EPA/600/R-93/209
September 1993
MULTILEVEL PUMPING WELLS AS A MEANS FOR
REMEDIATING A CONTAMINATED
COASTAL AQUIFER
Exposure Assessment Group
Office of Health and Environmental Assessment
U.S. Environmental Protection Agency
Washington, D.C.
Printed on Recycled Paper
-------
DISCLAIMER
This document has been reviewed in accordance with U.S. Environmental Protection
Agency policy and approved for publication. Mention of trade names or commercial products
does not constitute endorsement or recommendation for use.
11
-------
CONTENTS
Tables iv
Figures . ., v
Foreword vii
Preface . viii
Authors and Reviewers ix
1. EXECUTIVE SUMMARY 1
2. INTRODUCTION 3
3. REVIEW OF SALTWATER ENCROACHMENT . 5
3.1. REGIONAL FRESHWATER/SALTWATER INTERFACE 5
3.2. SALTWATER ENCROACHMENT 7
4. THEORY OF SALTWATER INTERFACE UPCOMING 10
4.1. HYDRAULICS OF VERTICAL SALTWATER MOVEMENT 10
4.2. DEVELOPMENT OF MATHEMATICAL THEORY 15
5. MULTILEVEL PUMPING WELLS 24
5.1. BACKGROUND 24
5.2. THEORETICAL SOLUTION 26
5.3. DESIGN . 34
6. APPLICATION 37
6.1. FRESHWATER PRODUCTION WELLS 37
6.2. REMOVAL OF FLOATING IMMISCIBLES 48
7. CONCLUSIONS 51
8. REFERENCES 52
111
-------
TABLES
1. Ground-water conditions at the Semadar well field 18
2. Ground-water conditions at the Semadar well field assuming the
existence of a multilevel pumping-well system 29
3. Ground-water conditions at La Trocha well field assuming the
existence of a multilevel pumping-well system . 36
IV
-------
FIGURES
1. Cross-sectional view of saltwater encroachment due to an
advancing interface toe 6
2. Plan view of saltwater encroachment due to an advancing interface toe ..... 6
3. Upconing of the saltwater interface as a result of pumping from the
freshwater zone of a coastal aquifer 7
4. Upconing of an abrupt interface below a pumping well 7
5. Schematic figure depicting equipotential lines and flow of saltwater
for a fully penetrating aquifer that is isotropic with respect to
horizontal and vertical hydraulic conductivity . 9
6. Schematic figure depicting equipotential lines and upward flow
of saltwater for a partially penetrating well in an aquifer that is
isotropic with respect to horizontal and vertical hydraulic conductivity 10
7. Schematic figure depicting equipotential lines and upward flow
of saltwater for a partially penetrating well in an aquifer
in which the horizontal hydraulic conductivity is greater than the
vertical hydraulic conductivity . 11
8. Schematic figure depicting equipotential lines and upward flow
of saltwater for a partially penetrating well in an aquifer
in which the vertical hydraulic conductivity is greater than the
horizontal hydraulic conductivity . 11
9. Schematic figures depicting equipotential lines and upward flow
of saltwater in response to ground-water pumping fully penetrating
wells and a partially penetrating well, each with vertical differences
in horizontal hydraulic conductivity ...;... . 12
10. Upconing of an abrupt interface below a pumping well
with emphasis on the effect of the critical rise .................... 1.5
11. Theoretical rise of the interface at the Semadar well field
after pumping for 84 days . 19
12. Theoretical effect of superimposing two pumping wells on a coastal aquifer . . 21
-------
13. Saltwater upconing at the Semadar well field versus model prediction ...... 29
14. Net freshwater/saltwater interface movement resulting from pumping
both above and below the interface concurrently . 30
15. Net freshwater/saltwater interface movement resulting from
pumping both above and below the interface concurrently but
with an expanded y-axis to allow visualization of the actual
effect on the interface 31
16. Schematic representation of La Trocha well used by the U.S.
Geological Survey to test the multilevel pumping-well theory
for the production of freshwater 37
17. Chloride concentrations of water drawn from La Trocha upper intake
and lower intake pumping simultaneously 38
18. Model simulation of the pumping scenario at La Trocha well
demonstrating the similarity between the model results and
actual field-test data . . ; 40
18a. Model simulation same as for Figure 18 but with an expanded y-axis
to provide a clearer indication of the effect on the interface
produced by the multilevel pumping-well system 41
19. Model simulation of the pumping scenario at La Trocha well
demonstrating the similarity between the model results and the actual
field-test data . . ... . 42
19a. Model simulation same as for Figure 19 but with an expanded y-axis
to provide a clearer indication of the effect on the interface
produced by the multilevel pumping-well system 43
20. Model simulation of the pumping scenario at La Trocha well
demonstrating the similarity between the model results
and the actual field-test data 44
20a. Model simulation same as for Figure 20 but with an expanded
y-axis to provide a clearer indication of the effect on the
interface produced by the multilevel pumping-well system of
La Trocha well at 72 gpm and the lower level at 18 gpm ..... .'..'"'. .... 45
21. Schematic figures depicting a two-pump system using two small-
diameter wells and a two-pump system employing one recovery well 48
VI
-------
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. Protection of the environment involves searching 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.
This document is the result of an initiative to design and mathematically model a
ground-water withdrawal system that would increase well yields at two Superfund sites with
contaminated coastal aquifers, without inducing the movement of saltwater up into the
freshwater zone of the aquifer. Implementing the model equation before initiating a pump-
and-treat effort or operating a freshwater production well should roughly predict how a
coastal aquifer will likely behave under new stress conditions imposed by the operation of a
pumping system on the aquifer. The equation is fairly simple and easily implemented on a
computer. The operation of a multilevel pumping-well system has been shown to be
effective in improving overall well yields.
Michael A. Callahan
Director
Exposure Assessment Group
Vll
-------
PREFACE
The Exposure Assessment Group of the Office of Health and Environmental
Assessment (OHEA) has prepared this document at the request of Region II. It describes a
mathematical model to be used hi controlling the upconing of saltwater into coastal aquifers
and/or the downconing of light nonaqueous phase liquids (LNAPLs) into aquifers. Further,
it provides technical support for any coastal area, either with a contaminated aquifer or with
an aquifer contaminated by LNAPLs, for which a pump-and-treat operation in planned. The
analysis provided here will help minimize exposure to contaminated ground water while
maximizing removal and treatment of the contaminated ground water.
The purpose of this document is to serve as a technical guide in maximizing the
removal of contaminated ground water from an aquifer hi which two-phase flow is evident
and thus minimize exposure to contaminated ground water. It will be used by the Office of
Solid Waste and Emergency Response in implementing RCRA and CERCLA.
The literature search to support the models discussed hi this document is current to
January 1992.
vm
-------
AUTHORS AND REVIEWERS
The Exposure Assessment Group within the U.S. Environmental Protection Agency's
Office of Health and Environmental Assessment was responsible for the preparation of this
document and provided overall direction and coordination during the production effort. The
research was funded, wholly or hi part, by the U.S. Environmental Protection Agency under
Contract No. 68-01-7361 to PRC, Inc.
AUTHORS
Malcolm S. Field
Exposure Assessment Group
Office of Health and Environmental Assessment
U.S. Environmental Protection Agency
Washington, DC
Michael Critchley
PRC, Inc.
Fairfax, VA
REVIEWERS
Eva L. Davis
Robert S. Kerr Environmental Research Laboratory
U.S. Environmental Protection Agency
Ada, OK
Eugene Simpson
University of Arizona
Tucson, AZ
A. Richard Smith
Texas Dept. of Health
Bureau of Solid Waste Management
Austin, TX
Allen Zack
U.S. Geological Survey
San Juan, PR
IX
-------
-------
1. EXECUTIVE SUMMARY
Releases of chemical wastes that reach coastal aquifers can be difficult to remediate
because the operation of a conventional pump-and-treat system may exacerbate ground-water
quality problems by inducing upward migration of denser saltwater into the freshwater zone,
an occurrence known as interface upconing. Interface upconing occurs because pumping
solely from the freshwater zone in a coastal aquifer redistributes the hydraulic head potentials
in the two fluids. The rate of upconing initially proceeds slowly, but increases over time
until a new equilibrium is established. Each new pumping rate results in a new equilibrium
until the critical rate of rise is exceeded and saltwater freely flows into the pumping wells.
Interface upconing may be overcome by use of multilevel pumping wells, consisting of one
well installed in the freshwater zone and one well installed in the saltwater zone. By
pumping both wells simultaneously, hydraulic head gradients can be maintained throughout
the entire saturated thickness of the aquifer, thus preventing any net movement of the
freshwater/saltwater interface.
