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Groundwater mixing using pulsed dipole injection/extraction wells

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Title:
Groundwater mixing using pulsed dipole injection/extraction wells
Creator:
Radabaugh, Cristyn R
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English
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x, 71 leaves : ; 28 cm

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Subjects / Keywords:
Groundwater -- Mixing ( lcsh )
Injection wells ( lcsh )
Groundwater flow -- Mathematical models ( lcsh )
Groundwater flow -- Mathematical models ( fast )
Groundwater -- Mixing ( fast )
Injection wells ( fast )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Bibliography:
Includes bibliographical references (leaves 70-71).
General Note:
Department of Civil Engineering
Statement of Responsibility:
by Cristyn R. Radabaugh.

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University of Colorado Denver
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Auraria Library
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698192041 ( OCLC )
ocn698192041
Classification:
LD1193.E53 2011m R32 ( lcc )

Full Text
V
GROUNDWATER MIXING USING PULSED
DIPOLE INJECTION/EXTRACTION WELLS
by
Cristyn R. Radabaugh
B.E., Vanderbilt University, 2000
A thesis submitted to the
University of Colorado Denver
in partial fulfillment
of the requirements for the degree of
Master of Science
Civil Engineering
2011


This thesis for the Master of Science
degree by
Cristyn R. Radabaugh
has been approved by
David C. Mays
Roseanna M. Neupauer
Zhiyong Jason Ren
s/>s/:
-QlO
Date


Radabaugh, Cristyn R. (M.S., Civil Engineering)
Groundwater Mixing Using Pulsed Dipole Injection/Extraction Wells
Thesis directed by Assistant Professor David C. Mays
ABSTRACT
Mixing is notoriously difficult in groundwater aquifers, because the Reynolds
number is very small. This can limit site remediation, and inducing mixing within
the groundwater aquifer could speed the chemical processes or otherwise reduce
the amount of time needed to meet site remediation goals. A recent analytical
model suggests that mixing in groundwater aquifers may be achieved through
pulsed dipole injection and extraction from groundwater wells. Building on past
work, this study uses MODFLOW, a finite-difference groundwater flow model
code developed by the U.S. Geological Survey, to simulate the flow of
groundwater and the movement of particles within a two-dimensional confined
aquifer. The analysis shows the effects of pulsing the wells and modifying the
frequency of pulsing. Mixing within the groundwater aquifer is illustrated
through the pathlines of tracked particles within the aquifer and quantified using
(1) separation distance, to determine if the flow is chaotic, and (2) dilution index,
to quantify when greatest mixing occurs. Current results do not indicate the
presence of chaotic advection during a single pass from the injection well to the
extraction well.


This abstract accurately represents the content of the candidates thesis. I
recommend its publication.
Signed
1 David C. Mays


DEDICATION
I dedicate this thesis to my husband, Patrick, who gave me the support, patience,
and reassurance necessary to allow me to complete my research and thesis.


ACKNOWLEDGEMENT
Many thanks to my advisor, David Mays, for his contributions and support of my
research. I also wish to thank my co-advisor Roseanna Neupauer for her immense
modeling assistance and understanding. Thanks to all the members of my
committee for their valuable participation.


TABLE OF CONTENTS
Figures................................................................ix
Chapter
1. Introduction.........................................................1
1.1 Chaotic Advection................................................1
1.2 Mixing and Stirring..............................................2
1.3 Chaotic Advection Applied to Groundwater.........................3
2. Model................................................................5
2.1 Conceptual Model.................................................5
2.2 Numerical Model..................................................6
2.3 Numerical Code...................................................9
3. Methods to Analyze Mixing..........................................11
3.1 Separation Distance.............................................11
3.2 Dilution Index..................................................12
4. Results and Discussion..............................................19
4.1 Particle Tracking...............................................19
4.2 Pathline Crossing...............................................22
4.3 Separation Distance.............................................22
4.4 Dilution Index..................................................27
4.5 Sensitivity Analysis............................................29
5. Conclusions and Recommendations for Future Work.....................37
5.1 Conclusions.....................................................37
5.2 Recommendations for Future Work.................................38
5.2.1 Comparison with Standard Dipole..........................38
5.2.2 Recovery Periods.........................................39
5.2.3 Reinjection..............................................39
vii


5.2.4 Heterogeneity...............................................40
Appendix
A. Input Parameter File (chaos.par).......................................42
B. Matlab Script (gwmixing.m).............................................44
C. Dilution Index Function (kitanidis.m)..................................57
D. MODPATH Output (chaos.lin).............................................59
References.................................................................70
viii


