&EPA
United States
Environmental Protection
Agency
Robert S. Kerr Environmental
Research Laboratory
Ada OK 74820
EPA/600/2-86/062
July 1986
Research and Development
Performance and
Analysis of Aquifer
Tracer Tests with
implications for
Contaminant
Transport Modeling
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EPA/600/2-86/062
July 1986
PERFORMANCE AND ANALYSIS OF AQUIFER TRACER TESTS
WITH IMPLICATIONS FOR CONTAMINANT
TRANSPORT MODELING
Fred J. Molz, Oktay Gliven, Joel G. Melville
Civil Engineering Department
Auburn University, AL 36849
and
Joseph F. Keely
Robert S. Kerr Environmental Research Laboratory
U.S. Environmental Protection Agency
P.O. Box 1198, Ada, OK 74820
CR-810704
Project Officer
Joseph F. Keely
Robert S. Kerr Environmental Research Laboratory
Ada, OK 74820
U.S. Environmental '•.
; vs*;lon 5, Library {:'.'
,00 t!. Dearborn Str-. . -
> £0604
ROBERT S. KERR ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
ADA, OK 74820
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DISCLAIMER
The information in this document has been funded wholly or in part
by the United States Environmental Protection Agency under assistance
agreement number CR-810704 to Auburn University. It has been subject to
the Agency's peer and administrative review, and it has been approved
for publication as an EPA document.
11
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FOREWORD
The U.S. Environmental Protection Agency was established to coordinate
administration of the major Federal programs designed to protect the quality
of our environment.
An important part of the Agency's effort involves the search for
information about environmental problems, management techniques and new
technologies through which optimum use of the Nation's land and water resources
can be assured and the threat pollution poses to the welfare of the American
people can be minimized.
EPA's Office of Research and Development conducts this search through a
nationwide network of research facilities.
As one of the facilities, the Robert S. Kerr Environmental Research
Laboratory is the Agency's center of expertise for investigation of the soil
and subsurface environment. Personnel at the laboratory are responsible for
management of research programs to: (a) determine the fate, transport and
transformation rates of pollutants in the soil, the unsaturated zone and the
saturated zones of the subsurface environment; (b) define the processes to be
used in characterizing the soil and subsurface environment as a receptor of
pollutants; (c) develop techniques for predicting the effect of pollutants on
ground water, soil and indigenous organisms; and (d) define and demonstrate
the applicability and limitations of using natural processes, indigenous to
the soil and subsurface environment, for the protection of this resource.
This report contributes to that knowledge which is essential in order
for EPA to establish and enforce pollution control standards which are
reasonable, cost effective and provide adequate environmental protection for
the American public.
Clinton W. Hall
Director
Robert S. Kerr Environmental
Research Laboratory
m
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Abstract
Due to worsening national problems, hydrologists are being asked to
identify, assess or even anticipate situations involving groundwater con-
tamination, and a large fraction of the regulation activities of the U.S.
Environmental Protection Agency is in the groundwater area. In both regula-
tion and assessment, increasing use is being made of complex mathematical
models that are solved with the aid of a digital computer. Typically, such
models are collections of partial differential equations that contain a
number of parameters which represent aquifer physical properties and must be
measured in the field. Of the various parameters involved, the hydraulic
conductivity distribution is of major importance. Other parameters such as
those relating to sorption, hydrodynamic dispersioon, and chemical/biologi-
cal transformation are important also, but hydraulic conductivity is more
fundamental because combined with head gradient and porosity it relates to
where the water is moving and how fast. Therefore, this communication is
devoted mainly to the conceptualization and measurement of hydraulic
conductivity distributions and the relationship of such measurements to
dispersion (spreading) of contaminants in aquifers.
For the most part, contemporary modeling technology is built around
two-dimensional models having physical properties, such as transmissivity,
that are averaged over the vertical thickness of the aquifer. In such a
formulation, the major aquifer property related to contaminant spreading is
forced to be longitudinal dispersivity. This is not due to any fundamental
theoretical limitation. The major limitation is that dependable and
economical field approaches for measuring vertically-variable hydraulic
iv
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conductivity distributions are not available. In the absence of such data,
one has no choice in a modeling sense but to use some type of vertically-
averaged advection-dispersion approach built around full aquifer longitudi-
nal dispersivities.
In order to begin to overcome this limitation, a series of single-well
and two-well tracer tests were performed at a field site near Mobile,
Alabama, and a major objective of this communication is to describe these
tracer tests and discuss some practical implications of the results with
regard to modeling of contaminant dispersion in aquifers. The tests utilize
multilevel sampling wells which have to be designed and installed carefully.
Tracer test results along with theoretical studies suggest that the follow-
ing working conclusions are warranted.
I. Local longitudinal hydrodynamic dispersion plays a relatively
unimportant role in the transport of contaminants in aquifers.
Differential advection (shear flow) in the horizontal direction
is much more important.
II. The concept of full-aquifer dispersivity used in vertically-
averaged (area!) models will not be applicable over distances of
interest in most contamination problems. If one has no choice
but to apply a full-aquifer dispersion concept, the resulting
dispersivity will not represent a physical property of the
aquifer. Instead, it will be an ill-defined quantity that will
depend on the size and type of experiment used for its supposed
measurement.
III. Because of conclusion II, it makes no sense to perform tracer
tests aimed at measuring full-aquifer dispersivity. If an area!
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model is used, the modeler will end up adjusting the dispersivity
during the calibration process anyway, independent of the
measured value.
IV. When tracer tests are performed, they should be aimed at
determining the hydraulic conductivity distribution. Both our
theoretical and experimental work have indicated that the vari-
ation of horizontal hydraulic conductivity with respect to
vertical position is a key aquifer property related to spreading
of contaminants.
V. Two- and three-dimensional modeling approaches should be utilized
which emphasize variable advection rates in the horizontal
direction and hydrodynamic dispersion in the transverse direc-
tions along with sorption and microbial/chemical degradation.
VI. In order to handle the more advection-dominated flow systems
described in conclusion V, one will have to utilize or develop
numerical algorithms that are more resistant to numerical
dispersion than those utilized in the standard dispersion-
dominated models.
Much of contemporary modeling technology related to contaminant trans-
port may be viewed as an attempt to apply vertically homogeneous aquifer
concepts to real aquifers. Real aquifers are not homogeneous, but they are
not perfectly stratified either. What is being suggested, therefore, is
that the time may have arrived to begin changing from a homogeneous to a
vertically-stratified concept when dealing with contaminant transport,
realizing fully that such an approach will be interim in nature and not
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totally correct. Field calibration will still be required. However, the
performance and simulation of several single- and two-well tracer tests
suggests that the stratified approach is much more compatible with valid
physical concepts, and at least in some cases results in a mathematical
model that has a degree of true predictive ability.
An obvious implication of the study reported herein is that any type of
groundwater contamination analysis and reclamation plan will be difficult,
expensive and probably unable to meet all of the desired objectives in a
reasonable time frame. Therefore, one can not overemphasize the advantages
of preventing such pollution whenever it is feasible.
vn
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CONTENTS
Foreword iii
Abstract iv
Figures x
Tables xii
1. Introduction 1
EPA's Site-Specific Modeling Efforts 2
EPA's Generic Modeling Efforts 3
Subsurface Transport Models 4
The Hydraulic Conductivity Distribution 6
The Mechanisms of Dispersion 9
Simulation of Advection-Dispersion Processes 11
2. Types of Tracer Tests 18
3. Design and Construction of Multilevel Sampling Wells 23
4. Performance and Results of Single-Well and Two-Well
Tracer Tests at the Mobile Site 37
Single-Well Test 44
Two-Well Test 52
5. Computer Simulation of Single-Well and Two-Well
Test Results 61
Simulation of Single-Well Tests 61
Simulation of Two-Well Tests 68
6. Discussion and Conclusions 79
References 86
IX
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FIGURES
Number Page
1 Hypothetical velocity distribution 14
2 Schematic diagram of contaminant concentrations 15
3 Vertical cross-sectional diagram of single well test 19
4 Two-well test geometry in a stratified aquifer 22
5 Various types of multilevel sampling systems 25
6 Pickens et al. multi-level sampling/observation well 26
7 Moltyaner and Killey multilevel, dry, access tube system
for use with radioactive tracers 27
8 Schematic diagram of the basic construction plan for a
multilevel sampling well with a removable insert 29
9 Multilevel sampling well with sampling zones isolated with
inflatable packers and silicone rubber plugs 31
10 Details concerning the geometry and installation of
inflatable packers 32
11 Diagram of a completed multilevel sampling well 33
12 Diagram illustrating the scheme for causing mixing in the
various isolated sampling zones and obtaining samples
for laboratory analysis 34
13 Diagram illustrating what may happen during drilling and
installation of various types of screens 35
14 Possible beneficial effects of drilling mud left behind
in the formation 36
15 Diagram of the subsurface hydrologic system at the Mobile site .... 39
16 Piping and valving scheme associated with pumping wells at
the Mobile site 42
17 Diagram showing the main features of the surface hydraulic
system used in the single- and two-well tracer tests at the
Mobile site • 43
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18 Bromide concentration in the injection/withdrawal well (12) 46
19 Bromide concentration breakthrough curves at the seven
levels of well E3 during experiment #4 47
20 Electrical conductivity breakthrough curves at various
levels of well E3 during experiment #4 48
21 Inferred normalized hydraulic conductivity distribution 53
22 Injection well tracer concentration versus time during the
first 80 hours of the two-well test 56
23 Measured tracer concentration versus 'time in the withdrawal
well during the two-well test 57
24 Measured and predicted breakthrough curves at the 7 levels
of observation well E3 59
25 Normalized hydraulic conductivity distribution inferred from
travel times measured during the two-well test 60
26 Hydraulic conductivity profile 63
27 Unsteady injection concentration during the Pickens and Grisak
(1981) single-well field experiment 64
28 Comparison of SWADM results with field data for the flow-weighted
concentration from an observation well one meter from the
injection-withdrawal well 66
29 Comparison of SWADM results with field data for the flow-weighted
concentration from an observation well two meters from the
injection-withdrawal well 67
30 Comparison of SWADM results with field data for the concentration
leaving the injection-withdrawal well 69
31 Results of various simulations of the two-well test 73
32 Calculated tracer concentration versus time in the withdrawal
well 76
33 Comparison of measured and calculated tracer concentration
versus time in the withdrawal well 78
34 Preliminary results of four single well tests performed at the
Mobile site 83
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TABLES
Number Page
1 Particle size distribution data for the seven disturbed
cores obtained during construction of well E3 41
2 Sampling zone elevations, arrival times for fifty
percent breakthrough, apparent dispersivity values
and inferred normalized hydraulic conductivity
values for experiment #4 49
3 Two-well test parameters supplied to Geo-Trans, Inc.
for their 3-dirnensional simulations based on the
advection-dispersion equation 71
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Introduction
Due to worsening national problems and potential problems relating to
industrial waste disposal, municipal waste disposal, radioactive waste dis-
posal and others, there is increasing pressure on hydrologists to identify,
assess or even anticipate situations involving groundwater contamination.
In order to meet these demands, subsurface hydrologists have turned
increasingly to the use of complex mathematical models that are solved with
the aid of a digital computer. Some of the principal areas where
mathematical models can now be used to assist in the management of EPA's
groundwater protection programs are:
(1) appraising the physical extent, and chemical and biological
quality, of groundwater reservoirs (e.g., for planning purposes),
(2) assessing the potential impact of domestic, agricultural, and
industrial practices (e.g., for permit issuance, EIS's, etc.),
(3) evaluating the probable outcome of remedial actions at hazardous
waste sites, and of aquifer restoration techniques generally,
(4) providing exposure estimates and risk assessments for
health-effects studies, and
(5) policy formulation (e.g., banning decisions, performance
standards).