The main effort of this research was to develop a model that would determine the
potential effectiveness of an enhanced recovery or containment system for contaminated
ground water in coastal aquifers. Based on a modification of existing theories, the multilevel
pumping-well concept is not commonly used because of the added expense of pumping and
disposing of unwanted saltwater, yet this method could be used not only in contaminated
coastal aquifers but also in coastal aquifers where larger yields of fresh drinking water are
desired, or in inland aquifers where floating nonaqueous phase liquids are present. In the
latter instance, multilevel pumping wells have been proposed recently as a means of
enhancing the removal of contaminated ground water.
The need for this study is evident by the numerous industrial sites located in coastal
areas. Industrial facilities are located along coastal areas for a variety of purposes (shipping,
waste discharge, etc.). At two Superfund sites in Puerto Rico with evidence of severe
ground-water contamination by industrial solvents, the contaminant plumes are migrating
within coastal aquifers that cannot be readily remediated. In fact, an EPA contractor
recommended "writing off the contaminated aquifer at one site because of the difficulty
1
-------
associated with remediating the aquifer and because of serious upconing problems already
evident in the area. However, by simultaneously pumping from different levels in the
aquifer, it is possible that real remediation may be achieved with minimal damage to the
aquifer.
The approach to solving the upconing problem was to modify proven analytical
equations that describe the process of upconing to take into account the effect of two wells
pumping from a coastal aquifer, with one well above the freshwater/saltwater interface and
one well below the interface. By assuming equal conditions throughout the aquifer (a
simplifying albeit unrealistic assumption), it is possible to set the existing governing equation
for interface upconing equal to a modification of itself so that the net effect is a steady
interface. The modifications are necessary to account for different pumping depths, different
fluid densities, and so forth so that a neutral effect may be obtained. Due to the complexities
of mathematically modeling a moving interface, achieving even preliminary results took a
great deal of effort. However, test results from various sources indicate that the model can
be useful in roughly predicting the likely response of a multilevel pumping-well system
before its implementation, provided the input parameters are relatively realistic and the user
has a reasonable expectation of the model.
-------
2. INTRODUCTION
Remediation of contaminated ground water is a topic of extensive research at present.
In every instance, a principal goal of the engineers and scientists involved in remediation is
to use a remediation strategy that is successful in restoring a contaminated aquifer to its
original, pristine condition in no more than a few years. In reality, this rarely occurs. In
fact, remediation of some aquifers is so difficult, expensive, and time consuming that some
individuals advocate "writing off these aquifers (Freeze and Cherry, 1989). The most
commonly chosen remediation strategy involves some form of pump-and-treat technology.
For that strategy to be reasonably effective, detailed knowledge of the site hydrogeology is
essential. No amount of knowledge may be enough because contaminant extraction often
causes an initial decrease in contaminant concentration that rapidly levels off to a point where
further removal may take decades or longer (Mackay and Cherry, 1989), an impractically
long time.
Misapplication of pump-and-treat technology may also cause deleterious effects on an
aquifer. For example, pump-and-treat technology may exacerbate ground-water quality
problems through overpumping the freshwater zone of an aquifer underlain by seawater.
Overpumping occurs at oceanic islands, elongated peninsulas, and coastal aquifers where
freshwater production wells are placed seaward of an advancing toe of saltwater or where an
interface bypasses an existing production well (Bear, 1979, p. 414). Excessive freshwater
pumping produces a rise in the interface separating the freshwater zone from the saltwater
zone toward the pumping well. This interface upconing can create serious chloride
contamination of the freshwater zone in a coastal aquifer, rendering it unusable as a drinking-
water supply. Thus, a pump-and-treat remediation strategy for a coastal aquifer must
account for density stratification in the aquifer.
Because interface upconing can result in such severe contamination of a coastal
aquifer, use of conventional pump-and-treat technology is severely limited. Some groups
recommend against implementing a pump-and-treat strategy to remediate a contaminated
aquifer solely to avoid upconing. A multilevel pumping-well system can, however, facilitate
the removal of aquifer contaminants without further exacerbating aquifer contamination.
-------
Much of the following discussion centers on the effect of pumping a coastal aquifer,
but the method need not be limited to freshwater/saltwater interface problems. It is equally
applicable to inland aquifers contaminated by a light nonaqueous phase liquid (LNAPL),
which tends to float on top of the aquifer due to density differences and the lack of
miscibility (Blake and Lewis, 1982).
-------
3. REVIEW OF SALTWATER ENCROACHMENT
Coastal aquifers consist of a freshwater lens overlying saline water as a result of
density differences and lack of mixing. Numerous publications on the subject of saltwater
encroachment describe the physics of a migrating interface. Because it is not the purpose of
this paper to review the literature on saltwater encroachment, only specific references related
to a particular topic are included in this paper. Kashef (1977) and Custodio (1988) provide
comprehensive reviews of the literature.
3.1. REGIONAL FRESHWATER/SALTWATER INTERFACE
Understanding saltwater encroachment processes requires an understanding of the
behavior of the freshwater/saltwater interface under natural conditions. The well-established
Badon Ghyben-Herzberg Relationship addresses the main physical controls on the position of
the interface. By assuming simple hydrostatic conditions in a homogeneous, unconfined
coastal aquifer, it was shown that the interface separating saltwater from freshwater must
project into the aquifer at some angle a < 90° (Freeze and Cherry, 1979, p. 376). With
saltwater density of 1.025, freshwater density of 1.0, and hydrostatic conditions, the weight
of a unit column of freshwater extending from the water table to the interface is balanced by
a unit column of saltwater extending from sea level to the same depth as the point on the
interface (Freeze and Cherry, 1979, p. 377). Thus, under static conditions, by utilizing
Equation (1)
(1)
Ps - Pf
the interface is calculated to be 40 meters below sea level where Zz = depth to the interface,
Zw = depth to ground water, p^ = density of freshwater, and ps = density of saltwater.
Equation (1) states that a stationary interface at any distance from the sea will be below sea
level 40 times the height of the water table above sea level (Bear and Verruijt, 1987, p.
203). Lowering the water table just one meter results in a 40-meter rise in the interface.
-------
As a result of two significant problems, the true depth of the.interface is
underestimated when this relationship is employed. First, no freshwater discharge is allowed
in this relationship. Hubbert (1940) demonstrated that the interface and the sea do not
intersect at the coastline. Rather, they intersect along a plane extending out from the
coastline along which ground water discharges. Second, ground water is dynamic, not static.
Using the theory of potentials, Hubbert showed that, because dynamic flow conditions exist,
the position of the interface will be controlled by the head distribution. This is shown in
Equation (2)
sin e = -^ = A
OX SH
- Pf
pg - pf di
(2)
where
subscripts/and s are freshwater and saltwater, respectively;
6 = the angle of the trace of the interface with the horizontal;
g = gravity;
i *= the trace of the interface in a vertical plane; and
(3)
(4)
Units qd and q^ are the components of the specific discharge along the trace of the interface.
It follows that because pf < ps, as the rate of freshwater flow increases, sin 0 will also
increase, and the interface will slope upward in the direction of flow. Because the specific
discharge q is a function of the hydraulic conductivity, the latter plays a crucial role in the
-------
dynamic behavior of the freshwater/saltwater interface. The single parameter, -
-------
Fully Penetrating
Pumping Well
Unconfined
Interface Flow
Interface
altwater Tip
S = Stagnation Point
Figure 1. Cross-sectional view of saltwater encroachment due to an advancing interface toe
(modified from Strack, 1976).
Streamlines
Coast
Ocean
Unconfined Unconfined
Interface Flow Flow
S = Stagnation Point
Figure 2. Plan view of saltwater encroachment due to an advancing interface toe (modified
from Strack, 1976).
8
-------
Interface
Figure 3. Upconing of the saltwater interface as a result of pumping from the freshwater
zone of a coastal aquifer.
X
of
o
nj
-------
4. THEORY OF SALTWATER INTERFACE UPCON1NG
The hydraulics of vertical saltwater movement is extremely complex and, as such, is
not easily explained from either a conceptual or a mathematical point of view. Two
investigators, however, have developed good discussions of the subject of interface upconing.
Zack (1988) provides an excellent overall conceptual discussion of the upconing process,
while Schmorak and Mercado (1969) present an elegant mathematical analysis of the process.
Both discussions are reviewed here because of their direct relevance to this report.
4.1. HYDRAULICS OF VERTICAL SALTWATER MOVEMENT
Saltwater is produced from a coastal aquifer as a result of several factors, all of which
are of crucial importance. These factors are (1) pumping rate; (2) location of the
freshwater/saltwater interface; (3) vertical positions of well screens in the aquifer; and (4) the
distribution of horizontal and vertical hydraulic conductivity within the aquifer, which
determines the distribution of hydraulic heads likely to develop in the aquifer during pumping
(Zack, 1988). Other factors are relative densities of the various fluids of interest,
permeabilities of the solid medium, and length of time of pumping. The degree of
importance of any one factor compared with the others is highly variable and depends on the
specific attributes of the aquifer under study and the well completion characteristics. Hence,
individual factors by themselves may not be regarded as inconsequential even when
considered against the cumulative effect of all other factors. As a result, all relevant factors
must be considered together if the extent of interface upconing is to be assessed properly.