LIST OF FIGURES
Figure
1. Plan view of groundwater flow for a standard dipole. Dashed lines indicate
the hydraulic head contours and the solid lines indicate the pathlines within
the homogeneous aquifer. Figure modified from Fitts (2002)............7
2. Plan view of pulsed dipole injection/extraction wells. Filled circles denote
injection wells; open circles denote extraction wells; and arrows denote flow
directions............................................................7
3. Schematic of model cycle showing injection and extraction cycling...........8
4. Flow chart of process followed by Matlab script............................10
5. Cross section of pipe flowing full showing standard parabolic velocity
distribution. Image obtained from University of Waterloo (2006)........... 13
6. Movement of two particles within a pipe flowing full and indication of
separation distance (SD) at t = 0, 1, and 3 min..........................13
7. Linear growth of separation distance versus time for two particles within a
pipe flowing full, indicating non-chaotic flow............................14
8. Example of exponential growth of separation distance, indicating chaotic
flow......................................................................14
9. (a) Mass in two small plugs versus (b) mass distributed normally. Adapted
from Kitanidis (1994)..................................................... 15
10. Example model space divided into nine grid blocks with nine particles shown
by the solid circles......................................................17
11. Example model space divided into nine grid blocks with nine particles shown
by the solid circles......................................................18
12. Pathlines of the 72 particles tracked from t = 0 d to t = 6 d in the pulsed
dipole model. The injection well is located toward the top of the domain at
IX


(x,y) = (712.5 m, 922.5 m) and the extraction well is located toward the
bottom of the domain at (x,y) = (712.5 m, 592.5 m). The cross formed by the
pathlines near the injection well is a numerical artifact from the modeling. 20
13. Paths of 72 particles from t = 0 dtot = 3din model operating as standard
dipole. The cross formed by the pathlines near the injection well is a
numerical artifact from the modeling.....................................21
14. Pathlines of 144 particles with 72 injected at t = 0 d (solid lines) and an
additional 72 particles injected at t = 0.5 d (dotted lines).............23
15. Close-up of crossing pathlines..........................................24
16. Plan view of model with 72 particle pathlines. Particles are numbered from
due east as Particle 1, and particle numbers increase counterclockwise... 25
17. Separation distance plots for (a) particles 5 and 7 and (b) particles 55 and 57.
........................................................................26
18. Dilution index for (a) 23 particles and (b) 45 particles................28
19. Dilution index for (a) 90 particles and (b) 360 particles...............30
20. Plot of E/Emax for (a) 90 particles and (b) 360 particles...............31
21. Plot of pathlines for simulation with (a) standard simulation, (b) 2Q, (c) 2T,
(d) 0.5n, (e) 0.5b, and (f) 0.707L.......................................33
22. Plot of particle pathlines normalized based on the distance between the
injection and extraction wells when L = (a) 345 m and (b) 240 m.........34
23. E/Emax versus t for (a) 0.5b and (b) 0.125b.............................35
24. E/Emax versus t for (a) 2b and (b) 8b...................................36
25. Schematic of model showing pumping periods, of duration T, and recovery
period of duration R.....................................................40
x


1. Introduction
Some groundwater remediation methods rely on the injection of chemicals,
microbes, or carbon sources into the aquifer to enhance or encourage degradation.
This process typically involves injection at one or more wells and the extraction
of groundwater at downstream wells. For this type of in-situ remediation to be
successful, it is important that the substances introduced into the aquifer spread
throughout the region of concern. Unfortunately, the injected substance can
spread slowly within the aquifer due to low groundwater velocities inside of the
laminar flow system. Encouraging accelerated mixing in contaminated
groundwater aquifers through pumping could speed remediation processes.
In this research, groundwater flow modeling is used to study the mixing created
by pulsing a pair of injection and extraction wells. The mixing within the aquifer
is then quantified.
1.1 Chaotic Advection
Molecular diffusion is the basic process in mixing, but little mixing occurs
without advection because molecular diffusion is very slow. Past research
demonstrated the potential for enhanced mixing in laminar flows through a
process categorized under the heading of chaotic advection (Aref 2002). Chaotic
advection, as the name implies, involves advection in a chaotic system.
Advection is the movement of particles with a fluid and is sometimes referred to
as passive advection to emphasize that the particles must follow the fluid. Chaos
is the idea that even systems described by analytical equations can be difficult to
1


predict because small variations in the initial conditions can lead to major changes
in the output (Gleick 1987). Chaos is commonly explained as a sensitive
dependence on the initial conditions. This is often illustrated through the
butterfly effect. The butterfly effect, simply stated, is the connection between a
butterfly flapping its wings and stirring the air in east Asia which leads to change
in storm systems and eventually contributes to the formation of a hurricane in the
Atlantic.
Fluid mechanics research suggests that mixing in laminar flows can be enhanced
by chaotic advection, which is characterized by exponentially increasing
separation distances between fluid particles with time (Aref 1984). The
exponential increase in separation distance leads to initially nearby particles
ending up far apart.
Further, the fluid mechanics literature indicates that three independent variables
are necessary for chaotic advection. In a 2D flow system, time-dependent flow is
necessary to produce chaotic particle motion whereas steady flow can produce
chaotic advection in a 3D system (Aref 2002). The present study focuses on a
time-dependent 2D system. The reorientation of pathlines and the transient flow
field are necessary criteria for chaotic advection to occur within the aquifer, as
explained by Aref (1984). For further explanation on the theory of chaotic
advection in 2D incompressible flow, see Aref (1984), Jones and Aref (1988), or
Aref (2002).
1.2 Mixing and Stirring
There is a common distinction between mixing and stirring in the fluid mechanics
literature cited above. In fluid mechanics, stirring refers to the stretching, pulling,
2


