completed with 10-cm
diameter PVC. A slotted screen was placed throughout the saturated zone. No backfill was used in the
saturated zone because the formation tended to collapse around the casing. This resulted in at least a 5-cm
disturbed zone around the well. The presence of a 5-cm disturbed zone is common around monitoring wells
unless special precautions are taken during the drilling and completion of the well. From the drilling, u is
known that the site consists of alluvial deposits 5 to 15m thick composed of sand and gravel overlying a
massive silt and clay deposit. The silt unit is part of the Tertiary Muddy Creek formation and is assumed to
act as an aquitard. Depth to water varies from 3 to 8 m along the Lateral.
Method 1 - Borehole Geophysical Logging
Many, but certainly not all, ground-water contamination problems are associated with a pore fluid that
has an anomalously high electrical conductivity. This will influence the electrical conductivity of the forma-
tion, which can be measured with an induction log. Induction tools can only measure the electrical conduc-
tivity of the formation. Although this is influenced by the conductivity of the pore fluid, there are oilier
significant factors that also influence formation electrical conductivity. A simple model of the electrical
conductivity of the formation was presented in the section on the single-well electrical tracer tesi. For
convenience. Eq. (20a) has been repeated here:
63
-------
a = tortuosiiy. approximately 1 for unconsolidated sands (Jackson et al.. 1978)
m = cementation factor, approximately 1.5 for unconsolidated sands (Jackson et al , 1978)
af = electrical conductivity of the pore fluid
9 = porosity
This shows that m addition to the electrical conductivity of the pore fluid, changes in porosity, tor-
tuosity, and the conductivity of the formation matrix will affect the formation electrical conductivity and
hence, the induction log.
Because of the disturbed zone around the well, porosity tools that have a limited depth of mvesticanon,
such as gamma density and neutron absorption, will not yield accurate information in these wells. In addition
to this, Nevada and many other states severely restrict the use of borehole tools with radioactive sources in
water wells. At this site, sonic velocity logs could not be used to determine the porosity because of the low
sonic velocity and the variability of compaction typical of unconsolidated formations. Because of these
difficulties, porosity logs could not be obtained.
The electrical conductivity of the matrix is dependent in a complicated and not fully understood way
on the quantity, type and distribution of clays, and interaction between the clays and the pore fluid. A few
percent of a clay with a high cation exchange capacity can cause a factor of 5 change in formation electrical
conductivity (Kean et al.. 1984). Because such a !ow concentration of clay is not easily quantified and the
complex way in which clays influence the formation electrical conductivity, it is difficult to account for the
influence of clays. Natural gamma logging will detect some types of clays when they are m high enough
concentrations, but it is not possible to use a natural gamma log to remove the influence of clays on the
induction log unless significant amounts of other data on the cation exchange capacity of the clavs are
available (Waxman and Smits, 1968). Because of these difficulties, it was not generally possible to quantify
the influence of clays on induction logs.
Induction logs were run to determine the formation electrical conductivity (Figure 42). The increase in
formation electrical conductivity due to the contamination is seen in Wells 635 and 637 The contamination
causes an overall increase of the electrical conductivity in these wells. These wells are known to be the most
contaminated from chemical analysis which were run as part of another project. Several of the induction Iocs
(Wells 629. 633, 635. 637. and 639) show significant vertical variation in the formation electrical conductiv-
ity.
The vertical variations could be caused by vertical stratification of the contaminants or by vertical
changes in the formation. Natural gamma logs were run to see if these variations could be correlated with
lithology (Figure 43). Natural gamma logs measure the naturally occurring radiation emitted by the forma-
tion. Because clays tend to retain naturally occurring radioisotopes, an increase in the natural gamma log is
usually associated with an increase m clay content. The natural gamma logs show considerable vertical and
horizontal variability. However, a relationship that is common to the saturated zone in all the wells is that the
64
-------
FORMATION ELECTRICAL CONDUCTIVITY
621 623 625 627 629 631 633 635 637 639
641
ON
0
8-
10-
15-
to-
0 1200
HORIZONTAL SCALE (m)
I
100
200
MUDDY CREEK FORMATION
FIGURE 42. Induction Logs at Henderson, Nevada.
-------
NATURAL GAMMA RADIATION
621 623 625 627 629 631 633 635 637 639 641
6-
*"* <
'>-'
t 10-
o
18-
20-
MATURAL QAIIMA (CP8)
60 300
HORIZONTAL SCALE (m)
I
0
too
200
MUDDY CREEK FORMATION
FIGURE 43. Natural Gamma Logs at Henderson. Nevada.