Fully penetrating wells (wells that fully penetrate the aquifer, Figure 1) and partially
penetrating wells (wells that penetrate only some proportion of the aquifer, Figure 3) produce
different effects. It does not take much insight to recognize that fully penetrating wells will
draw in both freshwater and saltwater. For this reason, coastal aquifers are usually
penetrated only partially, with the well screen(s) set at some preset vertical distance above
the interface to minimize the chances of saline water entering the well bore. Unfortunately,
partially penetrating wells tend to cause vertically upward movement of the interface during
10
-------
pumping. Until some new equilibrium is established, the upconing process continues.
Eventually, brackish water will enter the well bore followed by saline water.
In reality, the migration of saline water into a well bore is not as simple as just
described. According to Zack (1988), saltwater cannot easily rise to a pumped well in a
partially penetrating well because the energy required to "lift" the saltwater to the well is
greater than that in fully penetrating wells. Thus, the degree and behavior of vertical change
in the interface depend on the horizontal and vertical distributions of hydraulic conductivity,
the extent of well penetration, and the pumping rate; a greater pumping rate will likely result
in a greater "pull" on the interface.
Full penetration of a coastal aquifer that exhibits isotropy with respect to horizontal
hydraulic conductivity will not produce a vertical flow component (Figure 5) regardless of
variations in vertical hydraulic conductivity (Zack, 1988), pumping rate, porosity, or any of
the other factors. This results from the differing fluids entering the well at the same rate at
every point along the well bore. As can be seen in Figure 5, vertical movement of the
interface is not a realistic possibility because the draught pressures are distributed equally
throughout the aquifer and the horizontal hydraulic conductivity remains uniform throughout
the aquifer.
(—Fully p«n«tr«tlnfl w«ll
EXPLANATION
„
._..
TRANSVERSELY
ISOTROPIC
(KH-Kv) ,
u
EQUIPOTENTIAL LINE Of
PRESSURE HEAD
SHAPE OF SALTWATER
MOUND AT DIFFERENT
DEPTHS WITHIN AQUIFER
K HORIZONTAL HYDRAULIC
H CONDUCTIVITY
K VERTICAL HYDRAULIC
w CONDUCTIVITY
Figure 5. Schematic figure depicting equipotential lines and flow of saltwater for a fully
penetrating aquifer that is isotropic with respect to horizontal and vertical hydraulic
conductivity (from Zack, 1988).
11
-------
Partially penetrating wells, on the other hand, will produce a vertically upward
movement of the interface (Figure 6) because the flow lines develop from all directions,
including a vertical component underneath the well bore.
Partially penetrating well
EXPLANATION
TRANSVERSELY
ISOTROPIC
(KH-Kv)
u
EQUIPOTENTIAL LINE OF
PRESSURE HEAD
SHAPE OF SALTWATER
MOUND AT DIFFERENT
DEPTHS WITHIN AQUIFER
KH HORIZONTAL HYDRAULIC
CONDUCTIVITY
Ku VERTICAL HYDRAULIC
CONDUCTIVITY
Figure 6. Schematic figure depicting equipotential lines and upward flow of saltwater for a
partially penetrating well in an aquifer that is isotropic with respect to horizontal and vertical
hydraulic conductivity (from Zack, 1988).
If the horizontal hydraulic conductivity is much greater than the vertical hydraulic
conductivity, then the horizontal flow components will be comparatively greater than the
vertical flow components (Figure 7).
Partially penetrating well
EXPLANATION
U
EOUIPOTENTIAL LINE OF
PRESSURE HEAD
SHAPE OF SALTWATER
MOUND AT DIFFERENT
DEPTHS WITHIN AQUIFER
Ku HORIZONTAL HYDRAULIC
' CONDUCTIVITY
K VERTICAL HYDRAULIC
V CONDUCTIVITY
Figure 7. Schematic figure depicting equipotential lines and upward flow of saltwater for a
partially penetrating well in an aquifer in which the horizontal hydraulic conductivity is
greater than the vertical hydraulic conductivity (from Zack, 1988).
12
-------
Alternatively, where discrete vertical pathways such as fractures or conduits exist in the
aquifer, a vertical hydraulic conductivity that is greater than the horizontal hydraulic
conductivity may result, with a comparatively greater vertical flow component than in the
horizontal direction (Figure 8). In the last case, saline water intrusion may enter the well
very rapidly.
Partially panatrating wall
EXPLANATION
U
EOUIPOTENTIAL LINE Of
PRESSURE HEAD
SHAPE OF SALTWATER
MOUND AT DIFFERENT
DEPTHS WITHIN AQUIFER
KH HORIZONTAL HYDRAULIC
CONDUCTIVITY
K VERTICAL HYDRAULIC
W CONDUCTIVITY
Figure 8. Schematic figure depicting equipotential lines and upward flow of saltwater for a
partially penetrating well in an aquifer in which the vertical hydraulic conductivity is greater
than the horizontal hydraulic conductivity (from Zack, 1988).
Aquifers made up of layers of differing geological materials form anisotropic
aquifers. Anisotropic aquifers tend to have varying vertical distributions of horizontal
hydraulic conductivity throughout the aquifer. The variability in vertical distribution of
horizontal hydraulic conductivity complicates the behavior of flow lines and equipotential
lines by causing the flow lines to converge to, and in, the more hydraulically conductive
layers (Zack, 1988). This effect occurs irrespective of whether the pumping well is fully or
partially penetrating (Figure 9). Hence, saltwater will migrate along the flow lines that
develop according to the ratios of horizontal to vertical hydraulic conductivity within the
aquifer, and the migration of saline water in a fully penetrating well will behave similarly to
that in a partially penetrating well when the vertical distribution of horizontal hydraulic
conductivity is very large (Zack, 1988).
13
-------
FULLY PENETRATING WELL
FULLY PENETRATING WELL
I
PARTIALLY PENETRATING WELL
I
EXPLANATION
| | HIGH HYDRAULIC CONDUCTIVITY
Hill"1;! LOW HYDRAULIC CONDUCTIVITY
L~Z3
VERY LOW HYDRAULIC
CONDUCTIVITY
EOUIPOTENTIAL LINE OF PRESSURE HEAD
SHAPE OF SALTWATER MOUND AT
DIFFERENT DEPTHS WITHIN AQUIFER
Figure 9. Schematic figures depicting equipotential lines and upward flow of saltwater in
response to ground-water pumping fully penetrating wells (A and B) and a partially
penetrating well (C), each with vertical differences in horizontal hydraulic conductivity (from
Zack, 1988).
14
-------
Pumping a well at a constant rate eventually will result in a new equilibrium in the
aquifer some time after pumping has begun. According to Zack (1988), the process of
interface upconing stabilizes at some point in time because of differences in the density and
dynamic viscosity of the freshwater and saltwater within the aquifer. Zack shows this to be
true by referring to Darcy's law, by which the amount of water entering a well bore depends
on the hydraulic gradient, the permeability of the aquifer materials, and the density and
dynamic viscosity of aquifer fluids at every point within the aquifer. As pumping begins, the
permeability of the various aquifer materials and the resulting hydraulic gradient will exert
the greatest control on the amount of freshwater and saltwater that will enter the well bore.
Over time, differences in hydraulic gradient along the well bore will become less, and fluid
properties (density and dynamic viscosity) will begin to achieve greater importance.
Eventually, a balance between the hydraulic gradient and the fluid properties will be
established, and the height and shape of the interface cone will be at equilibrium. As shown
in the section on mathematical theory of interface upconing, this is not entirely accurate and
is only true up to some critical level, at which point the interface will rapidly migrate up to
the bottom of the pumping well. Interface upconing beneath a partially penetrating well will
continue only until the upward hydraulic gradient becomes negligible (Zack, 1988) or, if the
critical level is exceeded, will accelerate up to the bottom of the well.
Having explained the process of interface upconing from a conceptual standpoint, we
now explain it from a mathematical standpoint. The next section serves as the basis for the
development of the equation that defines the effect of a two-well system stressing an aquifer
that contains two immiscible fluids separated by a sharp interface.