and folding of a substance whereas mixing only takes place through molecular
diffusion. In the groundwater community, the ideas of stirring and mixing are
often combined together and simply considered mixing. This may be because
stirring of groundwater is difficult to imagine in porous media. This thesis uses
the term mixing to refer to what Aref (1984) and others refer to as stirring.
1.3 Chaotic Advection Applied to Groundwater
Two recent studies have explored applications of chaotic advection to enhance
mixing in aquifers through injection and extraction. Sposito (2006) modeled
sequential injection and extraction from a pair of wells. Bagtzoglou and Oates
(2007) modeled mixing in groundwater by a system of three wells with random
flow assignments. Both analytical models focused on pulsed injection and
extraction in two-dimensional, confined, homogeneous aquifers. Sposito (2006)
assumed steady-state flow during each cycle. Bagtzoglou and Oates (2007) did
not specify whether their simulation was steady-state or transient during each
cycle. These two publications indicated that chaotic flow occurs, based on
exponential growth of the separation distance over multiple reinjection cycles
between two fluid particles that were initially adjacent to each other.
There are two components that need to be considered when evaluating mixing
through chaotic advection, (1) flow in the aquifer and (2) reinjection of particles
back into the aquifer through the injection well after they are removed at the
extraction well. Sposito (2006) and Bagtzoglou and Oates (2007) evaluated both
components together by modeling flow through porous media with recirculation
systems that reinjected the extracted groundwater back into the aquifer. The
reinjection itself or the assignment of particle injection angles based on particle
extraction angles was not evaluated in either model to determine the significance
3


of influence on the occurrence of chaotic advection. The effects of reinjection
alone were not evaluated.
The present study does not include reinjection and places Spositos (2006)
conceptual model in the framework of a numerical groundwater model in order to
evaluate if mixing can be achieved just by pulsed flow in the aquifer. In addition,
the current effort lays the groundwork for future work to determine the effect of
heterogeneity on mixing. Specifically, the degree of mixing resulting from pulsed
dipole injection/extraction during a single pass from the injection well to the
extraction well is investigated.
4


2. Model
MODFLOW (Harbaugh et al. 2000) and MODPATH (Pollock 1994) were used to
simulate advective mass transfer within the modeled aquifer to investigate
whether well hydraulics can enhance mixing in an aquifer. This chapter
introduces the conceptual model and numerical model used to simulate advective
mass transfer induced in the modeled system and presents numerical
implementation of the method using MODFLOW and MODPATH.
2.1 Conceptual Model
The standard dipole is two wells, of which one is an extraction well and the
second is an injection well, each pumping continuously at Q and Q in an aquifer.
In a standard dipole in a homogeneous aquifer, the head is evaluated as shown
below in Eqn (1). Eqn (1) assumes no background groundwater flow, and a
steady pumping (extraction) rate, -Q.
h =
In + C
2nr r2
(1)
where h = head
T = transmissivity of aquifer
-Q = pumping (extraction) rate
ri = distance from injection well to point where h is evaluated
r2 = distance from extraction well to point where h is evaluated
C = constant
5


The standard dipole leads to symmetric head contours and pathlines (Figure 1).
Standard dipole flow occurs in aquifers when the injection and extraction wells
are continuously pumping and there is no background hydraulic head gradient.
The pulsed dipole is when the standard dipole set-up of two wells, one injection
and one extraction, is modified by pulsing, alternately turning on and off the
injection and extraction wells, which creates transient conditions as opposed to
steady-state. Transient flow is necessary in order to have chaotic advection in two
spatial dimensions. Figure 2 is a plan view of a model showing an injection well
and an extraction well where only one well is operated at a time. In a pulsed
dipole system, the alternating injection and extraction cycles cause reorientation
of the particle pathlines due to radial flow either toward an extraction well or
away from an injection well.
The current research focuses on a series of simulations corresponding to
alternating injection and extraction cycles (Figure 3). Each injection or extraction
period corresponds to steady rate pumping for duration T.
2.2 Numerical Model
The standard model domain is for a 1,500 m by 1,500 m aquifer area divided into
100 15-m grid blocks in the x direction and 100 15-m grid blocks in the y
direction. The model is a single layer in the z direction, and is for a confined,
fully saturated aquifer. The confined aquifer has initial hydraulic heads of 200 m
throughout the entire model domain. The top of the model is at an
6


Figure 1. Plan view of groundwater flow for a standard dipole. Dashed lines
indicate the hydraulic head contours and the solid lines indicate the pathlines
within the homogeneous aquifer. Figure modified from Fitts (2002).
(b)
Extraction
Figure 2. Plan view of pulsed dipole injection/extraction wells. Filled circles
denote injection wells; open circles denote extraction wells; and arrows
denote flow directions.
7


+ Q
-Q
} Injection Well
Pumping
} Extraction Well
Pumping
Figure 3. Schematic of model cycle showing injection and extraction cycling.
elevation of 10 m, and the bottom of the model is at an elevation of 0 m. The
porosity is 0.35; hydraulic conductivity is 0.0015 m/s; storativity is 0.001;
specific storage is 0.0001 m'1; and there are constant head boundaries on all sides
of the model domain set to 200 m.
The model includes one fully penetrating injection well and one fully penetrating
extraction well located 345 m apart. The simulation uses an injection period of
T= Id, followed by an extraction period of T = 1 d (Figure 3), which is
considered to be one full cycle (27). A total of three cycles were run in each
simulation. The injection and extraction rates are 1.5 m3/s in the baseline
simulation.
Particles within the modeled aquifer are tracked throughout the simulation using
MODPATH. Using the particle tracking data, graphs can be created inside
Matlab showing the movement of particles within the aquifer.
8