-------
natural gamma log and the induction log are inversely correlated. This suggests that there is a strong
lithologic influence on the induction logs. A likely interpretation is that as the clay content increases (indi-
cated by an increase in the natural gamma log), the porosity of the formation decreases due to small clay
panicles filling the pores. The decrease in porosity will cause the formation conductivity (indicated by the
induction log) to decrease because there is less fluid to conduct the electrical current. Because of the high
electrical conductivity of the pore fluid, conduction by the pore fluid has more of an influence on the
formation conductivity than the matrix conductivity, which probably increases with the addition of clay to
the formation.
Because of the complicated relationships between clay content, natural gamma emissions and forma-
tion conductivity, it is difficult to use the natural gamma log to qualitatively remove the effects of lithology
from the induction logs. The vertically averaged formation conductivity is higher in Wells 635 and 637,
which are in the contaminant plume, and can be used as an indicator of contamination. The vertical vari-
ation shown on the logs is interpreted to be more of an indication of lithology than the pore-fluid conductiv-
ity. To verify this interpretation, two other methods were considered to sample the pore fluid from discrete
zones.
Method 2 - Pumping of Discrete Intervals
In an attempt to determine the vertical vanation of pore-fluid chemistry, a pump with an inflatable
straddle packer was used. The packer has two 10-cm bladders located 10 cm apart surrounding the pump
intake. The ability of the bladders to restrict the vertical movement of fluid in the casing was demonstrated
by the inability of the pump to deliver fluid from a nonperforated segment of casing which was submersed in
a water bath. Because of the well construction, it was suspected that piping could occur along the outside of
the casing. This would permit fluid from the main portion of the borehole to enter the pump even though
that interval was packed-off. To evaluate this possibility, a tracer test was performed.
The packer/pump assembly was set in the well and a tracer (Rhodamme-WT) was introduced into the
well above the packer (Figure 44). The borehole fluid above the packer was circulated with a pump on the
surface to evenly distribute the tracer in the borehole. The fluid in the circulating circuit was monitored to
determine when this occurred. After the tracer was evenly distributed, the packer isolated pump was oper-
ated continuously to collect samples.
The concentration of the tracer in the sample indicates how much of the sample is coming from the
portion of the well above the packer. Presumably, an equal portion of the sample is coming from below the
packer where there is no tracer. Therefore, to determine how much of the sample is coming from the well, it
is necessary to compare the concentration of the tracer in the well to twice the concentration of the tracer in
the sample. This is shown in Figure 45. The results indicate that after two minutes of pumping. 40 percent of
the sample comes from the packed-off portion of the well. After seven minutes, essentially all of the sample
is coming from the well by movement through the disturbed zone. This suggests a channel of high hydraulic
conductivity around the well bore. This could easily occur because of the 5-cm disturbed zone around the
well. The same situauon would occur if a gravel pack, which would presumably be of higher hydraulic
conductivity than the formation, had been installed.
67
-------
Flow Around Packer
Sample
Pump
Inlet
Packers
Disturbed Zone
FIGURE 44. Experimental Setup for Tracer Test.
68
-------
SAMPLE FROM PACKED INTERVAL
0.0
TIME (MIN)
FIGURE 45. Tracer Concentration Versus Time.
The results of the tracer test suggest that it is not possible to obtain samples of short discrete intervals
without some kind of a seal at the ends of the intervals between the casing and the formation. Since most
monitoring wells are not completed with sealed-off intervals, the method of pumping with a straddle packer
has limited application.
Method 3 - Dilution Sampling
A third technique was developed to investigate the possibility of stratified pore fluid. With the dilution
sampling method, a segment of the well is isolated with a straddle packer. An electrically anomalous tracer is
then injected into the packed-off segment. The tracer concentration decreases as dilution and advective
flow of ground water replace the fluid in the segment. When the fluid electrical conductivity in the secment
stabilizes, the fluid in the segment is considered to be representative of the adjacent pore fluid. The same
packer as used in the pumping from discrete zone method was used.