These activities can be broadly categorized as being either site-specific or
generic modeling efforts, and both categories can be further subdivided into
point-source or nonpoint-source problems. The success of these efforts
depends on the accuracy and efficiency with which the natural processes
controlling the behavior of groundwater, and the chemical and biological
species it transports, are simulated. The accuracy and efficiency of the
simulations, in turn, are heavily dependent on the applicability of the
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assumptions and simplifications adopted in the model(s), and on subjective
judgments made by the modeler and management.
EPA's Site-Specific Modeling Efforts
Whether for permit issuance, investigation of potential problems, or
remediation of proven contamination, site-specific models are necessary for
the Agency to fulfill its mandate under a number of major environment:.!
statutes. The National Environmental Policy Act (1970) stipulates a need to
show the impact of major construction activities in Environmental Impact
Statements and potential impacts are often projected by the use of
mathematical models. The Underground Injection Control (DIG) program, which
originated in the Safe Drinking Water Act (1974) (SDWA) and is now subject
to provisions of the Resource Conservation and Recovery Act (1984 Amend-
ments) (RCRA), requires an evaluation of the potential for excessive
pressure build-up and contaminant movement out of the injection zone.
Mathematical models are the primary mechanism for the required evaluation,
due in part to the difficulty of installing monitoring wells several
thousand feet deep.
UIC also calls for determinations of which aquifers serve, or could
serve, as underground sources of drinking water (USDW's), based on a lower
quality limit of 10,000 ppm total dissolved solids. Here, modeling has been
found to be a useful adjunct to gathering and interpreting field data, such
as in the U.S. Geological Survey's efforts to assist EPA in determining
USDW's (e.g., the RASA program). Another SDWA program, for the designation
of Sole Source Aquifers (SSA), has frequently employed the use of models for
establishing and managing water-quality goals. Designation of the Spokane
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Valley - Rathdrum Prairie SSA, for instance, included an evaluation of
nonpoint-sources of nitrates with a groundwater model developed for EPA by
the USGS.
Some of the most difficult site-specific problems facing the Agency
involve hazardous waste sites falling under the purviews of RCRA and
CERCLA/Superfund. Associated with most of these sites is a complex array of
chemical wastes and the potential for groundwater contamination. Their
hydrogeologic settings usually appear quite complicated when examined at the
scale appropriate for technical assessments and remediation efforts (e.g.,
100's to 1000's of feet). Groundwater models are used to assist in the
organization and interpretation of data gathered during remedial investiga-
tions, the prediction of potential contaminant transport pathways and rates
of migration, the setting of Alternate Concentration Limits, the design and
comparison of remedial alternatives, and the evaluation of the performance
of final ('as built1) designs at hazardous waste sites. They are also used
to help determine the adequacy of monitoring and compliance networks, and to
determine the feasibility of meeting clean-up targets.
EPA's Generic Modeling Efforts
There are a number of instances where the Agency has limited data or
other constraints, such that site-specific modeling is not feasible. As a
result, many decisions are made with the assistance of generic modeling
efforts. Generic efforts utilize analytical models, as opposed to numerical
models, to a much greater degree than occurs in site-specific efforts. This
is a logical consequence of the simplified mathematics of analytical models,
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the significantly greater data requirements of numerical models, and the
higher costs of numerical simulations.
The Agency has many statutory responsibilities which benefit from
generic modeling, including the estimation of potential environmental
exposures, and their integration with dose-response models to yield
health-based risk assessments. These are necessary, for example, in issuing
compound-specific rulings on products subject to pre-registrati on require-
ments under the Toxic Substances Control Act and the Federal Insecticide,
Fungicide, and Rodenticide Act. More generalized policy formulation
activities also benefit from generic modeling efforts. Examples include
making policy decisions about land disposal 'banning,' preparing Technical
Enforcement Guidance Documents (i.e., for monitoring network designs), and
'delisting1 under RCRA.
Subsurface Transport Models
The most common types of modern groundwater transport models are a
collection of partial differential equations and other mathematical/physical
relationships that embody our best understanding of the system of interest,
which in the present context is an aquifer. Virtually all groundwater
models contain a number of parameters, which are simply numbers or functions
that represent the physical and chemical properties of an aquifer and the
aqueous solution that it contains. In order to apply a model to a
particular problem situation, one must specify all the parameters (length,
width, thickness, hydraulic conductivity, dispersivity, retardation
coefficient, etc.) that pertain to 1}hat particular system. This is what
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distinguishes one system from another in the application of a mathematical
model.
In the actual process of using a mathematical model, the user puts all
necessary information into the model (geometry, physical properties, initial
and boundary conditions), and a computer is employed to rapidly solve the
resulting equations which generates the model output. Output, for example,
might include a predicted contaminant concentration distribution 10 years in
the future. Presently, this predictive process is far from satisfactory
(Konikow, 1986). Our understanding of all the physical and chemical
phenomena involved is imperfect, and there are immense difficulties in
measuring and specifying all of the required input data. If accurate
information is not put into a mathematical model, one cannot expect accurate
information to come out.
Over the past decade, a significant number of scientists have concluded
that the single most important barrier to developing an improved ability to
simulate groundwater contamination problems is our inability to measure,
specify and, therefore, understand the type of hydraulic conductivity
distribution that occurs in natural aquifers (Smith and Schwartz, 1981).
This is not to say that other parameters such as those relating to sorption,
hydrodynamic dispersion and chemical/biological transformations are not
important. It is simply that the hydraulic conductivity is more
fundamental, because together with the hydraulic head distribution and
porosity, it is the physical property that relates to where and how fast the
groundwater is moving. If one does not have the ability to specify the
location of a parcel of water at a given time, one can hardly specify what
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is going on chemically and biologically in that water. Therefore, this
communication is devoted mainly to the conceptualization and measurement of
hydraulic conductivity distributions and the relationship of such measure-
ments to dispersion (spreading) of contaminants in aquifers.
The Hydraulic Conductivity Distribution
Measurement of hydraulic conductivity is difficult because of aquifer
location (i.e., below the ground surface) and the nonhomogeneity of most
natural aquifers. (It is not uncommon for hydraulic conductivity to vary by
P
a factor of 10 or more within a given subsurface hydrologic system (Freeze
and Cherry, 1979).) As discussed by Schwartz (1977), almost a continuously
increasing scale of heterogeneity can be visualized in most aquifers. The
heterogeneities arise due to variations in grain sizes and pore sizes,
permeability trends due to stratification and variations in the original
depositional environment, anisotropy, fractures, overall stratigraphic
framework and more (Alpay, 1972). Because of the range of many of these
variations and the unique physical, chemical and biological environments
found in the subsurface, it is difficult or impossible to study spatial
variability in a definitive way with laboratory experiments.
According to Philip (1980) field heterogeneity can be classified as
either deterministic or stochastic. Deterministic heterogeneity refers to
hydraulic conductivity variations that are sufficiently ordered to be
characterized by a set number of measurements, although in practice the
measurements may be difficult to make. Stochastic heterogeneity refers to
hydraulic conductivity changes that are essentially random, making it
pointless to try to measure then all. However, even these categories depend
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on scale of observation (problem size), because variations that can be
viewed collectively as stochastic on a sufficiently large scale (regional
scale) may have to be treated as deterministic on a smaller scale such as a
site-specific scale. In addition, stochastic variations are often embedded
in systematic trends (i.e., random variations within discrete strata).
Since a complete characterization of the spatial distribution of
hydraulic conductivity and hence a complete description of all the details
of the flow field in an aquifer are practically impossible, various
stochastic convection-dispersion models.for solute transport have been
proposed in recent years (e.g., Gelhar and Axness, 1983; Winter, 1982).
While these models may be useful under certain conditions, they also have
various limitations. Detailed discussions of the capabilities and
limitations of these models may be found in Gelhar et al. (1979), Matheron
and deMarsily (1980), Gelhar and Axness (1983), Dagan (1984), and Sposito,
Jury-and Gupta (1986). As reviewed in detail in the recent paper by
Sposito, Jury and Gupta (1986), all such models involve a conceptual
collection (ensemble) of statistically similar aquifers rather than a
specific real aquifer. Consequently, these stochastic models provide
results which are averages over the collection and, therefore, not directly
applicable to a single aquifer. In addition, only under very limited
conditions can measurements in a single real aquifer be related even
conceptually to the statistics of a collection of aquifers that contains the
real aquifer as one of its members. Essentially, the real aquifer must be
statistically homogeneous on the average and ergodic (Neuman, 1982; Sposito,
Jury and Gupta, 1986). Without going into details here, it is sufficient to
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say that such a condition is very restrictive and does not allow an aquifer
to have the type of general variability and persistent hydraulic conduc-
tivity trends that we believe are essential to understanding contaminant
transport, particularly in site-specific situations involving relatively
short travel distances. For these reasons and others, Sposito, Jury and
Gupta (1986) concluded that "much more theoretical research is required and
the stochastic convection-dispersion model does not yet warrant unqualified
use as a tool for physically based, quantitative applications of solute
transport theory to the management of solute movement at field scales."
In order to circumvent the fundamental difficulties of the stochastic
convection-dispersion approach discussed in the previous paragraph and to
deal at the same time with the problem of prediction uncertainty caused by
data limitations, Smith and Schwartz (1981) (see also Dagan, 1984) have
suggested the use of conditional simulations, a technique originally
developed in the field of geostatistics (see, e.g., Journel and Huijbregts,
1978). Recent developments in the application of geostatistical estimation
methodology in the groundwater field (Kitanidis and Vomvoris, 1983; Hoeksema
and Kitanidis, 1984) make this approach promising. The geostatistical
conditional simulations approach allows one to make direct use of all the
available field data in solute transport predictions for a given aquifer,
and also to provide estimates of the uncertainty in these predictions.
Using this technique, the known features of the aquifer and the flow are
taken into account in a deterministic manner while the unknown features are
approximated and dealt with in a probabilistic manner. A major difference
between this approach and the stochastic convection-dispersion model is that
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the geostatistical methodology takes into account the actual spatial
variations of aquifer properties by conditioning the simulations on the
available measurements while the aforementioned stochastic models make use
of the available data only to estimate the statistical structure of the
assumed aquifer collection (ensemble). In fact, the results provided by the
stochastic models referred may be viewed as being equivalent to the averages
of the results which would be provided by unconditional simulations of the
geostatistical approach. Due to the lack of conditioning, considerable
uncertainty may exist in the predictions of the stochastic models when
compared with the predictions of conditional simulations as indicated by the
results of Smith and Schwartz (1981) and Gu'ven (1986). While the
geostatistical approach does appear promising in dealing with problems of
solute transport, it is presently at an early stage of development and
considerable theoretical work, improved numerical procedures, improved field
measurement techniques and field verification studies are needed before any
routine application of this approach in the field would be practical. In
the meantime, interim approaches are required to advance our capability of
modeling solute transport. More will be said about one such interim
approach later.
The Mechanisms of Dispersion
In order to improve our capability of modeling solute transport, it is
very important to understand the major physical mechanisms which affect the
evolution and probable future of an existing groundwater contamination plume
or the future course of an anticipated plume. The catch-all name given to
the spreading of a contaminant in groundwater is dispersion, a term which is
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familiar to almost everyone. However, as illustrated in Figure 1, many
different phenomena contribute to the dispersion process in aquifers. The
horizontal extent of the hypothetical tracer plume in Figure 1 is determined
mainly by the elapsed travel time and the difference between the maximum and
minimum values of the horizontal advective velocities. These velocity
variations result primarily from the variations of hydraulic conductivity.
Dilution within the plume and along the plume boundaries is caused by
pore-scale mixing (local hydrodynamic dispersion) due in part to molecular
diffusion, velocity variations within each pore, and the overall tortuosity
of the flow path. In the hypothetical situation depicted in Figure 1, there
is an overall trend of hydraulic conductivity increase from the top towards
the bottom of the aquifer. Four minor trends, resulting in hydraulic
conductivity peaks in both the upper third and bottom third of the aquifer,
are evident also, with the lower peak being more pronounced. The plume
concentration distribution is determined to a large extent by these trends.