2.3 Numerical Code
MODFLOW, a numerical finite difference code developed by the U.S. Geological
Survey (Harbaugh et al. 2000), is used to model the flow associated with injection
and extraction from a single-layer confined aquifer. The particle tracking within
the aquifer is performed using MODPATH Version 4.00 Release 3 (Pollock
1994). The model is set up using a parameter file which defines the input for the
model. A sample parameter input file is included in Appendix A. The use of the
parameter file allows changes to the model to be made simply by modifying a
single file.
A Matlab script (Appendix B) was written to read the parameter input file and
create the necessary files to run both MODFLOW and MODPATH (Figure 4).
The Matlab script file first creates the input files necessary to run MODFLOW by
reading in data from the parameter file and writing the input data to files named
according to the MODFLOW specifications. MODFLOW is then run externally
to execute the model. After the model has run, the Matlab script file creates the
additional files necessary to run MODPATH. Matlab then externally runs
MODPATH and reads in the output files from MODFLOW and MODPATH to
create a matrix of particle locations. The Matlab script then post-processes the
results.
9


Figure 4. Flow chart of process followed by Matlab script.
10


3. Methods to Analyze Mixing
For this research, mixing is evaluated quantitatively in two ways.
1. By calculating the separation distance between fluid particles
2. By calculating the dilution index at the end of each injection and
extraction period
The use of two metrics allows evaluation of the mixing in different ways and both
metrics are discussed in more detail in this chapter. Calculation of separation
distances allows an evaluation of chaotic movement as defined in past research.
The dilution index allows a quantitative measure of the mixing within the aquifer.
3.1 Separation Distance
Separation distance is the distance between two particles at a given time during
the groundwater simulation. For a selected pair of particles, the separation
distance is calculated as shown in Eqn (2).
SD,= [(x2-xi)2 + (y2-yi)2]0'5 (2)
where xi = x location of Particle 1 at time t
X2 = x location of Particle 2 at time t
yi = y location of Particle 1 at time t
y2 = y location of Particle 2 at time t
11


For example, consider the standard parabolic velocity distribution for laminar
pipe flow shown in Figure 5. Now, consider two particles moving within that
pipe (Figure 6). The separation distances between the particles at t = 0, 1, and
3 min are shown by SD0, SDi, and SD3. A plot of these SDs versus time is shown
in Figure 7 which indicates the separation distance is growing linearly which is
typical of laminar flow.
For a system that exhibits chaotic advection, the separation distance grows
exponentially as is illustrated in Figure 8. For this study, the separation distances
of pairs particles are plotted as a function of time to determine if the separation
distances grow exponentially which would indicate chaotic advection.
3.2 Dilution Index
Dilution index calculations are performed based on Kitanidis (1994) to evaluate
mixing. First, to understand the dilution index, a distinction must be made
between spreading and dilution. Kitanidis (1994) explains spreading as two small
areas of high concentration contamination located apart from each other (Figure
9a). If the goal is to obtain mixing of the injected substance, then the substance
needs to do more than simply move away from the injection well in order to
maximize its spatial distribution in the aquifer. In Figure 9a, the contaminant is
spread out but is not well diluted because the mass is distributed over a small
volume. Compare this with an equal contamination mass that is distributed into a
Gaussian (Figure 9b) where the mass is distributed over a larger volume and
more dilute. This example illustrates the difference between spreading and
12


Figure 5. Cross section of pipe flowing full showing standard parabolic
velocity distribution. Image obtained from University of Waterloo (2006).
\\ wwwww
i 1 kP\ SDo VDl N.

/z//y///////
Figure 6. Movement of two particles within a pipe flowing full and indication
of separation distance (SD) at t = 0,1, and 3 min.
13


8
y
E
IS
&
0
0 12 3
Time [min]
Figure 7. Linear growth of separation distance versus time for two particles
within a pipe flowing full, indicating non-chaotic flow.
8
E
&
o
CO
0 12 3
Time [min]
Figure 8. Example of exponential growth of separation distance, indicating
chaotic flow.
14


(a)
(b)
Figure 9. (a) Mass in two small plugs versus (b) mass distributed normally.
Adapted from Kitanidis (1994).
15


dilution, and although both have the same standard deviation of the contaminant
mass about the centroid, Figure 9(b) is considered by Kitanidis (1994) to be more
dilute.
The dilution index, E, is a measure of the degree of mixing within the aquifer and
for 2D flows, is given by
where Pk is the number of the particles in grid block k divided by the total number
of particles, and can be thought of as the probability that a certain particle is found
in grid block k; AA is the area of each grid block; n is the number of grid blocks.
For this analysis, dilution index grid blocks were the same size as the model grid
blocks (15 m by 15 m).
To help illustrate the concept of the dilution index, consider a 45 m by 45 m space
divided into 9 grid blocks, n = 9, each 15 m by 15 m (Figure 10). There are nine
particles within the model space. Let m be the number of grid blocks that contain
at least one particle. In this example, AA = 225 m2 and the particles are uniformly
distributed within the nine grid blocks such that m = n. The probability that the
particle is any grid block is 1/9, and using Eqn (3), E = 2,025 m .
Now, consider the same domain (45-m by 45-m space divided into nine grid
blocks, n = 9) with nine particles inside six grid blocks, m = 6 (Figure 11). In this
example, AA = 225 m2. The particles are not uniformly distributed within the
domain, and m < n. The probability that the particle is in any grid block is 0, 1/9,
(3)
16