4.2. DEVELOPMENT OF MATHEMATICAL THEORY
Interface upconing is a very complex process that depends' on several factors, not the
least of which are density differences. Interface upconing is affected by pumping rate,
relative depth of the interface, depth of the well screen, and distribution of vertical and
horizontal hydraulic conductivity. Head distribution within the aquifer is determined by
variations in hydraulic conductivity. For this discussion, it is assumed that the aquifer under
consideration is homogeneous, isotropic, nondeformable, and areally extensive. Both liquids
15
-------
(freshwater and saltwater) are considered incompressible, immiscible with each other, and
nonreactive with .the aquifer, are separated by a sharp boundary, and obey Darby's law. As
with previous assumptions, these assumptions do not occur in nature but are necessary for
simplification.
Interface upcoriing in the simplest sense Is a result of a partially penetrating well
pumping from the freshwater zone of a coastal aquifer. The process of upcoriing is not
instantaneous because of the added lift Tequired to pump up the saltwater. It may be
assumed that the interface is unstable while at rest, so that even an infinitesimal increase in
the pumping-well discharge will be .sufficient to induce movement of the interface (Strack,
1976). By using a velocity potential that satisfies laplace's equation and a linearized
approximate solution based on the method of small perturbations, Dagan and Bear 0:968) and
Bear (1972, pp. 538-544 and 569-573) were able to obtain an analytical solution for small
deviations from which ;an initial steady interface was derived. The work of Dagan and Bear
later served as a basis for the work by Schmorak and Mercado (1969), which they applied to
a specific field condition in Israel. Their work is briefly reviewed here because it serves as
the basis for the research presented in this paper.
Schmorak and Mercado presented Dagan and Bear's (1968) solution for the position
of the interface as a function of time and radial distance from the pumping well that partially
penetrated a relatively .thick confined aquifer (Figure 10), For a partially penetrating well
screened in the freshwater zone, the following equations have been developed:
t)
R2 /
-------
ei|j MO|eg
jo asm ssaiuoisueuijQ • p/z
o
.8
I
co
'i
f
I
i
.s a
*!
II
^
o|
85
•I? I
-------
Q = pumping rate of the well;
= dimensionless ratio of density differences between the two fluids;
d = distance between the well's bottom and the interface at t=0;
r = radial distance from the well;
/ = time elapsed since start of pumping; and
R and r represent dimensionless distance and time parameters as provided by:
(Ap/pf)K
2nd
(6)
(7)
with
n = porosity of the aquifer; and
Kz and Kx, the vertical and horizontal hydraulic conductivity, respectively.
For r=0 (i.e., just below the pumping well), Equation (5) takes the form
2x(Ap/p)Kxd
i -
(8)
Figure 10 schematically displays the properties of Equations (5) and (8). By introducing T
from Equation (7) into Equation (8) and rearranging, Schmorak and Mercado obtained
K^
(Ap/pf)Kz
2nd
(9)
which may be simplified to
18
-------
Z/t = aQ - ftz
(10)
where a and /? are constants of the system as determined by tiie geometry and the physical
properties of the aquifer and the fluids. The linear relationship between the rate of interface
upconing Z/t and the extent of upconing Z has been shown to have a slope of -/3 and
intersects the ordinate at Z/t—a.
Allowing t-+ oo, Equations (5) and (8) become
Z(r,
2icd(Ap/pf)Kx
Hite
(11)
Z(r=0; t->
Q
2nd(Ap/pf)Kx
(12)
where Z is the ultimate interface rise at the new equilibrium and is directly proportional to
the pumping rate Q.
The linear approximation of the nonlinear potential boundary conditions limits the
linear relationship between Z and Q to the critical rise Zcr. Dagan and Bear (1968) noted
that as the rate of rise increases as Zcr is approached, the rate of interface rise will accelerate
according to the quantity given by Z/d > 1/3 -s- 1/2. From this relationship, it can be seen
that once Zcr has been exceeded, the upconed surface will reach the bottom of the pumping
well. Therefore, recognizing that this theory does not account for the effect imposed on a
transition zone, Dagan and Bear suggested that (Z/tf)max < 1/4 to ensure that overpumping
of the aquifer would not occur. Thus, the maximum permissible pumping rate is given by
Qa
(13)
recognizing the fact that Zmax ignores dispersion, which would require a further reduction in
19
-------
From Equation (13) developed by Schmorak and Mercado (1969), the importance of
Qmax becomes clear. For example, using the conditions that exist at the Semadar well field
(Table 1), Schmorak and Mercado noted that Qmax could not exceed 21.5 m3/hr (94.7 gpm)
or 516 nrVday (136,368 gpd). '
Table 1. Ground-water conditions at the Semadar well Held
Freshwater density
Saltwater density (ps)
Porosity (ri)
Horizontal hydraulic conductivity
Vertical hydraulic conductivity
Initial interface elevation (Z^)
Distance from bottom of
well to initial interface (d)
Pumping rate (0
Pumping period (?)
1.00 g/cm3
1.03 g/cm3
0.33
14.70 m/day
14.70 m/day
-30.75 m (MSL)
15.50m
348.00 nrVday
84.00 days
Even a modest increase in pumping above (?max would cause an unacceptable, accelerated
rise in the interface, but if contaminant plume control had been the desired goal, then this
pumping rate might not have been sufficient. Underpumping the aquifer might not be
adequate for controlling the migration of contaminants because the draught required for
plume removal and plume containment could require much greater pumping rates.
Figure 11 is a plot of the data recorded from the Semadar well field for a pumping
period of 84 days, when it became necessary to shut down the pumping system because the
rise in the freshwater/saltwater interface was rapidly approaching Zcr The data appear to
indicate that the pumping effect on the interface was leveling off and thus approaching a new
equilibrium, but this is incorrect. Once Zcr was reached, the rate of rise would have
accelerated rapidly and would have resulted in chloride contamination of the well.
20
-------
60 80
Time (days)
100
120
Figure 11. Theoretical rise of the interface at the Semadar well field after pumping for 84
days.
In reality, Equation (13) breaks down long before Zcr is reached because the upward
movement of brackish water along the interface readily occurs; even with a low pumping
rate, no limiting critical rise exists above which saline water will not rise (Todd, 1980, p.
504). Hence, any rate of continuous pumping will result in saline intrusion into the pumping
well(s). Todd relates this situation to Equation (13) by showing that as Ap approaches zero,
Qmsai must also approach zero, creating a thick transition zone that further reduces the rate of
safe withdrawal of freshwater. It should be noted that an aquifer as prolific as the one just
described could require a much greater pumping rate than proposed to contain a migrating
plume. To minimize the effect of upconing, Todd (1980, p. 505) recommends screening the
pumping wells as far above the interface as is possible. Unfortunately for contaminant plume
21
-------
control, the screened portion of the extraction well(s) must be placed at the depth of the
plume, which may not be very far above the freshwater-saltwater interface.
One pumping well is seldom adequate for plume containment or extraction because of
the large longitudinal and transverse dimensions of many plumes as a result of advection and
dispersion effects. The obvious solution to containment or extraction of a large contaminant
plume is to employ several extraction wells distributed throughout the length and width of the
contaminant plume. It then becomes a matter of applying the principle of superposition of
solutions to demonstrate the additional rise in the interface likely to occur. This is possible
because the Laplace equation is linear; it is accurate, however, only if the aquifer is
confined. If the aquifer is unconfined and upconing is significant in relation to the total
saturated thickness, the use of linear superposition will underpredict the actual total upconed
surface. If transmissivities are assumed to be equal throughout the aquifer and pumping rates
are equal for all extraction wells, it is possible to predict, with a reasonable degree of
accuracy, the additive rise in the interface surface. Figure 12 is a schematic representation
of the additive result that can be expected from the effects of well interference.
22
-------
Well 1
Well 2
Composite
Upconed
Surface
Figure 12. Theoretical effect of superimposing two pumping wells on a coastal aquifer
(modified from Bear, 1979, p. 423).
23
-------
5. MULTILEVEL PUMPING WELLS
Multilevel pumping wells, also known by names such as scavenger or production
wells, can be used effectively to produce relatively larger quantities of freshwater or water
polluted by chemical contaminants without creating the unwanted effects of saltwater
upconing. The concept is relatively simple. When two liquids are completely immiscible
and some sort of pumping apparatus is installed in one of the liquids, then the opposing
liquid is pulled toward the first liquid in an effort to achieve equilibrium. However, if
pumps are installed in both liquids and both are run at equal rates, assuming equivalent
physicochemical parameters for the two liquids (e.g., densities relatively equal), then there
should be no net movement of the interface separating the two liquids.
Although it has been well demonstrated that a sharp interface between saltwater and
freshwater is not really true and that such factors as density are significantly different, the
concept still holds, provided that the factors likely to affect the performance of such a system
are recognized before implementation and efforts are made to compensate for the expected
effects. This is not really difficult because the important differences are well understood by
the scientific community. Because the processes involved in saltwater upconing are so well
understood, the concept of using multilevel pumping wells for freshwater production has
been in existence for many years.