In addition, there are "wobbles" in the concentration distribution caused by
seepage velocity components in all directions at a scale smaller than the
scale of the minor trends noted above. Thus the actual concentration
distribution of the plume is determined by a combination of strata-scale
advective effects arising from the nonuniform velocity distribution and
pore-scale mixing effects caused by the concentration differences within the
plume and the basic nature of pore-scale flow. This pore-scale effect is
most pronounced at the plume boundaries because the concentration gradients
are largest there. In addition, wobbles in the concentration distribution
at an intra-stratum scale could, after a sufficient travel time, result in a
type of semi-local mixing, which some researchers have called macro-
dispersion (Gelhar and Axness, 1983). As the plume travels further
10
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downstream, the concentration gradients in the transverse direction would be
gradually smoothed out due to both hydrodynamic dispersion and seepage
velocity components in the transverse direction and a somewhat well-mixed
condition would develop at each streamwise station over the whole depth of
the aquifer after a sufficiently long travel time. However, the time
required for this behavior could be very large (see, e.g., Gelhar et al.,
1979; Matheron and deMarsily, 1980; Molz et al. 1983; Guven et al., 1984).
In many site-specific situations, such large travel times are usually not
involved, and variations of concentration over the depth of the aquifer are
expected to be an important consideration when dealing with particular
site-specific problems.
Simulation of Advection-Dispersion Processes
Historically, the field of subsurface hydrology developed mainly in
response to groundwater supply problems. To solve such problems there was
often little need to develop detailed information concerning the spatial
variability of hydraulic conductivity within a given aquifer. Knowledge of
the average transmissivity and storativity of the aquifer was adequate, along
with specification of the vertical aquifer boundaries (water table or
confining layers) and in some cases the lateral boundaries. For these
conditions, one-dimensional, horizontal, transient flow in a confined
homogeneous aquifer may be written as (Freeze and Cherry, 1979)
2
3 h _ S ah ,n
'
where x = length in the direction of flow, t = time, h = hydraulic head, S =
storativity and T = transmissivity. Typically, the average S and T values
would be determined by a pumping test utilizing fully-screened, fully-
penetrating pumping and observation wells (Freeze and Cherry, 1979).
11
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More recently, when societal trends shifted from groundwater supply to
groundwater contamination problems, it seemed logical to work with the
contaminant transport version of equation (1). For steady horizontal flow
but transient (time changing) dispersion of a conservative solute in a
confined aquifer, this equation is given by (Freeze and Cherry, 1979)
H + v If = °L
where c = solute concentration, V = uniform seepage velocity and D. = longi-
tudinal dispersion coefficient. D, is given by the product a, V, where a. is
the longitudinal dispersivity, which represents the random local mixing
properties of the aquifer. But what happens if one attempts to blindly
apply equation (2) to the situation depicted in Figure 1? First of all, one
would have to work with some average horizontal velocity, V, an average
concentration, c, and some type of apparent or effective dispersion coeffi-
cient, D£, which we will call the "full aquifer" dispersion coefficient.
With these assumptions, solutions of equation (2) would predict tracer
distributions similar to those shown in Figure 2. Comparison of the
predicted distributions (which, as a result of the assumptions are uniform
in the vertical direction) with the more realistic distribution (Figure IB)
shows this approach to be generally unsatisfactory. A lot of useful
information has been lost by not incorporating the vertical distribution of
hydraulic conductivity. This example highlights the problem that results
when attempting to solve groundwater contamination problems with approaches
found to be useful in water supply problems. Two-dimensional versions of
equation (2) are the so-called area! advection-dispersion models; they are
based on the same vertically-averaged approach and thus suffer from the same
limitations.
12
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If one considers explicitly the vertical variation of hydraulic conduc-
tivity for the transport problem illustrated in Figure 1 with flow, V(z),
parallel to the stratification in a horizontal stratified aquifer, the
governing equation becomes (Molz, Guven and Melville, 1983)
ft + Vfzlff . DL(z)4 + if - (V(z)-V)£ » - (DT(z)||) - \- <(Y(2)-V)c) (5)
In this form it is particularly illuminating to compare equations (2) and
(5), because one can see in mathematical /physical terms an implication of
the discrepancy illustrated graphically in Figures 1 and 2. If one forces
equation (2) to fit a dispersion process properly described by equation (5),
then the full aquifer dispersion term will have to model solute spreading
13
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(A)
Hypothetical
.» /Velocity
•^ / Distribution
Tracer at
Time=0
V,
V
max
mm
(B)
Tracer Distribution
at Time >0
Multiple of
Figure 1. Part (A) shows a hypothetical velocity distribution and an initial
distribution of tracer while part (B) shows how the tracer would
be dispersed by the moving groundwater at several different scales.
Three common mechanisms of pore scale dispersion (velocity variation
within a pore (a); flow path tortuosity ($), and molecular diffusion
due to concentration differences (y) ) are illustrated also.
14
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(A)
Tracer at
time=0
J
£\ 1
Tracer at later
times t, and t2>0
(B)
-------
due to a combination of local mixing, D_(z)3c/3z, and differential advec-
tion, (V(z)-V)c. Combining local mixing and differential advection within a
single dispersion term is not reasonable physically and not strictly
possible mathematically, as discussed by Molz, Guven and Melville (1983) and
elaborated in more detail by Guven, Molz and Melville (1984). The overall
approach makes the full-aquifer dispersivity, a£, scale-dependent, which
means that it is not a unique property of the aquifer or of anything else in
particular. The full-aquifer dispersivity simply becomes a parameter used
to fit equation (2)-type solutions to vertically-averaged concentration dis-
tributions when the desirable information concerning hydraulic conductivity
profiles is not available. Not only is the fit often poor, but the
numerical size of such "fitted" dispersivity values is usually several
orders of magnitude larger than laboratory measurements of true hydrodynamic
dispersivities (Pickens and Grisak, 1981; Anderson, 1983). This suggests
that the differential advection arising from the overall hydraulic
conductivity distribution plays a major role in the dispersion process.
These remarks are not provided simply to discredit area! advection-
dispersion models because such models have been applied productively.
However, the fitting process associated with the identification of full-
aquifer dispersivity values means that the use of such models as truly
predictive tools is highly questionable. Their success to date has been
severely limited by the non-unique and ill-defined nature of the
full-aquifer dispersivity. Partly because of this, examination of
down-gradient impacts of a contaminant plume usually requires major
re-calibration of a full-aquifer model developed for the local site.
Despite these limitations, areal advection-dispersion models continue to
serve a useful purpose because of the lack of adequate and practical field
16
-------
techniques for determining the hydraulic conductivity distribution. Only
recently have experiments with the objective of measuring vertical
distributions of horizontal hydraulic conductivity been performed (Pickens
and Grisak, 1981; Molz et al., 1985, 1986). Thus the required instrumenta-
tion and testing techniques are neither fully developed nor widely
available. In the absence of vertically-distributed data, one has no choice
in a modeling sense but to use some type of vertically-averaged advection-
dispersion approach built around full aquifer dispersivities. However, we
believe that much more can be done with existing instrumentation and
techniques than is typically done during field investigations of groundwater
contamination incidents.
As supported by the previous arguments, it is likely that any real
advance in our ability to simulate the contaminant dispersion process in
aquifers will have to be built upon more detailed measurements of hydraulic
conductivity and head distributions so that the advection field is defined
in more detail. It is particularly important to move away from the exclu-
sive use of vertically-averaged aquifer properties and flow variables.
Recently, we have performed single-well and two-well tracer tests at a site
near Mobile, Alabama with the objective of measuring relative travel time
distributions across the vertical dimension of an aquifer, assuming
horizontal flow on the average. We conducted those experiments because
tracer tests provide the most definitive data with which to infer hydraulic
conductivity distributions. A major purpose of this communication is to
describe these tracer tests and testing procedures and to discuss some
practical implications of the results with regard to modeling of contaminant
dispersion in aquifers.
17
-------
Types of Tracer Tests
It is generally agreed that tracer tests are currently the most relia-
ble field methods for obtaining data to describe dispersion in groundwater.
Most tracer tests can be placed in two major categories—natural gradient
and forced gradient. As the name implies, natural gradient tests involve
various means of placing an inert, non-adsorbing chemical (tracer) in an
aquifer and allowing it to move with the natural groundwater flow (Sudicky,
Cherry and Frind, 1983). Stanford University, in cooperation with the
University of Waterloo, has recently completed a detailed natural gradient
test soon to be reported in Water Resources Research. Herein we are con-
cerned mainly with forced gradient tests which employ pumping wells
(injection and/or withdrawal) to move a tracer through the test aquifer.
Normally, the selected pumping rates are such that the resulting hydraulic
gradients are much larger than the natural gradient. For this reason,
forced gradient tests are much shorter in duration than natural gradient
tests. The most common types of forced gradient tracer tests are single-
well tests and two-well tests. Over the past two years, both types have
been performed at the Mobile site (Molz et al., 1985, 1986), and both types
have been studied in some theoretical detail relative to their analysis and
interpretation in stratified aquifers (Guven et al., 1985, 1986). The
stratified aquifer assumption represents the simplest aquifer idealization
having a horizontal hydraulic conductivity distribution that depends on the
vertical coordinate (Guven, Molz and Melville, 1984).
Shown in Figure 3 is a typical configuration for a single-well test.
The term "single-well" represents the fact that only one pumping well is
required in order to perform the test. As detailed in Guven et al. (1985),
an observation well with multilevel samplers is required in order to obtain
18
-------
INJECTION
0=QIN
WITHDRAWAL
Q=OOUT
UPPER
s s / / / / ///////////
B
1
K(z)
II
CONFINING LAYER
INJECTION-
-^-WITHDRAWAL
WELL
OBSERVATION
WELL
WITH
MULTILEVEL
SAMPLERS
/////// / / /
LOWER CONFINING LAYER
Figure 3. Vertical cross-sectional diagram showing single-well
test geometry.
19
-------
tracer travel time data at several vertical positions in the aquifer. One
or more such observation/sampling wells may be used in any particular tracer
test. Actual test performance involves the injection of water having a
known concentration of tracer, C. .(t), in a well which is fully penetrating
I 11 J
and fully screened over the entire thickness of the aquifer (Figure 3).
After some time, the flow may be reversed and the tracer-labeled water
removed from the same well, although this withdrawal phase is not strictly
necessary. If there is a withdrawal phase in the experiment, the tracer
/s
concentration in the water leaving the well, CQUt(t), may be measured and
recorded as a function of time to produce a concentration versus time
breakthrough curve. Certain other useful information may be obtained also
scch as the percent of injected tracer that is recovered.
In a laterally isotropic, homogeneous confined aquifer or in a per-
fectly stratified confined aquifer, the flow during the single-well test is
horizontal, radially diverging during injection, and radially converging
during withdrawal. In the past, data analysis was accomplished by assuming
an equivalent homogeneous aquifer of constant thickness B (Fig. 3 with K(z)
constant). In such analyses, a withdrawal phase was necessary and the
concentration versus time data from the injection-withdrawal well were used
to estimate an effective longitudinal full-aquifer dispersivity (see, e.g.,
Fried, 1975; Pickens and Grisak, 1981). As mentioned previously, we believe
that an approach which does not rely on the vertically homogeneous aquifer
assumption is more reliable for predictive purposes.
In the single-well tests to be discussed, one or more observation wells
containing isolated multilevel sampling devices are installed around the
lection-withdrawal well (Fig. 3). Concentration versus time measurements
are then made at the different isolated points in each observation well
20
-------
during the experiment. The resulting tracer travel time information may be
used to infer vertical profiles of horizontal hydraulic conductivity. When
a single-well test is performed in this manner, the data from the multilevel
observation well(s) is what one is after. Therefore, a withdrawal phase is
not strictly necessary but is recommended, if for no other reason than to
remove tracer from the study aquifer.