o 0 15 30 45
x (m)
Figure 10. Example model space divided into nine grid blocks with nine
particles shown by the solid circles.
or 2/9, and using Eqn (3), E = 1,276 m2. The dilution index for the second
example is smaller because the particles are not uniformly distributed and are not
occupying as many grid blocks.
Let Emax be the maximum value of E for a given configuration. In the first
example, where m = n, Emax = nAA = A, the area of the model. This equation of
Emax is only true when the number of particles is equal to the number of grid
blocks. When the number of particles is less than the number of grid blocks
Emax = (number of particles) *AA, and Emax will be less than A.
17


x (m)
Figure 11. Example model space divided into nine grid blocks with nine
particles shown by the solid circles
According to Kitanidis (1994), the reactor ratio is defined as the ratio of the
calculated dilution index to the maximum dilution index (given all constraints):
M E/Emax (4)
In the first example, where m = 9, M = 2,025 m2/2,025 m2 = 1. In the sccunu
example, where m = 6, M = 1,276 m2/2,025 m2 = 0.63. The larger M indicates
more dilution and therefore more mixing within the model.
The dilution index and M were calculated at the end of each injection and
extraction period.
18


4. Results and Discussion
Mixing was evaluated first qualitatively by looking at space-filling of particle
tracks and pathline crossing, then quantitatively using separation distance and
dilution index. This chapter presents and discusses the results of the mixing
evaluations.
4.1 Particle Tracking
Seventy-two particles, located 5 degrees apart from each other in a circle of radius
5 m, were simulated from starting points surrounding the injection well. These
particles were then tracked through the aquifer for six days (three full cycles)
(Figure 12). In the figure, as in subsequent figures, the injection well is located
toward the top of the domain at (x,y) = (712.5 m, 922.5 m) and the extraction well
is located toward the bottom of the domain at (x,y) = (712.5 m, 592.5 m). Particle
tracking shows abrupt changes in particle trajectories which occur when injections
top and extraction begins and vice versa (Figure 12). This illustrates that
pathlines in the pulsed dipole system are reoriented during the simulation. For
comparison, pathlines for the standard dipole where both the injection and
extraction wells are pumping at the same time is shown in Figure 13. Generally,
the particles pathlines fill the space between the injection and extraction well. If
more particles were simulated around the injection well from t = 0 d the distance
between adjacent pathlines in Figure 12 would be reduced even more.
19


1100
_J___________________I_________________I_______________I--------------------1------------------1-----------------1
400 500 600 700 800 900 1000
X [meters]
Figure 12. Pathlines of the 72 particles tracked from t = 0 d tot = 6din the
pulsed dipole model. The injection well is located toward the top of the
domain at (x,y) = (712.5 m, 922.5 m) and the extraction well is located toward
the bottom of the domain at (x,y) = (712.5 m, 592.5 m). The cross formed by
the pathlines near the injection well is a numerical artifact from the
modeling.
20


1200 -
1100
1000
900
£
800
700
600
500 -
_l_______________I_______________I________________l_______________I________________I_________________1_
400 500 600 700 800 900 1000
X [meters]
Figure 13. Paths of 72 particles from t = 0 dtot = 3din model operating as
standard dipole. The cross formed by the pathlines near the injection well is
a numerical artifact from the modeling.
21


4.2 Pathline Crossing
To further picture the movement of particles within the aquifer, after 72 particles
were added at t = 0 d, an additional 72 particles were injected half-way through
the initial injection period, at t = 772 = 0.5 d. On Figure 14, the initial set of 72
particles is tracked with solid pathlines, and the second set of 72 particles is
tracked with dotted pathlines.
The pathlines of the particles injected at the beginning of the simulation cross the
pathlines of the particles injected at t = T/2. This is clearly shown in Figure 15, a
close-up view of the area between the injection and extraction wells. The pathline
crossing shown in Figures 14 and 15 is a qualitative difference from the standard
dipole where pathlines of particles within the aquifer, regardless of when they
were injected, would not cross. The crossing is due to the reorientation of the
pathlines caused by the pulsed pumping. It is not clear if the pathlines crossing is
indicative of additional mixing within the aquifer.
4.3 Separation Distance
Figure 16 shows the location of the 72 particles within a plan view of the model
domain. The particles are numbered from due east counterclockwise.
Separation distances were calculated for several pairs of particles, but none
showed exponential growth. There were two distinct types of curves that resulted
from the analysis (Figure 17). The first type of curve, shown in Figure 17(a),
indicates that the particle separation distance grows during each injection cycle
(7=1 d) and then stays fairly constant during each extraction cycle (7=1 d)
although the overall trend is toward a continually increasing separation distance.
22