5.1. BACKGROUND
Although the theory of multilevel pumping wells has been well known for many
years, these wells have rarely been used for freshwater production in the past because of the
additional cost of unwanted saltwater. Additional costs include installation of one or more
additional wells where only one well would normally have been installed, deeper installation
than is normally desired, additional lift required for saltwater removal, and disposal of
unwanted saltwater. Multilevel pumping wells also have uncertainties associated with well-
screen placement and the optimum conjunctive pumping rates required to produce a usable
quantity of freshwater (Zack, 1988). Zack states that the most efficient operation of
multilevel pumping wells has usually been by trial and error in adjusting well-screen
24
-------
placement and pumping rates. He improved operations by measuring the vertical movement
of saltwater within the well and within the aquifer as pumping stresses were applied and by
describing the appropriate hydraulic controls such as the vertical distribution of horizontal
hydraulic conductivity in the aquifer.
Determination of optimal freshwater production from a multilevel pumping-well
system by using chloride load (chloride concentration X flow rate), graphically represented
as a chloride-load curve (see Figure 8 in Zack, 1988), provides significant hydraulic
information about the pumping wells and the aquifer system. Such information is invaluable
in the final setting of optimal pumping fates, but the setting is still based on trial and error.
To overcome this problem, an analytical model was developed that predicts the effect of
operating a multilevel pumping-well system' for producing freshwater. Although the model
cannot overcome the monetary limitations, it greatly reduces the trial-and-error work
associated with multilevel pumping wells in that the investigator may adjust well depths and
pumping rates with the model before initiating a production operation in the field.
The use of multilevel pumping wells for freshwater production is discussed by
Underbill and Atherton (1964), Long (1965), and Zack (1988). These authors provide
excellent discussions of the use of multilevel pumping wells, but Long (1965) sees little value
in their use because of the expense incurred from pumping and disposing of saltwater. He
suggests a modification of the system that allows some degree of upconingj but this would be
unacceptable in most cases, especially where several well locations are employed because of
the additive effect on the upconed interface. Underhill and Atherton (1964) discuss a suitable
modification in the case of a thick transition zone in which wells are screened in the
freshwater, brackish, and saltwater zones. Because the work by Zack (1988) provides the
best overall discussion of the theory of upconing from a well hydraulics point of view, the
theory of operation for multilevel pumping-well systems, and a method for predicting proper
pumping rates, it is essential reading.
To overcome the trial-and-error method of determining the optimum pumping rate for
a multilevel pumping-well system, we have developed a model that will reasonably predict
the optimum pumping rate (we believe) with sufficient accuracy to allow immediate
implementation, provided adequate input data are available. The model is based on the work
25
-------
originally developed by Schmorak and Mercado (1969), which has been shown to be accurate
for predicting the rate of upconing for any given circumstance.
5.2. THEORETICAL SOLUTION
A multilevel pumping-well system is designed to function in such a manner as to
produce both freshwater and saltwater simultaneously. This is achieved either in a nested
well system or, preferably, by two separate wells installed in the same location or very near
to each other; the shallower well is open to the freshwater zone only and the deeper well is
open to the saltwater zone only. Actually, this design stipulation of completely separating
each well from its respective couple is not entirely necessary (i.e., the well couples may be
in communication with each other), but separate wells are easier to handle from a hydraulics
point of view.
By pumping both the freshwater and saltwater wells simultaneously, a relatively
stationary interface can be maintained if aquifer heterogeneities and other factors are taken
into account. Theoretically, a pumping well installed below the interface and pumped in
conjunction with a freshwater production well will intercept the saltwater before it migrates
up into the freshwater zone of the aquifer.
Operation of a multilevel pumping-well system could conceivably result in saltwater
migrating into the freshwater zone of an aquifer if the system is not properly adjusted for the
given set of conditions although such migration might not actually meet the definition of
upconing. Migration could occur in heterogeneous, anisotropic aquifers because of the effect
imposed on the system by such widely varying hydraulic conductivities. Consider an aquifer
with large vertical distribution of horizontal hydraulic conductivity and large vertical
hydraulic conductivity. According to Zack (1988), vertical hydraulic conductivity exerts the
greatest control on the vertical movement of saltwater nearest the well (where the hydraulic
heads across the stressed aquifer are most disparate). If the freshwater zone has the greater
horizontal hydraulic conductivity, saltwater will migrate upward within the aquifer in
response to vertical differences in hydraulic heads in the pumped well. Flow lines will
converge in the freshwater zone where the greatest hydraulic conductivities occur. Zack
demonstrates this concept by showing that the converging flow lines provide an upward
26
-------
hydraulic gradient that influences the overall shape of the interface cone. Over time, as
equilibrium conditions become reestablished, the cone will broaden into a mound.
Zack points out that the converse is true. If the saltwater zone of the aquifer
possesses the greater horizontal hydraulic conductivity, a downward hydraulic gradient
develops and freshwater migrates downward. Flow lines now converge in the saltwater
zone, and a "downwarp" or "downcone" in the interface is produced.
Vertical migration of fluids of differing densities in response to operation of a
multilevel pumping-well system does not change the amount of freshwater or saltwater
entering the well bore. The proportions of freshwater and saltwater remain the same as
saltwater moves upward (or freshwater downward) within the aquifer in response to vertical
flow components (Zack, 1988). Hence, as shown by Zack, the saltwater zone becomes
thicker and the freshwater zone thinner (or vice versa) in the vicinity of the pumping wells as
the pumping rate increases, but the amount of water entering the borehole along its length
does not change.
From the conceptual basis from which to design a multilevel pumping-well system, it
is possible to formulate a mathematical equation that will define the process more clearly.
This is achieved by referring to the work of Schmorak and Mercado (1969). Consider the
case of potential saltwater upconing having the same aquifer characteristics used by
Schmorak and Mercado when they developed their model, but with a saltwater production
well superimposed on the system (Figure 12).
In Equation (5), if Z = 0, then no net movement of the interface occurs. We
considered that the best way to make Z = 0 is to modify Equation (5) so that it could be
added to its counterpart for pumping below the freshwater/saltwater interface. The
derivation of the appropriate equation that results in Z = 0 was relatively straightforward
because the equation representing interface upconing below a pumping well [Equation (5)]
had already been derived by Schmorak and Mercado (1969). Working with Equation (5), we
observed that the critical factors to be examined for deriving an equation to represent
offsetting effects on the freshwater/saltwater interface were the relative well depths and
freshwater/saltwater density differences. The resulting Equation (14) is actually a
modification of Equation (5). To correct for the process of upconing, an offsetting equation
27
-------
was added to Equation (5), which, when solved, results in no net movement of the interface
if specific attributes of the equation (e.g., Qu and Q7) are held equal. Because in reality this
is not necessarily true, Equation (14) is shown as
Z(X, tt_t) - ±
(14)
where t0 and tl are starting and ending times for the period of analysis, Qu and Ql are the
upper and lower pumping rates, A^and K^ are the average horizontal hydraulic
conductivities in the freshwater and saltwater zones of the aquifer, and the variables du and dl
are the distances of the centers of the upper and lower well screens from the
freshwater/saltwater interface. The values for du and dl are initially set equal to each other
even though du is above the interface and dt is below the interface. Density values were also
altered because of the relative positions of du and d{, respectively. The quantity (Apu/pj) in
Equation (14) is the same as (Ap/p^) in Equation (5), but the quantity (Ap/p^) in Equation
(14) is very different. Equations (15) and (16) are
(15)
(16)
expanded versions of the two density functions in Equation (14). A close inspection of
Equations (15) and (16) shows that Equation (15) is a positive quantity and Equation (16) is a
negative quantity. Both quantities are relatively small, but the net effect is substantial. It is
28
-------
also necessary to modify the light sides of Equations (6) ,and (7) to account for the
differences in density; hence, the designations^, Rf, TU, and Tjfbr the dimensionless
distance and time parameters are now given as
-R,, =
(17)
(20)
where K^ and K^ are vertical hydraulic conductivities in the freshwater and saltwater zones,
.£gf and K^ are horizontal hydraulic conductivities in the freshwater and saltwater zones, and
aiu and nt are effective porosities above and below the interface.
Equation (14) may now be restated as
'total
(Z
uppex
lovex)
where Ztotd represents the net interface change (rising or falling) in response to pumping
both above and below the interface. ^,pper ;and^]ower represent the interface changes were
pumping to occur only above or only below the interface, respectively, which when added
together produce a net interface change.
In actuality, none of the variables need equal their counterparts to run the model. In
fact, the model is most useful when different values are substituted into Equation (14) to
29
-------
provide for the best possible outcome. Several model runs using varying parameters will
likely yield the best results as far as determining the appropriate pumping scheme to use.