A typical configuration and flow pattern for a two-well tracer test is
illustrated in Figure 4. Here there are two pumping wells because the
experiment involves the simultaneous operation of an injection well and a
withdrawal well, both of which are fully screened and fully penetrating over
the entire thickness of the aquifer. Water is pumped into the injection
well at a steady flow rate, Q, and is removed from the withdrawal well,
usually at the same rate, although two-well tests have been performed in
which the flow rates in the two pumping wells were not equal (e.g., Gelhar,
1982). A conservative tracer of known concentration, Cin(t), is added at
the injection well for a period of time, t. , and the concentration of
>N
tracer in the water leaving the withdrawal well, C t(t), is measured and
recorded as a function of time to give a concentration versus time
breakthrough curve. The tracer injection period is usually short compared
to the total time of the experiment.
Two-well tests may be carried out in either a recirculating or
non-recirculating mode. In the recirculating mode, the water pumped from
the withdrawal well is piped to the injection well, where it is injected
back into the aquifer. The concentration of tracer entering the injection
well during a two-well test with recirculation, C. .(t), will be equal to
I 11 J
s*.
C. .(t) = C. (t) + C .(t), approximately, assuming that the travel time in
inj in ou ^
the pipe joining the two wells is negligible. In the non-recirculating
21
-------
Injection well
(source)
Withdrawal well
(sink)
Plan view
Multi-Level
Observation
Well
^ywxyyv
4
f
*
II
1^.1
!!
ii
*
TSSSSSS/
/S//S/S//S/,
0
/w/'///'
Vertical section in x-z plane
Figure 4. Two-well test geometry in a stratified aquifer.
22
-------
mode, the water produced from the withdrawal well is wasted at a safe
distance from the test area. A separate water supply, usually a well in the
same aquifer but sufficiently far from the two test wells, so that
negligible hydraulic interference occurs, provides the injection water. The
injection tracer concentration in this case is C. .(t) = C. (t).
inj in
For the two-well tests discussed herein, observation wells containing
isolated multilevel samplers are installed between the injection well and
the withdrawal well in order to sample the tracer concentration at different
elevations in the aquifer during the experiment. From the tracer arrival
times at several isolated sampling points in a multilevel sampling
observation well, the variation of horizontal hydraulic conductivity in the
vertical may be inferred (Pickens and Grisak, 1981). As will be described
in more detail later, the inference assumes that the aquifer is perfectly
stratified and of constant thickness and porosity in the vicinity of the
test wells.
Design and Construction of Multilevel Sampling Wells
As explained in the previous section, the most unique aspect of the
single- and two-well tests that we are discussing is the use of one or more
multilevel sampling wells to obtain tracer travel time data at different
elevations in the study aquifer. This changes the objective of the tests
from attempting to determine a number for the so-called full aquifer longi-
tudinal dispersivity a£ (which we believe is rather meaningless at the scale
of practical tracer tests) to one of gathering information about the advec-
tion pattern in the aquifer, which in most situations will dominate the
early tracer dispersion process as illustrated in Figure 1. (Field evidence
in support of this statement will be presented later.) Because of the
emphasis on obtaining accurate tracer travel times at isolated elevations in
23
-------
the study aquifer, it is vital that multilevel sampling wells be constructed
so that dependable data are obtained. Unfortunately, a satisfactory
solution to the multilevel sampling well construction problem is not yet
available.
Shown in Figure 5 are three multilevel sampling well types. In recent
tracer tests with which the authors are concerned, various versions of type
I have been attempted. Type I and related types have appeal because of the
convenient vertical location of the sampling zones, and the potential
economy of installation. Illustrated in Figure 6 is the multilevel sampling
system described by Pickens et al. (1978) and later used in single- and
two-well tracer tests (Pickens and Grisak, 1981). The system was designed
for shallow water table applications and was usually forced into position
using a high pressure water jet (Pickens et al., 1978). Identical or
similar systems have been utilized or tested by other research groups
(Stanford University, Tennessee Valley Authority, personal communications).
For the Pickens et al. (1978) system to perform acceptably, the study
aquifer must collapse around the sampler and make good contact so that
spurious high vertical permeability pathways are not created along or near
the aquifer-sampler boundary (Fig. 14). Apparently, this was not a problem
in the clean sandy aquifer studied by Pickens and Grisak (1981). However,
in more cohesive aquifers with lower vertical hydraulic conductivities and
higher vertical head gradients, problems have been observed (Tennessee
Valley Authority, personal communication).
Moltyaner and Killey (1986) have developed an automated multilevel
sampling system designed for use with radioactive tracers. This system,
which uses a dry access well monitoring technique, is illustrated in Figure
7. With this arrangement Moltyaner and Killey (1986) made the equivalent of
24
-------
ro
en
Packer
Measurement
zone
II
III
Figure 5.
Various types of multilevel sampling systems.
-------
to vacuum
flask
Surface
PVC pipe
End cap
.tubing
Rubber
stopper
PVC pipe
Screen
///////////•/ /// / // / / 771
Figure 6. Pickens et al. multi-level sampling/observation well,
26
-------
Steel
Casing
(6")
AQUIFER
The Insert will
Contain al
Instrumentation
'Solid PVC
Pipe (4")
Removable PVC
Insert Pipe (2")
Figure 7. Moltyaner and Killey multilevel, dry, access tube system for use
with radioactive tracers.
27
-------
750,000 point measurements using computer-controlled probe placement and
data aquisition, which illustrates one of the tremendous labor-saving advan-
tages associated with the use of radioactive tracers.
Presumably, the dry access tube(s) could be implaced using a variety of
drilling techniques, each of which would have a different effect on the
tube-aquifer boundary. If the tubes were jetted into the study aquifer or
placed in auger holes with the idea of having the formation collapse around
them, then the same potential vertical leakage problem discussed previously
would seem to exist. If thick drilling mud were used, however, and the
access tube placed in a mud-lined hole, it would seem that the potential for
spurious vertical leakage would be diminished greatly.
Molz et al. (1985) describe the design and construction of a multilevel
sampling well system for use with chemical tracers in a variety of confined
and unconfined aquifers. The actual sampling system is not perfected and
should be viewed as a prototype. However, it appeared to work in a satis-
factory manner at the Mobile site.
As shown in Figure 8, the screened portions of the multilevel observa-
tion wells are not of a standard design. The screens themselves are com-
posed of 91 cm (31) slotted sections alternating with 213 cm (71) solid
sections. Although 5 slotted sections are shown in Figure 8 for purposes of
illustration, the actual screens contained 7 slotted sections.
As also shown in Figure 8, a 5.1 cm (2") diameter PVC insert was
constructed with slotted and solid portions that matched with those of the
observation well screen. The insert was designed to hold any wires, tubing,
or instrumentation that ultimately would be placed in an observation well.
Composed of threaded 3.05 m (101) sections, the inserts extended all the way
to the land surface. In order to isolate the various sampling zones, the
28
-------
Steel
casing
(6")
Silicons
Rubber
Plugs
Grout
Solid PVC
Pipe (4")
Inflatable
Packers
Isolated
probes
Aquifer
Figure 8. Schematic diagram of the basic construction plan for a multilevel
sampling well with a removable insert.
29
-------
inserts were fitted externally with cylindrical annular inflatable packers
as illustrated in Figures 9 and 10. After the required probes, tubing and
wires were placed within the inserts, the sampling sections were isolated
internally with silicone rubber plugs. The complete insert was constructed
on the surface, then placed in the well, using a crane, positioned and the
packers inflated. After installation, each isolated 91 cm (3') sampling
zone appeared as shown in Figure 11. A conductivity probe was placed near
the zone center, and two lengths of vacuum tubing connected the sampling
zone to the surface. This tubing could be used with peristaltic pumps to
mix the contents of the sampling zone and to obtain groundwater samples for
analysis as illustrated in Figure 12.
In designing the multilevel sampling wells for use at the Mobile site,
the drilling and well development process illustrated in Figure 13a,b was
visualized. After removal of the drilling equipment, the drilling mud and
disturbed aquifer material are mixed significantly as shown in Figure 13a.
The cleaning and development procedure then was to pump and surge the wells
until the water was clear and devoid of drilling mud and fine material. As
shown in case (b), Figure 13, this procedure probably left some drilling
mud adjacent to the solid casing segments and a disturbed (perhaps more
permeable) aquifer material near the slotted segments where samples were to
be collected. Such mud remnants would not be left behind (see Figure 13c)
if a fully slotted screen had been used. The potentially beneficial effects
of a partially slotted (segmented) screen with respect to a fully slotted
screen, and a vertical leakage path possible in the fully slotted case, are
illustrated further in Figure 14. The drilling mud remnant adjacent to the
solid portion of the screen may result in a barrier to vertical flow that is
very desirable. For the fully slotted screen, very little mud remains after
30
-------
Steel
casing
(6")
Silicone
Rubber
Plugs
Grout
'Solid PVC
Pipe (4")
Inflatable
Packers
Isolated
probes
Aquifer
Figure 9. Multilevel sampling well with sampling zones isolated with
inflatable packers and silicone rubber plugs.
31
-------
Top View
JL
Side View
vy
-Tubing To
Surface
1
1
1
1
1
1
1
\ty
1 1
1 1
1 1
i ;
r PVC
-Packer
Section
•2"
Figure 10. Details concerning the geometry and installation
of inflatable packers. The packers were inflated
with water.
32
-------
00
CO
70ft..
(2 Im)
ILL
.aquifer
3'(0.9 I m)
T.
7'<2. Im)
2" PVC removable insert
vacuum
tubing
Plug
. ''electrode
inflatable
packer
Figure 11. Diagram of a completed multilevel sampling well. This and similar
systems were used at the Mobile site.
-------
Tubing
Peristaltic
Pump Drive
To Sample,
Bottle-2^
•Pump
Head
From
Sampling
Zone
Nylon Tee
Clamps
To Sampling
Zone
Figure 12. Diagram illustrating the scheme for causing mixing in the various
isolated sampling zones and obtaining samples for laboratory
analysis.
34
-------
mud
' remnants
Figure 13. Diagram illustrating what may happen during drilling and
installation of various types of screens.
35
-------
packer
fa"! segmented
fully-slotted
Figure 14. Details concerning the possible beneficial effects of drilling
mud left behind in the formation (a) and possible leakage paths
associated with fully-slotted screen
36
-------
development and a disturbed aquifer material of possibly higher permeability
would result along the entire length of screen.
The most thought out and best designed multilevel sampling system from
a vertical integrity viewpoint of which the authors are aware appears to be
the multiple port system manufactured by Westbay Instruments, Ltd. of Van-
couver, B.C. In its present configuration, however, the system is suited
for groundwater monitoring but not tracer testing which requires the ability
to sample rapidly and simultaneously from a number of elevations. Lack of a
solution to the vertical integrity problem valid in a broad range of aquifer
types coupled with the unavailability of economic, dependable and flexible
commercial equipment is a major impediment to the practical application of
most types of multilevel tracer testing.
Performance and Results of Single-Well and Two-Well
Tracer Tests at the Mobile Site
Using the multilevel sampling wells described in the previous section,
a series of single-well and two-well tracer tests were performed at the
Mobile site over the past two years. The major purpose of these tests was
to measure the tracer travel times between an injection well and one or more
multilevel sampling wells. Subject to several assumptions to be discussed
later in this section, the resulting travel time data allows one to infer a
vertical distribution of horizontal hydraulic conductivity. We view the
experiments to be described as the simplest and most convenient tracer tests
which yield some information about the variation of aquifer hydraulic
properties with respect to the vertical position in the aquifer. The basic
experimental plan was to conduct a series of single-well and two-well tests
at different locations in an attempt to build up a three-dimensional picture
of the hydraulic conductivity distribution. We did not attempt to make
point measurements or nearly point measurements as was done by Pickens and
37
-------
Grisak (1981). Our objective was to average tracer travel times over a
suitable aquifer thickness. Thus the inferred hydraulic conductivity
distribution that results may be viewed as being based on a type of spatial
average.