Because of the level of contamination associated with the ground water at the study site, fresh water
(low electrical conductivity) was used as a tracer. The method was employed on Well 635 because the
alternative to the previously discussed interpretation is that this well is stratified. Measurements were made
69
-------
starting below the water surface and continuing along the entire screened length, at intervals between 0.5
and 1.0 m. Experimental procedure consisted of setting the downhole tool at the desired depth, inflating the
bladders, and noting the background electrical conductivity. An experiment was initiated by pumping fresh
water into the borehole segment until the electrical conductivity within this segment decreased by at least a
factor of two. The dilution of the fresh water by native pore fluid was then monitored at the surface by
recording the electrical conductivity as a function of time. An experiment was considered complete when
the electrical conductivity of the borehole fluid in the packed-off segment had stabilized. When this oc-
curred, a final measurement of electrical conductivity was made. The downhole tool was then removed from
the well, and the electrical conductivity cell and meter were calibrated using prepared standards. Thus,
calibration curves were generated for each dilution experiment as a means of removing the effects of instru-
ment drift from the final measurement of borehole fluid conductivity.
Figure 46 is a plot of the dilution curves at varied depths within the test well before the cell was
calibrated at each depth. Notice that the conductivity has stabilized at the end of each measurement. The
different recovery rates are due to different rates of transport of the tracer from the borehole. Figure 47
compares the pore-fluid electrical conductivity to the formation electrical conductivity. The final value for
the pore-fluid electrical conductivity as measured at each depth interval is within +5 percent of the average '
value. This is considered to be within the error range of the measurement technique. This indicates that: 1)
either the stratification of electrically anomalous pore fluid is minimal; or 2) that the movement of fluid
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FIGURE 46. Dilution Curves Versus Time for Various Depths for Dilution Sampling Method.
70
-------
2
I
111
Q
2-
4-
6-
8-
10-
12-
ELECTRICAL CONDUCTIVITY
200 400 600 800 1000 1200
FORMATION (mS/m)
PORE FLUID (>iS/m)
FIGURE 47. Comparison of Electrical Conductivity of the Pore Fluid and Formation in Well 635.
through the disturbed zone surrounding the borehole is such that any pore-fluid stratification is masked.
Given the short length of the wells and the geologic environment, it is considered unlikely that significant
vertical differences in head existed in the interval adjacent to the well. This reduces the possibility of vertical
mixing in the disturbed zone. Hence, the pore fluid is not considered to have significant stratification.
71
-------
SECTION 5
INDUCED POLARIZATION
BACKGROUND
Due to the large influence of clays on log interpretation, it was desirable to investigate the use of an
additional clay indicator log besides the natural gamma log. Ideally, such a log would have a depth of"
investigation similar to the induction log and would be sensitive to the electrical influence of clays. The
Induced Polarization (IP) log meets this criteria and, hence, was selected for consideration.
The IP effect is an electrical phenomenon that can be thought of as the ability of the formation to
temporarily store electrical energy. In environments that do not have metallic mineralization, the predomi-
nate cause of the IP effect is membrane polarization. If electrical current is applied across a fluid-formation
contact, the positive ions are attracted towards the contact and the negative ions are repelled from the
contact. After the current is turned off. the ions take a short amount of time to return to the initial condition.
During this time, a current is created in the formation by the movement of the ions. The process is strongly
dependent on the size of the pores through which the current is being conducted (Telford et al , 1976). The
membrane IP effect is largest when clay minerals with small pore sizes are present (Keller and Fnschknecht,
1966). The IP effect is related to cation exchange capacity (Telford et al., 1976), which also controls the
electrical conductivity of clay-bearing formations (Waxman and Smits. 1968). The relationship between
clay content and IP is nonlinear, reaching a maximum value at some percentage clay content and then
decreasing with additional clay content. The percentage of clay corresponding to the IP maximum is in-
fluenced by the pore-fluid chemistry, and clay type and distribution (Roy and Elliott. 1980; Worthmgton
and Collar. 1982; Vacquier et al., 1957). No model has been developed that can qualitatively account for all
of these effects without the use of extensive measurements on core samples (Park and Dickey, 1989; Atwa-
ter. 1986). Negative IP signatures occur when the current after turn-off flows in the opposite direction of the
applied current and can occur when there are polarizable bodies with limited dimensions (Sumner. 1976;
Benin. 1968; Nabighian and Elliot, 1976; Roy and Elliot. 1980).
The IP effect can be measured in the frequency domain by measuring the formation resistivity at
several different frequencies. It can also be measured in the time domain by measuring the decay of current
after a direct current is abruptly turned off. In the time domain, results are commonly expressed as charge-
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ability, which is the percentage of current remaining during a given time window after the abrupt turn-off In
theory, the two measurement methods give identical results, but due to practical limitations on the type and
amount of data that can be collected, it is generally not possible to directly transform field data from one
form to the other.