Equation (14), when viewed as Equation (21), may be used to produce three separate
line plots: one line that shows the potential upconing from pumping a single well above the
interface (Zupper versus time), one that shows the effect from a single well pumping from
below the interface (Zlower versus time), and a line that displays the net effect of pumping the
two wells simultaneously (Ztotal versus time). This model, although still being tested, has
been shown to accurately reproduce the model data generated from the Semadar well field
[Figure 8 in Schmorak and Mercado (1969)] and appears to adequately predict the effect of
pumping from both above and below the interface separating the freshwater zone from the
saltwater zone (if the effects of dispersion are neglected). Figure 13 graphically displays the
measured effect of pumping from above the freshwater/saltwater interface solely and plots
the results of the model prediction; note the excellent fit between the measured data and the
predicted effect.
The values listed in Table 2 represent a modification of the Semadar well-field data
on the assumption that a multilevel pumping-well system had been installed in the aquifer.
Figure 14 shows (1) the effect of pumping from above the interface only, (2) the effect of
pumping from below the interface only, and (3) the net effect of both run concurrently.
Figure 15 is the same as Figure 14 with an expanded y-axis to demonstrate the actual effect
on the interface of pumping from both above and below the interface at the same time. Note
that the interface does not remain in a constant position; rather, it rises sharply, then declines
slowly until equilibrium is again established. This fact provides insight into the initial effect
on the interface when a stress is applied to the system.
30
-------
Model Fit of
Semadar Data
125
150
175
Time (days)
Figure 13. Saltwater upconing at the Semadar well field versus model prediction. Field data
from Semadar indicate that the upconing will occur as shown by the four data points. The
solid line represents the model prediction based on the simulations. Note the excellent fit
between the measured data and the predicted effect.
Table 2. Ground-water conditions at the Semadar well field assuming
the existence of a multilevel pumping-well system
Freshwater density
Saltwater density (p5/
Porosity (ri)
Horizontal hydraulic conductivity
Horizontal hydraulic conductivity
Vertical hydraulic conductivity (Kz^i
Vertical hydraulic conductivity (Kzs)
Initial interface elevation (Z0)
Distance from upper well to
initial interface (du)
Distance from lower well to
initial interface (dj)
Pumping rate for upper well 02M)
Pumping rate for lower well (Qj)
Pumping period for both wells (*)
OJOI-dH „
i.00 g/cmj
1.03 g/cm3
0.33
14.70 m/day
14.70 m/day
14.70 m/day
14.70 m/day
-30.75 m (MSL)
15.50 m
15.50 m
348.00 m3/day
348.00 m3/day
84.00 days
31
-------
to
Effect of Pumping from
the Upper Well Only
Net Effect of Pumping Both
the Upper and Lower Wells
Simultaneously
Effect of Pumping from
the Lower Well Only
60 80
Time (days)
100
120
Figure 14. Net freshwater/saltwater interface movement resulting from pumping both above
and below the interface concurrently.
32
-------
D)
sn
•
C O
to
-------
By varying the pumping rates and depths of the wells in the model, the behavior of
the interface may be estimated before implementing any pumping system. A more useful
advantage of this model is the ability to gain a general sense of whether a multilevel
pumping-well system is even the proper ground-water extraction system for a given set of
conditions. Hence, a rough prediction of the effect likely to be produced by a multilevel
pumping-well system versus a single-level pumping-well system can be compared and
evaluated as part of the decision-making process.
Changing the variables assists in estimating the overall effect of a multilevel pumping-
well system on the environment and thus helps in preliminary design work for a system.
Additionally, if some parameters have been previously determined from existing conditions
(e.g., use of an existing pumping well for production purposes), then it is possible to
determine what alterations to other variables are necessary for the system to function
efficiently.
Several model runs with varied parameters allow a reasonably accurate solution to
Equation (14). This solution should only be considered a rough approximation of what may
actually be occurring in the subsurface, but it does provide some insight into what some
parameters are likely to be at any particular site. The value of conducting several model
runs with varying parameters is that it provides an indication of whether a multilevel
pumping-well system is correct for a particular site and, possibly, how well it may actually
function.
5.3. DESIGN
Design and implementation of a successful multilevel pumping-well system, either for
freshwater production or for contaminant containment or removal, are not overly difficult but
do require a considerable amount of site-specific hydrogeologic information. Information
such as porosity, horizontal hydraulic conductivity, and vertical hydraulic conductivity in
both the freshwater and saltwater zones, for example, is essential. Additionally, Zack (1988)
listed five important assumptions that must be made if the design and operation of a
multilevel pumping-well system are to be properly implemented. These assumptions pertain
34
-------
to aquifers that display radial flow under pumping conditions and to wells that are nearly 100
percent efficient over a wide range of pumping rates. They are:
First, equilibrium conditions in an aquifer under constant pumping are
developed in terms of the upward movement of saltwater and the
corresponding stabilization of chloride concentration. Depending on the
vertical distribution of horizontal hydraulic conductivity of the aquifer
materials open to the well-screen interval, equilibrium conditions could
develop within minutes after start of pumping or could require hours or days
to be achieved if the differences in fluid properties (density and dynamic
viscosity) between the saltwater and the freshwater are greater.
Second, the placement of the intakes of the scavenger and production
wells is not particularly critical if the production well is placed in the upper
part of the freshwater section and the scavenger well is in the upper part of the
saltwater section of the well profile. The placement becomes more critical as
the well diameter decreases, transmissivities decrease, or pumping rates
increase.
Third, depending on the distribution of saltwater, freshwater, and
transverse (horizontal) hydraulic conductivity within the aquifer, the chloride
load of the pumping well develops a linear relation to the pumping rate and
reflects the movement of saltwater (or freshwater) toward more conductive
parts of the aquifer. Saltwater actually replaces freshwater in the lower part of
the freshwater zone in the aquifer near the pumping well.
Fourth, the total chloride load produced from a well at a particular
pumping rate represents the sum of the chloride loads and pumping rates when
the scavenger well and the production well pump simultaneously from the
same well, regardless of the placement of the two pump intakes.
Fifth, a maximum chloride concentration is reached by the scavenger
well as the pumping rate of the production well is increased. The chloride
concentration becomes constant and equal at all scavenger-well pumping rates
and represents the chloride concentration of the saltwater intercepted while
moving toward the production well.
The basic design of a multilevel pumping-well system is not very complex, but as
with any ground-water extraction system, the basic aquifer and contaminant characteristics
must be well understood. For the system to be effective, the aquifer in question must have
35
-------
been well characterized, as well as any plume of contamination to be remediated. This
facilitates proper vertical and horizontal placement of the appropriate extraction wells
necessary to maximize the removal or containment of the contaminant plume.
Based on a good understanding of the aquifer system and, if necessary, plume
behavior, several well locations are chosen, at each of which at least two wells are installed.
One of the two wells is installed in the freshwater zone with the well screen placed to
intercept the majority of contamination. The second well is installed below the interface
separating the freshwater zone from the saltwater zone. If a thick transition zone exists at
the site of ground-water remediation, then a third extraction well may be needed in the
transition zone to pump brackish water. All wells installed at a single location should be
separated from each other vertically to ensure that no hydraulic connections exist between
them.
One set of multilevel pumping wells installed at the site probably will be insufficient
for contaminant removal or containment, so a somewhat uniform distribution of these
multilevel pumping wells will be required. Three major items must still be addressed before
installation, however. First, a methodology for monitoring interface migration must be
determined. Second, a suitable methodology for disposing the potentially large volumes of
unwanted saltwater must be found. Third, plans must be established for carefully monitoring
the plume and for modifying the system to provide the most effective remediation with the
least amount of saltwater upconing. These three items are not the subject of this paper and
are not discussed here. Zack (1988) provides an excellent discussion of a methodology for
monitoring chloride migration into the well system.
36
-------
6. APPLICATION
The model equation derived to evaluate the methodology is considered applicable to
both the problem of saltwater upconing into freshwater wells in coastal aquifers (for either
freshwater production wells or for contaminant extraction wells) and the problem of
removing light nonaqueous phase liquids often found as contaminants floating on top of
aquifers. Use of the model equation and design of an appropriate multilevel pumping-well
system depend on recognizing the most important parameters and making reasonably realistic
assumptions about the aquifer system in question.
6.1. FRESHWATER PRODUCTION WELLS
The model was tested using data acquired from the U.S. Geological Survey (Giusti,
1978; Zack, 1988); several model runs were implemented. If the model functions as
previously described, then the model output should closely match the published results of
Zack.
Figure 16 schematically shows the design of the La Trocha well used by the U.S.