The project site is located in a soil borrow area at the Barry Steam
Plant of the Alabama Power Company, about 32 km (20 mi) north of Mobile,
Alabama. The surface zone is composed of a low-terrace deposit of Quater-
nary age consisting of interbedded sands and clays that have, in geologic
time, been recently deposited along the western edge of the Mobile River.
These sand and clay deposits extend to a depth of approximately 61 m (200
ft) where the contact between the Tertiary and Quaternary geologic eras is
located. Below the contact, deposits of the Miocene series are found that
consist of undifferentiated sands, silty clays and thin-bedded limestones
extending to an approximate depth of 305 m (1000 ft). The study formation
is a confined aquifer approximately 21 m (69 ft) thick which rests on the
Tertiary-Quaternarty contact.
Except for the well diameters, Figure 15 is a vertical section scale
drawing of the subsurface hydrologic system at the Mobile site. Included in
the drawing are 3 pumping wells (El, 12 and E10) and 4 multilevel observa-
tion wells (E5, E3, E7 and E9) all situated at approximately the same
vertical plane. (A schematic plan view showing the wells El and 12 and the
supply well S2 is given in Figure 17). The study aquifer is well confined
above and below by clay-bearing strata that probably extend laterally for
several thousand feet or more, and the natural piezometric surface of the
confined aquifer at the test site is at a depth of 2 to 3 m (6 to 10 ft)
below the ground surface. In experiments performed to date, vertical
hydraulic gradients within the aquifer have been small. A medium to fine
38
-------
CO
to
B
E
o
Q
0)
GO
CL
0)
Q
0-
I 0-
20-
30-
40-
50-
60-
El E5
E3 12 E7
E9 EIO
-40
. • i
' • i
.' "i
. • i
.'•i
. • i
'. .' '
• i
Sandy
(Aquifer)
Sand
Clay
Sandy
Clayey
Mainly
i • . • . — .
1 (Aquifer) .' • • -.
1 ."•'•.'.'•'•'.'.''•'
- • • • Medium •
i ••.•••-.-.-•
...•-.
i • • • • . •
Sandy
i i t
30 -20 - 1 0
...
C
. -_
— —
)
Clay
Gravel
Lenses
Clay
Sand
Clay
'• Sand '.;. ' '•
• . ' • ' . . •
• • ,
. — —
Clay
10 20 30
i
• -. .
i
i • •
i • . •
— _
i
40
Horizontal Distance (m)
Figure 15. Diagram of the subsurface hydrologic system at the Mobile site
where tracer tests were performed. Wells El, 12 and EIO are
pumping wells, while E5, E3, E7 and E9 are multilevel sampling
wells. All wells shown are situated at approximately the same
vertical plane. See Figure 17 for a schematic plan view showing
wells El and 12.
-------
sand containing approximately 3 percent silt and clay by weight composes the
main aquifer matrix at well E3. (At other locations in the aquifer the
fines vary from 1% to 15% by weight.) When E3 was constructed, moderately
disturbed cores were obtained at 7 locations throughout the depth of the
study aquifer using a Shelby tube. The resulting particle size and
distribution data, which we believe are accurate despite the moderate
disturbance, are presented in Table 1. Further details concerning
aquifer/aquitard hydraulic and other physical properties may be found in
Parr et al. (1983).
The pumping wells are constructed of 20.3 cm (8") steel casings with
15.2 cm (6") stainless steel, wire wrapped screens and are grouted from the
top of the study aquifer to the land surface. As illustrated in Figure 16,
the piping and valve system associated with each pumping well is designed so
that the well can be used for injection or withdrawal of tracer solution.
In the single-well test to be reported in detail herein, tracer solution was
injected through well 12. As illustrated in Figure 17, supply water was
obtained from a well (S2) screened in the study aquifer about 244 m (800 ft)
east of 12. This separation was sufficiently large so that the hydraulic
effects of S2 pumping did not affect the tracer experiments in the vicinity
of 12. Concentrated tracer solution was mixed in a 4800 liter (1270 gal)
tank and added to the 10.2 cm (4 in) pipeline connecting S2 and 12 using a
metering pump. The pipeline travel distance from the metering pump to the
study aquifer was at least 160 m (525 ft) which was more than sufficient to
insure complete mixing of the tracer. It was assumed that the piezometric
head distribution in the injection well screen was uniform with depth since
the screen diameter was 15.2 cm (6 in) which resulted in a maximum average
vertical fluid velocity in the screen of 0.84 m/s (2.75 ft/s) (during
40
-------
Table 1. Particle size distribution data for the seven disturbed cores
obtained during construction of well E3.
Depth of Core
(m)
40.2
43.3
46.6
49.7
52.7
56.1
59.1
D60
(mm)
0.46
0.36
0.58
0.46
0.49
0.59
0.94
D30
(mm)
0.35
0.26
0.45
0.27
0.28
0.44
0.56
D10
(mm)
0.21
0.13
0.21
0.12
0.15
0.26
0.19
Percent Passing
#200 Sieve
(%)
1.8
1.4
3.0
5.6
3.5
1.2
3.8
41
-------
4" Pipe and Fittings
Figure 16. Piping and valving scheme associated with
pumping wells at the Mobile site.
42
-------
-S2(Supply Well)
Pipeline
Tracer
Tank
Instrument
Trailer
Figure 17. Diagram showing the main features of the surface hydraulic system
used in the single- and two-well tracer tests at the Mobile site.
43
-------
experiment #4). Thus the maximum velocity head was only 0.037 m (0.12 ft)
and the head losses due to friction along the 21 m (69 ft) length of screen
would be less than 0.10 m (0.33 ft). These totals when compared to the
injection head of approximately 3 m (9.8 ft) are consistent with the
assumption of constant head in the well screen interior.
As discussed in detail by Molz et al. (1985), several preliminary tests
were conducted with the objective of assessing the vertical integrity of the
multilevel sampling wells and the effect of mixing the water within each
sampling zone which was approximately 0.91 m (3 ft) high. It was concluded
that sample zone isolation was adequate for tests which were to follow.
There was a significant difference between breakthrough curves at the seven
sampling zones depending on whether sample zone mixing was induced. There-
fore, it was concluded that mixing within each isolated sampling zone is
desirable. For a sampling zone of finite length it is possible for the
tracer to enter the zone anywhere along the slotted length and then be
recorded depending on unknown natural mixing and probe position. Imposed
mixing forces an integration effect causing tracer concentration to be more
representative of the entire length of the sampling zone. (This relates
back to the moving average concept discussed previously.) Without imposed
mixing, the effective sampling length in the vertical direction is unknown.
Single-Well Test
The first complete single-well tracer test conducted at the Mobile site
was labeled "experiment #4" and utilized the multilevel sampling well E3
(Figure 15). To start the experiment, supply groundwater without tracer was
injected into 12 until the initial transients disappeared and a steady
injection rate resulted (approximately 2 hours). Then at time zero tracer
was added to the injection water, and the actual test initiated. Shown in
44
-------
Figure 18 are the bromide concentrations measured in 12 (injection/
withdrawal well), while the concentration breakthrough curves measured in E3
(multilevel sampling well) are shown in Figure 19. (Water samples were
obtained from the injection/withdrawal well using a faucet in the pipeline.)
During the experiment tracer solution at an average concentration of 242
mg/1 was injected at the rate of 0.915 m /min (242 gpm) for the first 32
hours. This injection rate, without tracer added to the water, was
maintained for the next 22 hours at which time injection was halted. One
hour and 15 minutes later withdrawal pumping was initiated at the rate of
1.19 m /min (314 gpm) and continued for two weeks so that virtually all
tracer was removed from the system. Note that Figure 18 contains both
injection and withdrawal data while Figure 19 contains only injection
breakthrough data.
Table 2 contains the time for 50% of breakthrough for each level based
on the electrical conductivity measurements for experiment #4 shown in
Figure 20 and the concentration data shown in Figure 19. With the probable
exception of level 1, the concentration data look quite good. On the
average, the arrival times based on electrical conductivity lag those based
on concentration by about 2 hours. (We will refer to this as the "two-hour
rule" later on.) This is largely due to the fact that the electrical
conductivity of the supply water, which is ultimately mixed with tracer, is
lower than that of the native groundwater in the vicinity of 12 by about
16%, caused in part by water chemistry changes induced by previous aquifer
thermal energy storage experiments at the same site (Molz et al., 1983).
Thus as the tracer solution approaches a conductivity probe, the reading
will decrease initially even though the bromide concentration is increasing.
The net effect of this interaction is to cause the electrical conductivity
45
-------
300-1
240^
o
I 80-
o
0 I 20-
cr
QQ
60-
30
60 90 120
TIME (HOURS)
I 50
Figure 18. Bromide concentration in the injection/withdrawal well (12)
during experiment #4. Tracer injection ended at t=32 hours;
injection ended at t=54 hours. Withdrawal began at t=55.25
hours.
46
-------
200
~ 180
"£, i60
£ 140
e 120
— 100
2 80
"g 60
« 40
20
O
O
Level I
Level 2
Level 3
10 20 30 40 50 10 20 30 40 0 10 20 30 40 50
Time (hrs)
200
~ 180
^> 160
.§ 140
e 120
^ 100
O
£ 80
« 60
g 40
O 20
Level 4
Level 5
•• / Level 6 •
Level 7
10 20 0 10 20 30 40 0 10 20 10 20 30 40 50
Time (hrs)
Figure 19. Bromide concentration breakthrough curves at the
seven levels of well E3 during experiment #4.
47
-------
25
o
M
O
•q
1
o
o
o
UJ
Sf
"g
o
•5
o
E
.a.
>>
^•c
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c*
O
O
u
U
400-
380-
360-
340-
320-
300-
280-
260-
240-
/% /*« -- *,
/ IS * \f
' 1 /
P 7 o'
/ I /
/ / /
i i i
/ i 7
'? / J
/ L«vel .Level
p ' (' 2 ^ Level
V^' "^o-fk * ',
t i i i i i i i i *^i i i i i i t
10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 60
380-
360-
340-
320-
300-
280-
260-
24O-
£-- ^i Time (hrs)
0>' ^^
^jrt ' >V
'^' k '* ^-^" ^
/ ' *
v^ '
^ ^^
/ t
^9 t •
it i
t i :
Y i
? Level J f
i ^ ^^ft Level ^
y / Level
^ &Q-<*-^ 7
10 20 30 40 50 0
10 20 30 40 10 20 30 40 50 60
Time (hrs)
Figure 20. Electrical conductivity breakthrough curves at various
levels of well E3 during experiment #4.
48
-------
Table 2. Sampling zone elevations, arrival times for fifty percent break-
through, apparent dispersivity values and inferred normalized hydraulic
conductivity values for experiment #4.
Arrival Times Arrival times
from Normalized Apparent from Normalized
Level Mid-Zone Concentration Hydraulic Disper- Electrical Hydraulic
# Elevation Measurements Conductivity sivity Conductivity Conductivity
Measurements
1
2
3
4
5
6
7
-40.7 m
-43.8 m
-46.8 m
-49.9 m
-52.9 m
-56.0 m
-59.0 m
33.4 hr?
24.3 hr
20.5 hr
14.0 hr
19.0 hr
8.0 hr
32.4 hr
0.24
0.33
0.39
0.57
0.44
1.00
0.25
0.07+0.01 m
0.18+0.02 m
0.17+0.06 m
0.12^0.04 m
0.32+0.08 m
0.50+0.03 m
0.04+0.01 m
29.0 hr
27.3 hr
—
16.0 hr
21.8 hr
10.0 hr
33.2 hr
0.34
0.37
—
0.63
0.46
1.00
0.30
49
-------
data to overestimate the actual mid-rise arrival time. Presumably, this
could be corrected by adding additional ions, other than bromide, to the
supply water. However, we did not attempt this because the probe recordings
were used mainly to orient ourselves qualitatively as to what was happening
in the subsurface. Ultimately, calculations of normalized hydraulic
conductivity were based mainly on arrival times deduced from concentration
data measured in the laboratory. The results of both are shown in Table 2
mainly for comparison and information purposes.