1100 -
Figure 14. Pathlines of 144 particles with 72 injected at t = 0 d (solid lines)
and an additional 72 particles injected at t = 0.5 d (dotted lines).
23


Figure 15. Close-up of crossing pathlines.
24


1100 -
-J__________I____________I____________I____________I------------1-----------1-----
400 500 600 700 800 900 1000
X [meters]
Figure 16. Plan view of model with 72 particle pathlines. Particles are
numbered from due east as Particle 1, and particle numbers increase
counterclockwise.
25


40
35

I____________i___________i____________i___________i___________i___________
0 1 2 3 4 5 6
time [d]
(a)
Figure 17. Separation distance plots for (a) particles 5 and 7 and (b) particles
55 and 57.
26


The second pattern which occurred (Figure 17 (b)) indicates some increasing and
decreasing separation distances based on whether the cycle is injection or
extraction but the overall trend is to initially increase in separation distance and
then decrease. Particles 5 and 7 used for the separation distance calculations in
Figure 17(a) are travelling on similar paths which respond the same way during
each injection or extraction period. Particles 55 and 57 used for the separation
distance calculations in Figure 17(b) are travelling between the injection and
extraction well and are pulled in different directions during each injection or
extraction period which explains the difference between the plots in Figure 17.
The difference between the exponential curves obtained by Sposito (2006) and
Bagtzoglou and Oates (2007) which indicated the presence of chaotic advection
and the separation distance curves obtained from the current research which did
not indicate chaotic advection could be due to the reinjection of particles. Sposito
(2006) and Bagtzoglou and Oates (2007) simulated many injection/extraction
cycles, so particles were extracted at the extraction well and reinjected at the
injection well. The current research is focused on a single pass from the injection
well to the extraction well and does not model any reinjection or mixing outside
of the aquifer.
4.4 Dilution Index
The dilution index is calculated throughout each simulation at the end of each
injection and extraction period. All of the particles are started in the same grid
block since the radius of the initial particle circle is 5 m and the grid blocks are 15
m square.
27


The analysis indicates that in instances where a small number of particles are
tracked, the dilution index increases substantially after the initial injection period
and then remains constant thereafter, until it decreases when the particles
converge near the extraction well (Figure 18). These results indicate that the
(a)
Figure 18. Dilution index for (a) 23 particles and (b) 45 particles.
28


dilution within the simulated aquifer occurs during the initial injection cycle and
not as a function of the continued pulsing within the aquifer. To evaluate if this
behavior is the result of the small number of particles, dilution index calculations
were also preformed for simulations with larger numbers of particles. As shown
on Figure 19, for larger numbers of particles the dilution index generally increases
over time as the particles move further from the injection well.
To further evaluate the dilution, E/Emax was calculated for 90 and 360 particles
(Figure 20). The maximum dilution index would occur when each particle is
uniformly distributed within the aquifer in its own grid block. For 90 particles,
the maximum dilution index is Emax = 20,250 m2. For 360 particles, the
maximum dilution index is Emax = 81,000 m2. Although Figure 19 shows an
increasing trend for the dilution index, neither simulation leads to the maximum
dilution, as shown on Figure 20.
4.5 Sensitivity Analysis
An analysis of the principles behind the model indicate that there is essentially a
single variable which combines many of the model parameters. This variable A2
is defined as follows and is modified from Jones and Aref (1988) to account for
flow through porous media.
A2 = QT/nbL2n (5)
Q is the pumping rate; T is the pumping duration; n is porosity; b is aquifer
thickness; and L is the distance between the injection and extraction wells.
29


(b)
Figure 19. Dilution index for (a) 90 particles and (b) 360 particles.
30


1
0.8 h
S 0-6}-
E
0.4 h
0.2
/
2 3
time [days]
(a)
Figure 20. Plot of E/Ema* for (a) 90 particles and (b) 360 particles.
31


Eqn (5) relates these parameters such that doubling Q or T has the same effect on
particle movement as halving b, halving n, or 0.5 5I. Figure 21 shows 72
particles tracked during the standard simulation and then 72 particles tracked
when one variable within A2 is modified. Figures 21(b) though (f) all show the
same particle paths indicating that modifying one variable correspondingly (e.g.,
2Q, 2T, 0.707L, 0.5n, or 0.56 as shown in figures) leads to the same results.
The particles in Figure 21(f) have not traveled as far as the particles in Figure
21(a-e) in absolute travel distance; however, in travel distances relative to L are in
fact identical. Figure 22 repeats Figure 21(b) Figure 21(f) with the x and y axis
normalized to x/L and y/L, with the appropriate L for each simulation. Figure 22
shows that the particles move the same relative distance during each injection and
extraction period and are the same shape.
A sensitivity analysis was performed to determine how changes in A2 changed the
E/Emax ratio
A2 was adjusted to 1/8, 1/2, 2, and 8 of its base value by adjusting the aquifer
thickness, b, in the simulations. Any parameter of A2 could have been modified
but b was chosen because the single number is easy to change in the parameter
file and track in the model. In order for the dilution index calculations to be
representative, the particles which enter the extraction well are removed from the
matrix of particles locations and are not considered in the separation distance or
dilution index calculations. Figure 23 presents E/Emax for two simulations where
b was reduced, and Figure 24 presents E/Emax for two simulation where b was
increased. The sensitivity analysis indicates that the dilution index is sensitive to
A2, but generally when particles are able to move farther from the injection well,
E/Emax increases.
32