INSTRUMENTATION A':,.,
A f fty
For the purposes of evaluating the borehole IP method for use in sfialtow contaminate investigations it
was desirable for the instrumentation to have the following characteristics: 1) a depth of investigation com-
parable to a readily as a liable induction tool; and 2) nonpolanzmg electrodes. The first requirement was
necessary so that the induction logs and IP logs could be readily compared. To meet this in the highly
conductive fluids (up to 18.000 uS/cm) at the Henderson study site (see Section 4), it was desirable to
separate the electrodes from one another with an inflatable packer to block current flow through the
borehole. The nonpolanzmg potential electrodes were desirable because of the large concentration of metal
ions in the fluid at the Henderson study site and the uncertainty to their influence on traditional lead elec-
trodes. Electrochemical effects across the porous electrodes were reduced by stacking the signal with alter-
nating polarity. :-
A review of commercially available IP borehole tools determined that such a tool did not exist. Com-
mercially available tools had lead electrodes with no way to block current flow in the borehole. It was
determined that an IP tool could be constructed that met the desired criteria for less than the cost of the
commercially available tools; primarily because the commercial tools were designed for greater depths and
pressures than required for this project.
A tool was constructed that was based on a Wenner array with an "a" spacing of 50 cm. Nonpolanzmg
porous pots (Cu-Cu2SO4) were used for the potential electrodes, lead was used for the current electrodes.
Electrical conduction through the borehole fluid was minimized by the use of inflatable packers which
isolated the electrodes. The wires to the potential electrodes and the wires to the current electrodes were run
in separate shielded leads which were held 6 cm apart by nylon spacers. A Scmtrex IPC-9/200 time domain
transmitter and IPR-10A receiver was used. To make a measurement, it was first necessary to ensure that
the tool was located in a perforated section of casing. This was accomplished by use of a preliminary survey
with a borehole television camera. The tool was lowered to the desired depth, the packers were inflated, and
and the IP response was measured with the Scmtrex unit on the surface. Although this tool is not suitable for
deep holes, it was felt that the use of the packers and porous pots would diminish problems related to
excessive current flow in the borehole and electrode polarization. The time windows during which the char-
geability was measured are listed in Table 2.
FIELD EFFORT
Two wells (633A and 633D) were selected for study because they have long perforated intervals and
interesting stratigraphy. Natural gamma, induction, and IP logs were run in both wells (Figures 48 and 49),
which are located 15 m apart. Six IP logs, one for each time window, are plotted for each well. The major
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TABLE 2. INDUCED POLARIZATION TIME WINDOWS
Window Stan (ms) End (ms)
130 390
390 650
650 910
910 1170
1170 1430
1430 1690
features on all the logs occur in both wells, indicating that measurements are representative of the formation.
Minor differences between the logs in the two wells are expected because of spatial variability.
The natural gamma and induction logs clearly show the occurrence of separate units. On the IP log. it
is more difficult to discern separate units. In addition, the IP log does not correlate well with either the
induction or the natural gamma log. If it were not for the correlation of the IP log between the two wells, the:
reliability of the IP log would be in question. Had additional funds been available, other electrode arrays
would have been tried which may have affected the ability of the IP system to identify units.
To investigate the influence of a zone with a different pore-fluid conductivity than the surrounding
formation, an injection experiment was performed. A half of a cubic meter of water with an electrical
conductivity of 490 jiS/cm was injected between two inflated packers in the interval 8.5 to 9.7 meters. The
native pore fluid has an electrical conductivity on the order of 12,000 jiS/cm. Induction logs run before and
after the injection (Figure 50) clearly show that the injected fluid has entered the formation and displaced
the native pore fluid. This has resulted in the change in formation electrical conductivity, which is noted on
the induction logs in this interval. Some smearing of the injection zone has occurred on the logs due to
vertical fluid flow in the formation during injection and vertical averaging by the induction tool.
The IP log was run three times before the injection to assure that the measurement was repeatable
(Figure 51). Some drift is evident, but the form of the log is consistent for all three runs. After the injection,
the IP log was run again (Figure 51). The major difference between the before and after injection logs is the
development of a trough centered on the injection zone which is bounded by two peaks. A lower IP response
was noted below 13 m after the injection, but this is attributed to instrument drift because the general shape
of the log is unchanged. This is an analogous geometry to the IP effect of a surface Wenner array traversing a
low conductivity vertical dike. This was modeled by Elliot (1971) and was found to produce the same effect
observed in this study of a trough bordered by peaks.