Tracer travel time data alone does not enable one to calculate an
absolute value of hydraulic conductivity. To calculate such a value for the
general nonhomogeneous case, one must know the flow path, porosity and
hydraulic head distribution along the flow path in addition to the travel
time. It was not feasible to measure all these quantities during our tracer
tests. However, if one approximates the real aquifer in the test vicinity
with a perfectly stratified aquifer of constant porosity and horizontal
layering, then for a fully penetrating injection well the Darcy velocity at
the elevation of each sampling zone will be horizontal and proportional to
the hydraulic conductivity at that level. Thus the following equations can
be written
2
where K.. = horizontal hydraulic conductivity at the ith level, B(R) =
e/(dh/dr) where e is the porosity and dh/dr is the hydraulic gradient at
radius R, v. = seepage velocity at the ith level, R = constant radial
distance between the injection well and a particular multilevel sampling
well, t. = tracer travel time between the two wells at the ith level, T =
50
-------
aquifer transmissivity, and Q = injection flowrate. At any particular
level, t. is taken as the time between the start of tracer injection and
when 502 of breakthrough occurs. In any given experiment there will be a
minimum arrival time, t . , which corresponds to the layer with the largest
hydraulic conductivity, Kma . and from equation (6)
fllaX
Forming the ratio of equations (6) and (7), one arrives at what can be
called the normalized hydraulic conductivity
(8)
max i
It is also possible to calculate the ratio K../K = i/t., where the "bar"
notation indicates average values (Pickens and Grisak, 1981). K could then
be equated, as a first approximation, to the hydraulic conductivity obtained
from a fully penetrating pumping test, as K = T/B where T is the trans-
missivity and B is the aquifer thickness. This would enable explicit values
to be calculated for each K..
We would like to re-emphasize that the simple equations (6) through (8)
all result from the "stratified aquifer" approximation which many hydrolo-
gists may consider too idealized to represent a real aquifer. There is
certainly some merit to this viewpoint. However, the only other practical
alternative that we see at the present time is to make the usual assumption
of a homogeneous or statistically homogeneous aquifer and go after a full-
aquifer dispersivity which, as discussed in the introduction, is a much
worse approximation. More will be said about this later.
51
-------
Based on equation (8), Figure 21 resulted which is a plot of normalized
hydraulic conductivity (K/Km,v) as determined from the concentration data of
Mia X
experiment #4. Since the concentration data for level 1 are not consistent
with that from the other levels (perhaps a tubing leak?), we used the
electrical conductivity data and the 2-hour rule (see page 22) to provide an
improved estimate of the level 1 relative permeability. At this level the
electrical conductivity data were normal in appearance and resulted in the
level 1 value on the curve shown in Figure 21. The results displayed
indicate the presence of a high permeability zone in the bottom third of the
aquifer, along the line connecting E3 and 12. This result is consistent
with the findings from previous thermal energy storage experiments at the
Mobile site which indicated the presence of a high permeability zone,
although at a slightly higher elevation in the aquifer (Molz et al., 1983;
Buscheck et al., 1983).
In displaying the data of Figure 21, it was decided to simply draw
straight lines between the points where hydraulic conductivity was known or
measured. In doing this use was made of nine points—the top and bottom of
the aquifer, where the clay confining layers force the permeability to
essentially zero, and the seven sampling points where tracer travel times
were recorded.
Two-Well Test
As described previously, a two-well test may be used with one or more
multilevel sampling wells to obtain tracer travel time information similar
to that obtained with a single-well test. However, the two-well test is
generally performed on a larger scale and, therefore, is more time
consuming. At the Mobile site our single-well tests lasted about 5 days,
while the two-well tests required 30 to 35 days followed by a month or more
52
-------
2 .3 .4 .5 .6 .7 .8 .9 I
K/Kmax
Figure 21. Inferred normalized hydraulic conductivity distribution
based on the results of experiment #4 and the stratified
aquifer assumption.
53
-------
of withdrawal to remove all remnants of tracer. Generally speaking, single-
well tests are suited for relatively low cost but small scale hydraulic
conductivity measurements because only a single pumping well is required. A
two-well test in the non-recirculating mode requires at least 2 pumping
wells but provides the advantage of being able to move water relatively
rapidly over larger travel distances.
Another aspect of a two-well test which was exploited in the present
study is that it offers a convenient vehicle for testing tracer transport
prediction capability. In several of our experiments at the Mobile site we
chose to employ the single-well test as a means for inferring the hydraulic
conductivity distribution in a relatively small aquifer region between an
injection well and a multilevel observation well (maximum tracer travel
distance of 5.5 m (18 ft)). The two-well test was then used to test
predictions over a relatively large aquifer region (minimum tracer travel
distance of 38.3 m (126 ft)) based on the vertical distribution of
horizontal hydraulic conductivity inferred from the single-well test. This
procedure helps to define what is actually being measured during a
single-well test and over what travel distances such a measurement might
have meaning. It also provides valuable insight concerning fundamental
properties of the flow field which was established during the experiments.
Predictions of two-well test outcomes based on single-well test results are
discussed in the next section entitled "Computer Simulation of Single-Well
and Two-Well Test Results."
At this time in the project, 2 two-well tests have been performed at
the Mobile site. The pairs of pumping wells used in the first and second
tests, respectively, were E1-I2 and I2-E10. Both tests were done in the
non-recirculating mode with El and 12 used as injection wells in the first
54
-------
test and second test, respectively. Herein, only the E1-I2 test will be
described in detail.
Preparation for the execution of a two-well test is similar in
philosophy to that for a single-well test. The first step is to establish
the flow field between the injection and withdrawal wells using groundwater
without tracer. As illustrated in Figure 17, the piping between El and 12
was valved off, and a pump in well S2 was used to inject water into El.
Simultaneously, a pump in 12 withdrew water which was then wasted.
Discharges were measured with standard turbine-type water meters and only
minor valve adjustments were required in order to get the injection and
withdrawal rates essentially equal and to maintain equality throughout the
test. Following flow field establishment, tracer injection was initiated
simply by turning on the metering pump in the line connecting the tracer
tank to the S2-E1 pipeline (Fig. 17). The E1-I2 test was performed within
the geometry illustrated previously in Figure 15. Both the injection well
(El) and withdrawal well (12) have 15.2 cm (6") diameter stainless steel
screens that fully penetrate the study aquifer. The observation wells (E5
and E3) are constructed of PVC pipe as described in the discussion of
multilevel sampling well design and construction.
The test began (tracer injection initiated) at 9:50 AM on August 31,
1984 and continued until 8:00.AM on October 2, 1984. Injection and
3
withdrawal rates averaged 0.946 m /min (250 gpm) and, typically, were equal
to within less than 1%. Tracer was added to the injection water during the
first 76.6 hours of the experiment which resulted in the injection
concentration versus time function shown in Figure 22. After approximately
70 hours, tracer began to appear in the withdrawal well. As shown in Figure
23, the withdrawal concentration versus time function was complex, and
55
-------
— .
\
o>
e
*"*
o
~
o
jz
c
-------
CONCENTRATION (MG/L)
era
c
(D
CO
rooi
01
p
b
ro
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tn
Ol
b
H- en
3 C
Q<5 i-i
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-------
measurable tracer concentrations persisted throughout the 32.5 day
experiment. The peak concentration occurred rather early in the experiment
(-210 hours), and the curve had a well-defined "tail" that was still 15% of
the peak value (-40 times the background value of 0.1 mg/1) when the
experiment was terminated. Computer simulations (see below) indicated that
the tailing was due to the late arrival of tracer being brought to the
withdrawal well along the flow lines which follow the longer and larger arcs
between the injection well and the withdrawal well shown in Figure 4.
Throughout the experiment, data were collected at the two multilevel
observation wells shown in Figure 15. There were seven 0.9 m (3 ft) long
isolated sampling zones in each well that were kept continuously mixed using
peristaltic pumps on the surface, just as in the previously described
single-well test. The peristaltic pumps were used also to obtain samples
for analysis. Shown in Figure 24 (lines connecting dots) are breakthrough
curves for the seven isolated levels in well E3. The data for well E5 is
not shown because it was invalidated by the presence of drilling mud that
was inadvertently left in the formation during the well construction process
(Molz et al., 1985).
A tracer travel time analysis similar to that described for the single-
well test and embodied in equations (6), (7), and (8) can be applied to the
two-well test (Pickens and Grisak, 1981). When this is done, using the
experimental data in Figure 24, the normalized hydraulic conductivity
distribution shown in Figure 25 results. Although there are some
differences, this distribution is quite similar to that shown in Figure 21
which resulted from the single-well test.
58
-------
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l-l I—
< h-
(U
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CONCENTRATION (mg/l)
CONCENTRATION (mg/l)
CONCENTRATION (mg/l)
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Computer Simulation of Single-Well and
Two-Well Test Results
The schematic diagram of tracer dispersion drawn in Figure 1 represents
an advection-dominated process. One of the objectives of the research
reported in this communication is to develop some indication of how much
information concerning tracer dispersion is actually contained in normalized
hydraulic conductivity distributions similar to the type determined in
single-well and two-well tracer tests subject to the stratified aquifer
approximation. Moreover, when such information is put into a mathematical
model, how much of the dispersion process due to true hydrodynamic
dispersion and other factors, such as spatial variations of hydraulic
conductivity not allowed in the stratified aquifer assumption, is left
unaccounted for? To begin to answer this question for aquifers where the
required information is available, computer simulations for various experi-
ments were developed which explicitly considered the vertical variation of
horizontal hydraulic conductivity as determined by single-well or two-well
tracer tests. Predictions of the computer models, which were made without
"calibration" of any model parameters, were then compared with actual field
results.
Simulation of Single-Well Tests
The first field tracer tests studied in this manner were the single-
well tests performed by Pickens and Grisak (1981). This particular test was
chosen for analysis because of the availability of very detailed data on
hydraulic conductivity, local dispersivity and concentration distributions
from the test. The computer model that was developed is called SWADM
(Falta, 1984; Guven et al., 1985). It takes into account depth-dependent
advection in the radial direction and local hydrodynamic dispersion in the
61
-------
vertical and radial directions (Gliven et al., 1985). The model is based on
the equation given by
3C _ 1 3 f n 3C] . 3 fn 3C]
Tr " r?r lrDr Trj + IT lDz TzJ
3C ,,
Ur
where r is the radial coordinate, C = C(r,z,t) is the tracer concentration,
U~ = U (r,z) is the radial seepage velocity, Dw = Drt + a JlL| is the radial
II i 0 r K
dispersion coefficient, DV = DQ + avlurl is the vertical dispersion coef-
ficient, DO is the effective molecular diffusion coefficient, and a and a
are the radial and vertical local dispersivities.
The very detailed single-well tracer dispersion experiment of interest
was performed in a shallow unconfined aquifer. A volume of 95.6 cubic
meters of tracer-labeled water was injected into an 8.2 m thick aquifer at a
3
rate of 3.2 m /hr for a period of 30 hours and then withdrawn at the same
rate. Withdrawal began immediately at the end of injection. The
previously-described samplers were located in the aquifer at observation
stations 1, 2, 3, 4 and 6 m from the injection-withdrawal well. From the
relative tracer arrival times at different elevations in the observation
wells, a radial hydraulic conductivity distribution in the vertical
(expressed as K../K) was calculated. Additionally, Pickens and Grisak (1981)
estimated the local longitudinal dispersivity at each sampling point and
found the values to be fairly constant with an average magnitude of about
0.007 m. The K/K distribution inferred from the breakthrough data at the
observation well at a distance of 1 m from the injection-withdrawal well in
test SW1 was used in the SWADM simulation. This profile is shown in Figure
26. The actual unsteady injection concentration, shown in Figure 27, was
used in the simulation (Pickens, 1983, personal communication), along with
local radial and vertical dispersivities of 0.007 m. The value used for the
62
-------
w
1.0
2.0
depth 3.0
from
upper
confining 4.O
layer
(meters) 5 Q
* 6.0
7.0
8.0
. j ,.,,,,,,
1 r=lm
|-^^^___
|
|
|
|
|
|
1
-..!..,....,
0
1.0
K/K
2.0
Figure 26. Hydraulic conductivity profile measured by
Pickens and Grisak (1981 ) and used in the present
calculations.