1500r 1500
0
0
500 1000 150
X [meters]
500 1000 1500
X [meters]
(a)
1500
(b)
1500
1000
500
0
0
500
X [meters]
(c)
1000
1500
1500
0
0
1500
500
X [meters]
(d)
1000
1500
1000
500
1000
E
500
0
0
500
X [meters]
(e)
1000
1500
500 1000
X [meters]
(f)
1500
Figure 21. Plot of pathlines for simulation with (a) standard simulation, (b)
2Q, (c) 2T, (d) 0.5/1, (e) 0.5b, and (f) 0.707L .
33


5
4.5
3.5
X/L [-]
(b)
Figure 22. Plot of particle pathlines normalized based on the distance
between the injection and extraction wells when L = (a) 345 m and (b) 240 m.
34


Figure 23. E/Emax versus t for (a) 0.5b and (b) 0.125b.
35


(a)
(b)
Figure 24. E/Emax versus t for (a) 2b and (b) 8b.
36


5. Conclusions and Recommendations for Future Work
This section briefly discusses the conclusions of the research and four topics for
further analysis: comparison with the standard dipole, varying recovery periods,
reinjection, and heterogeneity. Each is discussed in more detail below.
5.1 Conclusions
The particle tracking results indicate that the pathlines of particles injected
simultaneously do not cross during the pulsed dipole pumping simulation, but
when additional particles are injected midway through the injection period, the
pathlines cross for particles that were introduced at different times. The crossing
pathlines indicate a difference between the pulsed dipole pathlines and the
standard dipole pathlines.
The criteria necessary for chaotic advection, a time-dependent 2D flow system
and reorientation of pathlines, are met in the current model, but because the
separation distance between particle do not increase exponentially over time, the
results indicate that chaotic advection is not achieved during a single pass from
the injection well to the extraction well.
The results also indicate that the dilution index is a useful tool to evaluate mixing
within the simulated aquifer. For small numbers of particles, maximum dilution
is reached fairly quickly while for larger numbers of particles, the maximum
dilution is not met by the end of six days. This indicates the dependence of the
37


analysis on the number of particles and points out the importance to use a larger
number of particles for future analyses.
This study which focused on mixing during a single pass from the injection well
to the extraction well has not shown chaotic advection in the aquifer. This
research differs from past research by using a numerical groundwater model
instead of analytical codes, and the current research focused on evaluating the
groundwater mixing within the aquifer during a single pass. Past research
evaluated mixing over multiple passes using reinjection of extracted particles and
utilized predetermined and random injection angles for the particles that were
reinjected into the aquifer.
5.2 Recommendations for Future Work
5.2.1 Comparison with Standard Dipole
The difference between the currently reported simulations and the standard dipole
could be analyzed by comparing the particle locations and paths. The current
Matlab script could be used to track particles within the standard dipole and
output their locations throughout the simulation. These particles would move
twice as fast as those in a pulsed dipole simulation because in a standard dipole
the wells are working together to remove the particles. The simulation would
only need to be run for half of the standard time. A comparison of the particle
locations from the standard dipole may be used to evaluate the difference between
the separation distance of particles tracked for the standard dipole versus those
tracked for the pulsed dipole.
38


5.2.2 Recovery Periods
Future research may consider a recovery period between each pumping period
(Figure 25). During the recovery period, R, there would be no pumping but
particle movement could continue. This is an important factor to evaluate
because it is not clear how this additional movement would modify the mixing
within the aquifer. A schematic illustrating the pumping and recovery period is
shown as Figure 25.
5.2.3 Reinjection
The current research focused on a single pass through the aquifer, but other
researchers have evaluated injection/extraction simulations that include
reinjection of particles that have been extracted (Jones and Aref 1988, Stremler et
al. 2004, Sposito 2006, Bagtzoglou and Oates 2007). Their research has indicated
that chaotic advection is achievable, but their research made assumptions that may
be difficult for a groundwater reinjection system to meet. There would, in reality,
be mixing within the well, the pump, and the reinjection piping. The particles
would not all remain oriented the same from extraction to reinjection due the
turbulent mixing from the pumping (this indicates a difference between an actual
groundwater reinjection system and what was previously modeled analytically).
The effects of past researchers assumptions may be evaluated in further
groundwater modeling work along with an analysis of the importance of
reinjection in the assessment of chaotic advection.
39