Geological Survey in Puerto Rico to test the effect of pumping simultaneously from above
and below the freshwater/saltwater interface. Regardless of the pumping scheme chosen
(i.e., varying the withdrawal rates for both pumps), saltwater upconing was always produced
(Figure 17) although at a reduced rate due to the effect of pumping from below the interface.
Important to notice in Figure 16 is the placement of the upper pump in relation to the well
screen. The upper pump, installed at a depth of 60 feet, is far above the open area of the
well and is actually about 40 feet above the well screen. Hence, the upper pump may
actually be withdrawing brackish/saline water during operation. Equation (14) assumes that
flow enters at the upper intake area laterally and thus does not account for pumps installed
above the open zone of the well. Thus, flow into the upper part of the well occurs at a depth
of approximately 100-110 feet, which must be noted in implementing the model.
To test the importance of the flow intake depth, the model was adjusted to assume
that the upper intake exists at a depth of 100 feet. Other relevant factors are shown in
Table 3. Note that the lower well is only pumped at 18 gpm while the upper well is pumped
37
-------
o
Freshwater
Discharge "
20
40
o>
0)
fe. 60
•c
w 80
100
120
140
160
180
200
Freshwater
Intake
-Saltwater
Intake
Saltwater
Discharge
16-Inch Casing
20-Inch Surface Casing
Soil and Fill
Black Clay
White Rock, Limestone and Clay
Hard White Rock
Freshwater Pump
Soft White Rock
Hard White Rock
White, Limey Rock with Areas of
Little Cementation and Great
Porosity (Aymamon Limestone)
16-Inch Perforated Pipe
No Consistent Scale
Figure 16. Schematic representation of La Trocha well used by the U.S. Geological Survey to
test the multilevel pumping-well theory for the production' of freshwater. Note the placement
of pumps relative to the intake area(s).
38
-------
1600
1400
1200
sc
£
1000
3
800
600
400
200
.••*b<36)..••<
•
Chloride concentration of water withdrawn
by scavenger well pumping at indicated rate
(in gallons per minute) as production well is
pumped at various rates
I * S.
"5 0) O
I
I
I
I
I
20 40 60 80 100 120
PUMPING RATE OF PRODUCTION WELL, IN GALLONS PER MINUTE
140
Figure 17. Chloride concentrations of water withdrawn from La Trocha upper intake (solid
lines, e-i) and lower intake (dotted lines, a-d) pumping simultaneously. Pumping rates for the
lower intake are constant (gpm) while those for the upper intake vary (from Zack, 1988).
39
-------
at three different rates-36, 54, and 72 gpm--all for a total of 100 days. This model design
allows good visualization of the effects on the hydrogeologic system created by the pumping
scheme.
Table 3. Ground-water conditions at La Trocha well field assuming
the existence of a multilevel pumping-well system*
Freshwater density (pfi
Saltwater density (ps)
Porosity (ri)
Horizontal hydraulic conductivity (K^
Horizontal hydraulic conductivity (K^
Vertical hydraulic conductivity (K^
Vertical hydraulic conductivity (K^)
Initial interface elevation (Z0)
Distance from upper well to
initial interface (du)
Distance from lower well to
initial interface (dj)
Pumping rates for upper well (Qu)
Pumping rate for lower well 02/)
Pumping period for both wells (t)
l.OOg/cm3
1.03 g/cm3
0.18
285.00 ft/day
285. 00 ft/day ,
28.50 ft/day**
28.50 ft/day**
-200.00 ft (MSL)
20.00 ft
10.00 ft
36.00 gpm
54.00 gpm
72.00 gpm
18.00 gpm
100.00 days
* Values from Giusti (1978) and Zack (1988).
** Values estimated from site evidence.
40
-------
The model displayed an initial downconing effect and then some upconing when the
upper well was pumped at 36 gpm (Figures 18-20), but less than might be expected. Figure
18 shows this effect while Figure 18a displays this effect on an expanded y-axis. The
downconing effect occurs because the most important factor in the net change of the interface
shape appears initially to be the proximity of the intake area of a well to the interface.
However, the subsequent rise in the interface is a result of the vast majority of flow entering
the well bore occurring between 100 and 120 feet from the land surface, indicating that the
vertical distribution of horizontal hydraulic conductivity and pumping rates may eventually
overcome the effects created by well screen placement. This suggests that the upper pump is
actually drawing in more water than the lower pump and thus exerts a greater influence on
the overall system than is accounted for in the model. Figures 19 and 20 show the same
well construction and aquifer arrangements, but with the upper well pumping at 54 and 72
gpm, respectively. As can be seen in Figure 19, an initial downcone followed by a steady
increase in upconing occurs; Figure 19a displays this effect with an expanded y-axis. These
effects are not shown in Figures 20 and 20a, but the importance of placement of the intake
areas relative to the interface initially, followed by the need to account for the vertical and
horizontal hydraulic conductivities as pumping continues, is clearly established.
As described above, the most interesting observation is the importance of the
relationship of the well intake to the interface. The effects of pumping rates were almost
negligible initially in contrast to the effects of well intakes placed near the interface.
Clearly, for optimum performance, freshwater production wells should be placed as far
above the interface as feasible to allow for higher pumping rates while the saltwater wells
should be placed as near to the interface as is possible to allow for low pumping rates. This
design stipulation permits greater freshwater withdrawals while minimizing saltwater
upconing and the expense incurred from pumping saltwater. This observation provides for
better design criteria before the wells are installed and a reduced rate of saltwater withdrawal
in many instances. This design stipulation also conforms nicely to Zack's (1988) second
assumption (above).
41
-------
CD
O)
^
O 5
(0 O
t: 13
® m
Effect of Pumping from
the Upper Well Only
Net Effect of Pumping Both
the Upper .and Lower Wells
Simultaneously
Effect of Pumping from
the Lower Weir Only
80
100
120
Time (days)
Figure 18. Model simulation of the pumping scenario at La Trocha well demonstrating the
similarity between the model results and the actual field-test data. Pumping rates for the
lower and upper intakes are 18 gpm and 36 gpm, respectively.
42
-------
o
o
o
o
o
CM
I
CO
en
•«- T» ro
S
.£ co
c 0)
O CO
s
03 O
to
o
o
o
o
CM-
i
CO
o
o
o
o
CM'
Effect of Pumping from
the Upper Well Only
Net Effect of'Pumping Both
the Upper.and Lower Wells
Simultaneously
Effect of Pumping from
the Lower Well Only
120
Time (days)
Figure 18a. Model simulation same as for Figure 18 but with an expanded y-axis to provide
a clearer indication of the effect on the interface produced by the multilevel pumping-well
system.
43
-------
a1
o>
_
I
to
O>
cn
to
tn
o>
CD
a
o
a
OJ
o
/x
_^— £
^^
^~~~~^
\4
r- '
3— E
9 <:
N
3_ E
* T" •
v^ Effect of Pump
the Upper Well
\^ Net Effect of Pu
the Upper and I
L Simultaneously
Effect of Pump
/'"the Lower Well
j — * — 4
20
40 60 80
Time (days)
100
120
Figure 19. Model simulation of the pumping scenario at La Trocha well demonstrating the
similarity between the model results and the actual field-test data. Pumping rates !for the
lower and upper intakes are 18 gpm and 54 gpm, respectively.
44
-------
_
*^ 0>
Q>
CO -J
.E as
C.
*
o>
o>
a*
03
05
oi
en
I
CO
CO
' en
o> •
o> o>
c o>
CO — •'
x: r
O «\)
o>
ffl °*
o>
7
en
i
o
o
o
•
o
o
<\r
i
o
o
o
o
«\r
en
o
o
ev
t
03 O
i- O
ir
o
o
o fvf
UJ O
o
fu-
ll t
m
o
o
o
o
o
e\r
t
Effect of Pumping from
Net Effect of Pumping Both
the Upper and Lower Wells
Simultaneously
Effect of Pumping from
the Lower Welt Only
60
Tfme (days)
80
100
120
Figure 19a. Model simulation same as for Figure 19 but with an expanded y-axis to provide
a clearer indication of the effect on the interface produced by the multilevel pumping-well
system.
45
-------
CD
O
•S> CD
O) —
JE co
C™ QJ
O CO
IB
-j o
CO ...
o 5
co o
tr ~3
CM
O)
cn
en
cn
m
cn
(O
cn
cn
cn
co
cn
cn
cn
o
o
o
CM
/
K
- A. -------
\"
...........
^^
^— "
.— -«
3 <
ir— '
a- r — E
^
9- 4
^ V i
\^ Effect of Pumpin
,. .the Upper Well (
1
g $•
i
Net Effect of Pumping
^n the Upper and Lower
Simultaneously
"
f
I
Effect of Pumping fr
/the Lower Well Onl>
b-L A
20
40 60 80
Time (days)
100
120
Figure 20. Model simulation of the pumping scenario at La Trocha well demonstrating the
similarity between the model results and the actual field-test data. Pumping rates for the
lower and upper intakes are 18 gpm and 72 gpm, respectively.