63
-------
1.5
1.0-
C(t)
CQ
0.5-
0.0-
•EXPERIMENTAL DATA
[PICKENS, PERSONAL
COMMUNICATION, I 983]
INJECTION
I I I
•
•
•
-RECOVERY
0 10 20 30 40 50 60
TIME (HOURS)
Figure 27. Unsteady injection concentration during the Pickens
and Grisak (1981 ) single-well field experiment.
64
-------
radial dispersivity is based on the observations, but the value used for the
vertical dispersivity is arbitrary and it was chosen simply as a possible
upper limit for this quantity in this case as discussed in more detail by
Giiven et al. (1985). The effects of the well radius and molecular diffusion
were neglected. The porosity value used in the calculations was 0.38 as
given by Pickens and Grisak (1981, page 1197).
In Figures 28 and 29, the actual flow-weighted breakthrough curves from
observation wells located 1 and 2 m from the injection-withdrawal well
respectively (Pickens and Grisak, 1981b) are shown along with the flow-
weighted breakthrough curves calculated by SWADM. (The flow-weighted
+. ^ R -
concentration, C is defined as C = / (K(z)/K)Cdz/B, where B is the aquifer
thickness.) In Figure 29, the wavy appearance of the computed curve for a
time greater than about 10 hours is due to the unsteady injection
concentration used in the simulation. The experimental concentration versus
time data measured at the injection-withdrawal well is shown in Figure 30
along with the results of the SWADM simulation using the unsteady input
concentrations. The early part of the experimental data seems to show a
large amount of scatter; however, this part of the curve is closely modeled
by SWADM using the actual unsteady injection concentration. The later part
of the breakthrough curve is underestimated by SWADM. The reasons for this
are not clear. One possible contributing factor could be the presence of
small-scale, three-dimensional, very-low-permeability lenses embedded in the
aquifer, which the present model does not take into account. These lenses
could act as temporary storage zones for the tracer which may diffuse into
these zones during injection and then move out slowly during withdrawal,
leading to larger concentrations during withdrawal than predicted by SWADM.
Another possible contributing factor for the behavior noted above is that
65
-------
1.00-
0.75-
0.50-
0.25-
•EXPERIMENTAL DATA
[PICKENS AND GRISAK, I 98 I ]
NUMERICAL RESULT
= a = 0.007m
0.00-
0 I 5
TIME (HOURS)
20 25 30
Figure 28. Comparison of SWADM results with field data for the
flow-weighted concentration from an observation well
one meter from the injection-withdrawal well.
66
-------
LOCH
0.75-
0.50-
0.25-
0.00-
0
•EXPERIMENTAL DATA
[PICKENS AND GRISAK, I 98 I ]
— NUMERICAL RESULT
ar = a= 0.007m
10 15 20
TIME (HOURS)
25
30
Figure 29. Comparison of SWADM results with field data for the flow-
weighted concentration from an observation well two meters
from the injection-withdrawal well.
67
-------
according to the measured data, approximately 2.5 percent ror-e tracer was
shown to have been withdrawn than was injected. While this is certainly not
a large experimental error for a field experiment (in fact it is quite
small), it is enough to have significantly changed the slope of the later
part of the curve if that is where the error occurred. Since a mass balance
was not satisfied perfectly during this experiment, the net area under the
experimental curve is greater than the area under the calculated curve.
However, in obtaining the results shown in Figures 28, 29, and 30, no "model
calibration" of any type was performed. Only parameter values measured by
Pickens and Grisak (1981) were utilized. The resulting curves represent
very accurate simulations which indicate an advection-dominated dispersion
process with local dispersivities approaching those measured in the
laboratory. As also discussed in more detail by Molz et al. (1983) and
Guven et al. (1984), it is clear that if a full-aquifer dispersivity were
calculated from these data it would not represent a physical property of the
aquifer.
Simulation of Two-Well Tests
To date, simulations have been performed for two separate two-well
tests, the Pickens and Grisak (1981) test and the Mobile test described in a
previous section. Only the Mobile two-well test simulation will be pre-
sented in detail because the conclusions are similar to those that result
from simulation of the Pickens and Grisak (1981) test but are somewhat more
significant because of the larger scale of the experiment.
In our simulation of the E1-I2 two-well test we chose to employ the
single-well test as a means for inferring the hydraulic conductivity
distribution in a relatively small aquifer region between the injection well
and a multilevel observation well. The two-well experiment was then used to
68
-------
i.o-
0.8-
0.6-
0.4-
0.2-
0.0-
= 3.2m3/hr
= 8.2m
V, =95.6m3
©EXPERIMENTAL
DATA
[PICKENS AND GRISAK, .-
1981]%
- NUMERICAL
RESULT
ar=avs0.oo7m
o o
0.0 0.4 0.8 1.2 1.6
VOL. WITHDRAWN / VOL. INJECTED
Figure 30. Comparison of SWADM results with field data for the
concentration leaving the injection-withdrawal well.
69
-------
test the prediction capability over a relatively large aquifer region, based
on the vertical distribution of hydraulic conductivity inferred from the
single-well test shown in Figure 21. This procedure helps to define what is
actually being measured during a single-well test and over what travel
distances such a measurement might retain some meaning. It also provides
insight concerning fundanental properties of the flow fields which were
established at the Mobile site during the various tests.
Two separate and independent models were used to simulate the results
of the two-well test. Under contract to Auburn University, GeoTrans, Inc.,
developed a three-dimensional advection-dispersion model that took advantage
of our particular geometry (Huyakorn et al., 1986a, 1986b). The aquifer was
divided vertically into 12 layers of varying thicknesses (Table 3),
depending on the rate of change of the relative hydraulic conductivity
distribution, and flow between the injection and production wells was
assumed to be stratified, steady and horizontal within each layer. The
advection pattern for such a situation is well known (Davis and DeWiest,
1966, p. 209), so the Darcy velocity, U, could be calculated at any
particular point within the 12-layer system (Huyakorn et al., 1986a, 1986b).
Given the known velocity distribution, the advection-dispersion equation was
solved using a finite element approach (Huyakorn et al., 1986b) with the
governing equation written in three-dimensional curvilinear coordinates
(s,n,z), where s and n are the coordinates along and normal to a local
streamline, and z is the vertical coordinate. In this system the
transformed advection-dispersion equation is given by
70
-------
Table 3. Two-well test parameters supplied to GeoTrans, Inc. for their
3-dimensional simulations based on the advection-dispersion equation.
(Normalized Hydraulic Conductivity Distribution)
Layer # Layer Layer Normalized Cond.
(1) Center (z.) Thickness tK(z.)/Kmay)
1 1 flla A
12 20.4 m
11 17.97
10 15.62
9 13.37
8 11.50
7 10.00
6 8.50
5 7.00
4 5.50
3 4.00
2 2.50
1 0.87
2.40 m
2.46
2.24
2.25
1.50
1.50
1.50
1.50
1.50
1.50
1.50
1.75
0.15
0.31
0.34
0.38
0.48
0.57
0.51
0.44
0.72
1.00
0.65
0.25
(Additional Parameters)
Longitudinal dispersivity
Transverse (horizontal) dispersivity
Transverse (vertical) dispersivity..
Tracer injection time
Total injection time
One-half well spacing
Radius of injection and production w
Injection and production rates
Porosity
Aquifer thickness
Molecular diffusion coefficient.....
Screen location (Injection well)....
Screen location (Withdrawal well)...
E3 observation well coordinates
ells
. 0.15 m
. 0.05 m
. 0.01 m
. 3.19 days
. 32.5 days
. 19.14 m
. 0.08 m -
. 0.9464 m /min
. 0.35
. 21.6 m .
. 1x10 m /s
Fully penetrating
Fully penetrating
. (x=13.56 m, v = 0)
71
-------
where DS> Dn and DZ are principal components of the hydrodynamic dispersion
tensor in the longitudinal, transverse and vertical directions, respective-
ly, and hj and h2 are the scale factors of the curvilinear coordinate system
(Huyakorn et al., 1986a). The dispersion coefficients are defined as
Ds = aL U/e + DQ (Ha)
Dn = «T U/e (Hb)
Dz =
-------
CONCENTRATION (MG/L)
H-
OQ
C
n>
tjj
: po
o n>
(D en
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H- I—1
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ft>
rr O
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; B)
i-i
O H-
1-1 O
C
n en
c
I-i
ro
01
01
b
Ol
— — — — ro ro ro
O ro 01 ->i o ro 01
O 01 b 01 b 01 b
en
H*
3
C
I
Hi I—1
H. to
rt rt
rt H-
h1- O
3 3
OQ en
O O
3 ET
^ 0)
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o
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^ <
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< >
CO -r-
n ^
n
"^ o
c
—
Q
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=J
0
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a
O
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3
CD
3
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i
O
-------
recovery concentrations during the two-well test. Since the two independent
predictions agreed quite well, one can conclude that local hydrodynamic
dispersion played a very minor role in determining the time distribution of
tracer concentration in the withdrawal well. The entire experiment, which
involved estimated travel distances over individual flow paths ranging from
38.3 m to about 90 m in the most permeable layer, was highly advection-
dominated. The dominant role of advection in the two-well test was also
noted earlier by Hoopes and Harleman (1967) for the case of a homogeneous
aquifer.
We would like to emphasize that no prior calibration was done in order
to arrive at the results shown in Figure 31. All of the information
supplied to our subcontractor is listed in Table 3. They did not know the
result of the experiment they were attempting to simulate. With the excep-
tion of the dispersivity values and the porosity, all of the information
contained in Table 3 was measured directly in the field or calculated from
field measurements. The dispersivity values were chosen arbitrarily to have
relatively small finite values because the 3-D model would develop numerical
dispersion and/or excessive CPU time problems if the dispersivity got too
close to zero. Porosity was measured in the laboratory on disturbed core
samples obtained from well E3 during drilling operations. The seven samples
were compacted lightly and the porosity measured based on the determination
of solids specific gravity and saturated water content. The average for
well E3 was 0.41. It was reasoned that this value would likely be higher
than the undisturbed in-situ values, so an effective porosity of 0.35 was
chosen prior to any simulations. The 3-D model result in Figure 31, based
on the 0.35 porosity value, was obtained from a single computer run which
74
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required 8.5 hours of CPU time on a Prime 550-2 minicomputer (Huyakorn et
al., 1986b). Runs at Auburn University based on identical data using TV/AM
(Falta, 1984; G'liven et al., 1986) were performed independently of the
GeoTrans run.
The calculated withdrawal concentration functions in Figure 31 were
obtained from a flow-weighted average of the concentrations along the
withdrawal well screen and thus is a vertically integrated quantity. A
comparison between concentration breakthrough curves measured at the 7
discrete levels of observation well E3 and those predicted by the 3-D model
are shown in Figure 24. At levels 2, 4, 5, and 6, the agreement is good,
while at levels 3 and 7 it is poor. A valid comparison cannot be made at
level 1 because of an apparent leak in the tubing used to obtain the level 1
samples (Molz et al., 1985). The mixed results of Figure 24 are not unex-
pected because one would not expect the normalized hydraulic conductivity
distribution shown in Figure 21 to remain completely invariant in a fluvial
aquifer over the 38.3 m separation between the injection and production
wells. However, it is significant that the integrated prediction (Figure
31) remains quite good.