Both examples demonstrate the complexity of interpreting the IP log. The injection example demon-
strates the significant dependence of IP on pore fluid conductivity. This makes it difficult to separate the
effect of changes in clay content and type from changes in pore-fluid chemistry. This difficulty is com-
pounded because of the nonlinear complex influence of clay and pore-fluid chemistry (Worthmgton and
Collar. 1982) Both of the above examples demonstrate that IP effect is also strongly influenced not just by
74
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CHARGEABILITY (Vs/Vp)
0 10 20 30 40 50 60
6
10
12
E 14
o.
ui
O 16
18
20.
22-
24-
Tlme Window
\\//7/
NATURAL GAMMA (CPS)
75 100 125 150 175 200
CONDUCTIVITY (mS/m)
24-
100 200 300 400 500
24-
FIGURE 48. Log Suite for Well 633A.
-------
CHARGEABILITY (Vs/Vp)
0 10 20 30 40 50 60
6
10
12
14
t
LU
Q 16
18-
20-
22-
24-
NATURAL GAMMA (CPS)
75 100 125 150 175 200
CONDUCTIVITY (mS/m)
100 200 300 400 500
6
10
12
24-
I
EL
111
Q 16
18
20
22-
24-
FIGURE 49. Log Suite lor Well 63313.
-------
450'
400-
_L
_L
_L
PRE INJECTION
- ~ 20 MINUTES AFTER INJECTION
- - 120 MINUTES AFTER INJECTION
10
DEPTH (m)
FIGURE 50. Induction Logs Before and After Injection.
40
POST INJECTION
PRE INJECTION (multiple runs)
10
16
FIGURE 51. Induced Polarization Logs Before and After Injection.
77
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the formation adjacent to the logging tool, but also by the contrast to units above and below the tool. This
explains why the IP log does not indicate similar units as the induction and natural gamma log; instead, it is
strongly influenced by the contrast of adjoining units.
DISCUSSION
This work has highlighted several significant shortcomings of the IP log m relation to shallow ground-
water contamination investigations. A significant limitation is the need for a nonconductive perforated cas-
ing or open hole. Most monitoring wells are quickly cased with short-perforated intervals, which restricts the
utility of the borehole IP method. By contrast, the induction and natural gamma logs can be used m a
nonperforated. nonconductive casing. The IP response of a formation is also dependent on a wide number
of parameters (clay type, content and distribution; pore-fluid chemistry; adjacent units), which make a
unique interpretation very difficult even when other logs are available. Some investigations have sorted out
these effects for specific units by the use of extensive core studies, but it is not clear that this approach is cost
effective for the shallow wells typical of ground-water contamination investigations. Because ihe results of
this initial work were not encouraged, the IP method was not pursued further during this project.
78
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SECTION 6
CONCLUSIONS
For the determination of hydraulic properties in unconsolidated formations, the borehole geoph>sical
methods that are available are limited. The use of Stoneley wave attenuation methods to determine hydrau-
lic conductivity is limited by the need to utilize a sonic tool with a source of considerably lower frequency
than is commercially available. This method is also very equipment intensive and the presence of casing
creates additional difficulties. Methods that utilize the natural flow of fluid through the well to determine the
hydraulic conductivity of the formation were not successful because of the influence of near-hole drilling
disturbance and the difficulties of measuring small changes in the flow through the well.
The single-well electrical tracer method, which was developed as part of this cooperative agreement,
offers several advantages over the other methods that were considered, and other well known conventional
methods as well. The single-well electrical tracer method has the ability to determine the vertical distribution
of both hydraulic conductivity and porosity, even in wells with a large disturbed annulus, and can be used in
unconsolidated formations, even if clays are present.
It is difficult to determine the electrical conductivity of the pore fluid if the formation contains clays.
The combination of the natural gamma and induction log can be used to suggest zones of varying pore fluid.
but does not yield quantitative values of the pore-fluid electrical conductivity. The induced polarization log
is of limited value because of the need for a nonconductive perforated casing or open hole, and because of
the many interdependent parameters which effect it. The dilution sampling method, although tedious, is an
effective method to determine pore-fluid properties in a perforated or open hole.
79
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