46
-------
Effect of Pumping from
Net Effect of Pumping Both
the Upper and Lower Wells
Simultaneously
from
Well Only
40 60
Time (days)
100
120
Figure 20a. Model simulation same as for Figure 20 but with an expanded y-axis to provide
a clearer indication of the effect on the interface produced by the multilevel pumping-well
system.
47
-------
6.2. REMOVAL OF FLOATING EMMESCIBLES
Light nonaqueous phase liquids (LNAPLs) pose a unique problem for ground-water
remediation because they do not mix well with water and because they are significantly
lighter than water. Pumping from the phreatic zone causes a depression in the water table
and draws even more contamination into the phreatic zone. Overpumping the zone also may
leave some of the LNAPL behind, resulting in a prolonged period of removal.
To overcome the difficulties of removing LNAPLs from an aquifer, Blake and Lewis
(1982) and Abdul (1992) suggest various pumping arrangements, two of which use a
multilevel pumping-well scheme (Figure 21). The design and operation are identical to that
described above, but now freshwater production acts as the scavenger well (lower pumping
well) that also must be protected from drawing down too much of the contaminant. As in
the saltwater upconing approach, monitoring contaminant migration into freshwater zones is
crucial. Blake and Lewis recommend that a product detection probe with an automatic
shutoff be installed in the freshwater production zone to guard against any unwanted intrusion
by the floating LNAPL. Abdul points out that it is critical that removal of free product from
the aquifer be at a rate such that a continuous layer of free product remains in the free-oil
zone in the surrounding porous medium. If this free-oil zone is not maintained, then the
total fluid recovery of the LNAPL will not be achieved because the free product will migrate
into the region of the drawdown cone and establish a new set of equilibrium conditions. It
should be noted here that Abdul conducted extensive tests on the multilevel pumping-well
technology, both in the laboratory and in the field, and found it to enhance significantly the
recovery of LNAPLs over other more conventional techniques. However, a trial-and-error
pumping period was necessary before full implementation of the recovery program.
Blake and Lewis (1982) see several advantages to this type of system. Contaminant
removal from the subsurface is enhanced and does not need surface separators. This is
important, for example, for microbial degradation where as little water as possible is desired.
Too much water will result in a "kill-off' of the microorganisms. In other instances, if the
contaminant is a product (e.g., oil), it can be recovered and sold. Soluble hydrocarbon
components in the wastewater are minimized because mixing of water and the contaminant
has been minimized. The system can be highly efficient with full automation.
48
-------
CQ
3 o
-------
Disadvantages listed by Blake and Lewis (1982) include the same cost problems
described earlier in this paper (e.g., cost of two wells instead of one) and, most important,
the problem of initial startup and adjustment of the pumping system. Well depths and
pumping rates must be carefully evaluated to ensure that the interface is maintained at the
appropriate level. Our model can overcome some of the starting and adjustment problems by
providing the information necessary for the proper design and implementation of a multilevel
pumping-well system. The model is not exact, so adjustments will be necessary, but much
uncertainty will have been removed before any work is initiated.
50
-------
7. CONCLUSIONS
Use of multilevel pumping wells as a means of remediating contaminated coastal
aquifers and inland aquifers contaminated by LNAPLs has been shown to have great
promise. These pumps have rarely been used in the past for enhanced freshwater production
because of the added cost associated with the withdrawal and disposal of unwanted saltwater.
A significant difficulty associated with multilevel pumping wells is the inability to adequately
predict initial depths, pumping rates, and other necessary factors before implementing such a
system, forcing reliance on trial and error to acquire the appropriate parameters.
A model has been developed that not only mathematically solves the problem of
saltwater iipconing in coastal aquifers but also provides a means for estimating the correct
parameter values to use when designing and implementing a multilevel pumping-well system
for either freshwater production or for contaminant plume containment. Our mathematical
model is a modification of an equation developed by Schmorak and Mercado (1969)
originally designed to predict the extent of saltwater upconing in a coastal aquifer. The
model developed in this paper accurately reproduces their results and appears to adequately
produce the expected theoretical results if a multilevel pumping-well system were to be
implemented at the same site.
This model also may provide a reasonably good estimate of the effects likely to be
incurred at any aquifer with two or more immiscible fluids present and where a multilevel
pumping-well system is being considered, provided good quality input data are available.
Given the cost and difficulty of long-term remediation of aquifers contaminated by LNAPLs,
this model could result in enhanced contaminant removal.
51
-------
8. REFERENCES
Abdul, A. S. (1992) A new pumping strategy for petroleum product recovery from
contaminated hydrogeologic systems: laboratory and field evaluations. Ground Water
Monitoring Review 12: 105-114.
Bear, J. (1960) The transition zone between fresh and salt waters in coastal aquifers. Ph.D.
dissertation. Berkeley, CA: University of California.
Bear, J. (1972) Dynamics of Fluids in Porous Media. New York, NY: American Elsevier,
764 p.
Bear, J. (1979) Hydraulics of Groundwater. New York, NY: McGraw-Hill, 569 p.
Bear, J.; Verruijt, A. (1987) Modeling Groundwater Flow and Pollution. Dordrecht,
Holland: D. Reidel, 414 p.
Blake, S. B.; Lewis, R. W. (1982) Underground oil recovery. In: Nielson, D.M., ed.
Aquifer Restoration and Ground Water Rehabilitation~A Light at the End of the
Tunnel: proceedings of the Second National Symposium on Aquifer Restoration and
Ground Water Monitoring; Columbus, Ohio. Worthington, OH: National Water Well
Association; pp. 69-76.
Cooper, H. H., Jr. (1959) A hypothesis concerning the dynamic balance of fresh water and
salt water in a coastal aquifer. Journal of Geophysical Research 64: 461-467.
Custodio, E. (1988) Present state of coastal aquifer modelling: short review. In: Ground
Water Flow and Quality Modelling, NATO ASI Series, Series C: Mathematical and
Physical Sciences vol. 224. Dordrecht, Holland: D. Reidel; pp. 785-801.
Dagan, G.; Bear, J. (1968) Solving the problem of local interface upconing in a coastal
aquifer by the method of small perturbations. Journal of Hydraulic Research 6: 15-44.
Freeze, R. A.; Cherry, J. A. (1989) Guest editorial: What has gone wrong. Ground Water
27:458-464.
Freeze, R. A.; Cherry, J. A. (1979) Groundwater. Englewood Cliffs, NT: Prentice-Hall,
604 p.
Giusti, E. V. (1978) Hydrogeology of-the karst of Puerto Rico. U.S. Geological Survey
Professional Paper 1012. Washington, DC: U.S. Government Printing Office. 68 p.
52
-------
Hubbert, M. K. (1940) The theory of ground-water motion. Journal of Geology 48: 785-
944.
Kashef, A. A. I. (1977) Management and control of salt-water intrusion in coastal aquifers.
CRC Critical Reviews in Environmental Control 7: 217-275.
Kohout, F. A. (1960). Cyclic flow of salt water in the Biscayne aquifer of southeastern
Florida. Journal of Geophysical Research 65: 2133-2141.
Long, R. A. (1965) Feasibility of a scavenger-well system as a solution to the problem of
vertical salt-water encroachment. Department of Conservation, Louisiana Geological
Survey. Water Resources Pamphlet No. 15. 27 p.
Mackay, D. M.; Cherry, J. A. (1989) Groundwater contamination: pump-and-treat
remediation. Environmental Science and Technology 23: 630-636.
Schmorak, S.; Mercado, A. (1969) Upconing of fresh water-sea water below pumping wells,
field study. Water Resources Research 5: 1290-1311.
Strack, O. D. L. (1976) A single-potential for regional interface problems in coastal
aquifers. Water Resources Research 12: 1165-1174.
Todd, D. K. (1980) Groundwater Hydrology. New York, NY: John Wiley and Sons,
535 p.
Underbill, H. W.; Atherton, M. J. (1964) A coastal ground water study in Libya and a
discussion of a double pumping technique. Journal of Hydrology 2: 52-64.
Wagner, J.; Kent, D. C. (1985) Upconing of a salt-water/fresh-water interface below a
pumping well. Environmental Research Laboratory, Ada, OK; EPA report number
EPA/600-2-85/066.
Zack, A. L. (1988) A well system to recover usable water from a freshwater-saltwater
aquifer in Puerto Rico. U.S. Geological Survey Water-Supply Paper 2328. U.S.
Government Printing Office, Washington, DC; 15p.
53
•&U.S. GOVERNMENT PRINTING OFFICE: 1994 - 550-001/00151
-------
------- |