The prediction of concentration versus time in the withdrawal well is
sensitive to the normalized hydraulic conductivity distribution. Shown in
Figure 32 is the withdrawal concentration breakthrough that would result if
one assumed a homogeneous aquifer with a normalized hydraulic conductivity
of unity throughout. In such a situation, one would observe a longer travel
time for the first arrival of the tracer at the withdrawal well and a much
higher peak concentration than was realized during the actual experiment.
However, the general behavior of the tail of the curve does not appear sen-
sitive to the details of the normalized hydraulic conductivity distribution.
75
-------
o>
E
o
50
45
40
35
30
< 25
tr
UJ 20
I 5
I 0
00
40 80 I2O 160 200 240 280 320 360 400 44O 46O 520 560 6OO 640 68O 720 760
TIME (hrs.)
Figure 32. Calculated tracer concentration versus time in the withdrawal
well based on an assumed homogeneous, isotropic aquifer with
no local dispersion£circles) shown together with the results
of the present two-well test (full line).
76
-------
A good fit to the data results if one assumes a full-aquifer longitudinal
dispersivity of 4 m (Huyakorn et al., 1986b).
Further understanding of the implications of the data and computations
contained in Figures 24 and 31 can be obtained by selecting a normalized
hydraulic conductivity distribution so that the computed and measured
breakthrough curves of Figure 24 are made to agree with each other as far as
peak arrival times are concerned. (Essentially, this is equivalent to using
the two-well test itself to estimate the normalized hydraulic conductivity
distribution.) This was discussed previously, and the distribution shown in
Figure 25 was obtained. There is not a tremendous difference between the
normalized hydraulic conductivity distributions shown in Figures 21 and 25,
but the Figure 25 conductivity values in the upper half of the aquifer are
smaller. A TWAM simulation of the withdrawal well concentrations based on
the Figure 25 distribution is shown in Figure 33. While the rising limb of
the breakthrough curve is not simulated as well, there is closer agreement
between the data and computations for the falling limb than was obtained
previously (Figure 31) using the normalized hydraulic conductivity distribu-
tion shown in Figure 21. Overall, the simulations shown in Figures 31 and
33 are of comparable quality.
The single-well and two-well test simulations discussed in this section
pertained to different aquifers in widely separated locations. The
single-well test was performed in a clean, sandy, glaciofluvial aquifer in
Canada, while the two-well test was performed in a fluvial, low-terrace
deposit containing sand with appreciable amounts of clay. Both simulations
were quite accurate in an integrated sense and consistent with an advection-
dominated (shear flow) dispersion process. When advection was considered
77
-------
CO
C71
E
o
I-
<
LU
CJ
25.0
22.5
20.0
I 7.5
I 5.0
I 2.5
10.0
7.5
5.0
2.5
0.0
' H
° / \o
/
/
/' \w
/ Y°o .
\ ;> cf'
• ~O
.'
.
\
o\
\
O
./NO
o o
0 O O
o o
0
40 80 120 160 200 240 280 320 360 400 440 480 520 560 600 640 680 720 760
TIME (hrs.)
Figure 33. Comparison of measured and calculated tracer concentration versus
time in the withdrawal well based on the normalized hydraulic
conductivity distribution shown in Figure 25.
-------
explicitly, large, scale-dependent, full-aquifer dispersivities were not
required.
Discussion and Conclusions
In the recent past, some hydrologists advocated the use of single-well
or two-well tracer dispersion tests as a means for measuring full-aquifer
longitudinal dispersivity. However, our analyses of single- and two-well
tests in stratified aquifers indicate that if this is done, the resulting
number will have little physical meaning. In the case of single-well tests,
the full-aquifer breakthrough curves measured in observation wells are
determined mainly by the hydraulic conductivity profile in the region
between the injection-withdrawal well and an observation well if the travel
distance between the injection-withdrawal well and the observation well is
typical of most test geometries. Thus, information about the conductivity
profile is necessary for meaningful test interpretation. The relative
concentration versus time data recorded at the injection-withdrawal well
itself is primarily a measure of the combined local and (perhaps?) semi-
local dispersion which has taken place during the experiment. Of course,
the effects of such dispersion will depend in part on the hydraulic
conductivity distribution in the aquifer, and in part on the size of the
experiment. As the size of the experiment increases, the effects of local
vertical dispersion will become larger compared to the effects of local
radial dispersion (Guven et al., 1985).
The two-well test simulations show that the concentration versus time
breakthrough curve measured at the withdrawal well would be very sensitive
to variations of the hydraulic conductivity in the vertical. Without the
use of multilevel observation wells, the test would give little useful
information about the hydraulic or dispersive characteristics of the
79
-------
aquifer, such as aquifer stratification or values of local dispersivities.
Factors such as the length of the injection period, the use of recircula-
tion, and the physical size of the experiment all have a strong effect on
the breakthrough curve measured at the withdrawal well, making the interpre-
tation of field results difficult, unless aquifer stratification is measured
and properly taken into account (Guven et a!., 1986).
Based on the above observations and the large values for full-aquifer
dispersivities that consistently result from calibrated area! groundwater
transport models, we believe that the following working conclusions are
warranted.
I. Local longitudinal hydrodynamic dispersion plays a relatively
unimportant role in the transport of contaminants in aquifers.
Differential advection (shear flow) in the horizontal direction
is much more important.
II. The concept of full-aquifer dispersivity used in vertically-
averaged (area!) models will not be applicable over distances of
interest in most contamination problems. If one has no choice
but to apply a full-aquifer dispersion concept, the resulting
dispersivity will not represent a physical property of the
aquifer. Instead, it will be an ill-defined quantity that will
depend on the size and type of experiment used for its supposed
measurement.
III. Because of conclusion II, it makes no sense to perform tracer
tests aimed at measuring full-aquifer dispersivity. If an area!
model is used, the modeler will end up adjusting the dispersivity
during the calibration process anyway, independent of the
measured value.
80
-------
IV. When tracer tests are performed, they should be aimed at determin-
ing the hydraulic conductivity distribution. Both our theoretical
and experimental work have indicated that the variation of horizon-
tal hydraulic conductivity with respect to vertical position is a
key aquifer property related to spreading of contaminants.
V. Two- and three-dimensional modeling approaches should be utilized
which emphasize variable advection rates in the horizontal
direction and hydrodynamic dispersion in the transverse direc-
tions along with sorption and microbial/chemical degradation.
VI. In order to handle the more advection-dominated flow systems
described in conclusion V, one will have to utilize or develop
numerical algorithms that are more resistant to numerical
dispersion than those utilized in the standard dispersion-
dominated models.
As discussed in the introduction, much of our contemporary modeling
technology related to contaminant transport may be viewed as an attempt to
apply vertically homogeneous aquifer concepts to real aquifers. Real
aquifers are not homogeneous, but they are not perfectly stratified either.
What we are suggesting, therefore, is that the time may have arrived to
begin changing from a homogeneous to a vertically-stratified concept when
dealing with contaminant transport, realizing fully that such an approach
will be interim in nature and not totally correct. However, our performance
and simulation of several single- and double-well tracer tests suggests that
the stratified approach is much more compatible with valid physical con-
cepts, and at least in some cases, results in a mathematical model that has
a degree of true predictive ability. Nevertheless, real-world applications
will undoubtedly require calibration, which in the stratified approach would
81
-------
involve varying the hydraulic conductivity distribution rather than the
longitudinal dispersivity. The benefit is that when calibrating the K
distribution, one is dealing with the physical property that probably
dominates the dispersion process.
The change from a vertically-homogeneous to a vertically-stratified
approach will not be easy from a field measurement viewpoint nor will it be
inexpensive. The work of Pickens and Grisak (1981) and the work described
herein has developed some prototype technology and methodology for obtaining
the type of information shown in Figure 34. This figure presents the
results of a preliminary analysis of all single-well tests to date that have
been performed at the Mobile site and analyzed in the vertical plane shown
in Figures 15 and 34. The mean locations in the aquifer where the tests
took place are indicated in the bottom half of the figure.
Examination of the K/Kmax plots in Figure 34 reveal some interesting
trends. A high hydraulic conductivity zone in the bottom third of the
aquifer is evident in all four of the tests. A similar high hydraulic
conductivity zone appeared in the top third of the aquifer during the E5-E1
test and the E10-E9 test, but not in the two tests conducted in the vicinity
of 12. If one attempted to "fit" a stratified mathematical model to the
situation illustrated in Figure 34, the strict definition of a stratified
aquifer could not be maintained. As a practical necessity, one would have
to postulate a "local" or "quasistratified concept" wherein flow was
generally horizontal on the average with the vertical distribution of
horizontal hydraulic conductivity gradually shifting from one distribution
to the other. There are, however, other considerations that may make the
"approximately stratified" idealization work better than expected. While
the imposed flow was observed to be locally stratified in the present
82
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-40 -30
-20 - I 0 0 10 20
Horizontal Distance (m)
30
40
Figure 34. Preliminary results of four single well tests
performed at the Mobile site. All stations shown
are situated at approximately the same vertical
plane.
83
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experiments and in the experiments of Pickens and Grisak (1981), this does
not necessarily mean that the aquifer hydraulic conductivity distribution is
also stratified around the localities where the tests were performed; areal
variations of hydraulic conductivity could still be present at each level of
the aquifer around a test well. However, an overall stratified flow pattern
could still develop in a confined aquifer even if the hydraulic conductivity
distribution is not perfectly stratified. This is because the flow is
forced to be horizontal on the average in a confined aquifer, and a quasi-
stratified flow may develop along various flow paths in response to the
effective average value of the hydraulic conductivity at each level of the
aquifer along the flow path, as observed in the field experiments discussed
above. This behavior seems to be supported also by the results of some
ongoing numerical solute transport experiments presently being performed at
Auburn University. In a three-dimensional numerical experiment in a
confined aquifer with a completely random computer-generated synthetic
hydraulic conductivity distribution, it was observed, somewhat surprisingly,
that a quasistratified flow field developed along the entire travel path of
a contaminant slug introduced numerically into the aquifer, which resulted
in considerable longitudinal spreading (shear flow dispersion) of the
contaminant plume.
A question that should be considered further relates to the practical
feasibility of performing the tracer tests required by the stratified
approach. In most situations we view tracer tests as feasible technically
but only marginally feasible in a routine practical sense. As discussed in
the section on multilevel sampling wells, the unavailability of widely
accepted commercial equipment is a major practical impediment. However,
that problem may disappear in the near future, and the need to consider
84
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vertical aquifer property variations is very real. As illustrated by the
field work of Osiensky, Winter and Williams (1984), the use of full-aquifer
dispersion concepts to model what is essentially a shear flow dispersion
process does not result in a conservative estimate of contaminant concentra-
tions. Instead, the model induces a large amount of artificial mixing which
often leads to an unrealistically-rapid dilution of a contaminant plume.
Such an analysis at a site in central Wyoming concluded that the 1000 mg/1
sulfate contour line was located at a maximum distance of about 450 m
downgradient from the source. However, further study by Osiensky et al.
(1984) which considered the structure of the fluvial aquifer in more detail
showed that there were portions of the aquifer 1020 m downgradient that
contained sulfate concentrations in excess of 5000 mg/1. Occurrence of this
kind of potential mistake can be minimized only by including more
information about the actual geometry and hydraulic conductivity
distribution regardless of whether a mathematical model is part of the
analysis. The interim stratified aquifer approach to tracer test analysis
and modeling discussed herein is meant to be a step in that direction.
One obvious implication of our study is that any type of groundwater
contamination analysis and reclamation plan will be difficult, expensive and
probably unable to meet all of the desired objectives in a reasonable time
frame. This reinforces the time-honored saying that 0.0283 kg (1 oz) of
prevention is worth 0.454 kg (1 Ib) of cure, which in the case of
groundwater pollution is probably an understatement. One can not over-
emphasize the advantages of preventing such pollution whenever it is
feasible.
85
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GOVERNMENT PRINTING OFFICE : 1986-646-116/40654
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