T
T R
-M--M
T
>----<*
R
T
H--

+Q
-Q
R
x--x
}
}
Injection
Well
Extraction
Well
*
2(T+R) ---------M----------- 2(T+R) ----------
First Cycle Second Cycle
Figure 25. Schematic of model showing pumping periods, of duration T, and
recovery period of duration R.
5.2.4 Heterogeneity
The current project and subject of this thesis does not include an analysis of
mixing in a heterogeneous aquifer. The model created during this research is a
numerical model which does allow for analysis of the effects of heterogeneity
within the aquifer. Past models (Sposito 2006, Bagtzoglou and Oates 2007) were
analytical and therefore did not allow these types of calculations.
Work to evaluate mixing in a heterogeneous aquifer could proceed by modeling
a random hydraulic conductivity, K, field. The K field could be generated using
the Geostatistical Software Library (known as GSLIB) originally developed at
Stanford University (Deutsch et al. 1997) using a given correlation length scale
(recommended minimum is L/10 or 34.5 m) (personal communication, Dr.
Roseanna Neupauer, April 2009). The Matlab script would require
modification to use the input K file to generate a field of transmissivities to be
used by MODFLOW. Then a series of Monte Carlo simulations would be used
to generate multiple K files which would be used to run an equal number of
MODFLOW/MODPATH simulations. The output of each MODPATH
40


simulation would then need to be saved to preserve the particle tracking data
although these data would not need to be plotted with each run of the model.
The mixing metrics of separation distance and dilution index could then be
calculated for each simulation using the saved MODPATH output. The model
simulations using random K fields would be run until the histogram of the
output variable of interest stabilizes (the output variable of interest has not been
identified yet).
Future research into the effects of heterogeneity will allow better representations
of what may happen in an actual aquifer by providing data on a representation of
the preferred paths within the aquifer and will include randomization of the
hydraulic conductivity field within the aquifer through Monte Carlo simulations.
41


APPENDIX A
Input Parameter File
chaos.par
File originally developed by Roseanna Neupauer, Univ. of Colorado Boulder.
Modified by CRR.
0 1500 15
0 1500 15
10 0
6
2. 1. 1. 1. 1. 1
1 200.
1 200.
1 200.
1 200.
200.
0
0.0015
0
0.01
% xmin,xmax,dx
% ymin,ymax,dy
% top elevation, bottom elevation
% number of stress periods
% number of time steps per stress period
% B.C. at x=xmin: l=constant head, 0=no flow; if constant
head, specify value.
% B.C. at x=xmax: l=constant head, 0=no flow; if constant
head, specify value.
% B.C. at y=ymin: l=constant head, 0=no flow; if constant
head, specify value.
% B.C. at y=ymax: l=constant head, 0=no flow; if constant
head, specify value.
% starting guess for head
% aquifer type: l=unconfined, 0=confined.
% hydraulic conductivity (either homogeneous value, or
background K)
% is the aquifer homogeneous? 0=homogeneous, l=zones with
different K
% specific storage (mA-l)
42


2
48 39 1.50
48 62 -1.50
0.0
0.35
0
1
48 39 5. 72 0
5.18400e5
1
% number of wells (use a positive number to read from this
file, neg. to enter graphically)
% One line for each well: column, row, pumping rate (negative
for pumping)
% column, row, pumping rate for second well
% uniform recharge rate (unconfined aquifer only, use 0.0 for
no recharge)
% porosity
% number of lines of particles for particle tracking
% number of circles of particles for particle tracking
% x- and y-coordinates of center of circle, radius of circle,
number of particles, time of release of particles
% duration of particle tracking time
% direction of tracking: "1" for forward, "2" for backward
43


APPENDIX B
Matlab Script
gwmixing.m
% gwmixing
%
% This code is used to set up the input files for a one-layer,
% transient MODFLOW simulation for a homogeneous (or zonally-
% heterogeneous)rectangular domain with no-flow boundaries on all
% four sides.
% The column spacing is uniform, and the row spacing is uniform.
%
% This code is also used to set up the input files for MODPATH to
% track particles in a line(s) or a circle(s) as they move within % the aquifer.
%
% This code reads in parameters from a parameter file called
% fname.par, where "fhame" is a root name that is used in all
% file names.
%
% This code requires "MPath4_3.exe", "mf2k.exe", "kitanidis.m",
% and fname.par to be installed in the same directory.
%
% Last Revised, CRR 6/30/09. Original code created by Roseanna
% Neupauer, Univ. of Colorado Boulder.
pcolor='rgbm';
plotted=0;
% Get user input for name of parameter file
pfile=input('Enter the name of the parameter file. > \n','s');
[dummy,fhame,dummy,dummy]=fileparts(pfile);
fid=fopen(pfile,'r');
% Create all input files for MODFLOW
% Create .nam file
fidnam=fopen(strcat(fname,'.nam'),'w');
fprintf(fidnam,'LIST 3 %s.out \n',fhame);
44


% Read in model set-up information from fname.par
X=fscanf(fid,'%d',3);
fgetl(fid);
Y=fscanf(fid,'%d',3);
fgetl(fid);
elev=fscanf(fid,'%f,2);
fgetl(fid);
nstress=fscanf(fid,'%d', 1);
fgetl(fid);
ntstep=fscanf(fid,'%f,nstress);
fgetl(fid);
xmin=X(l);
xmax=X(2);
dx=X(3);
ncol=ceil((xmax-xmin)/dx);
ymin=Y(l);
ymax=Y(2);
dy=Y(3);
nrow=ceil((ymax-ymin)/dy);
xx=xmin:dx:xmax;
yy=ymin:dy:ymax;
% Create .dis file
fiddis=fopen(strcat(fhame,'.dis'),'w');
fprintf(fiddis,'# MODFLOW Simulation set up using %s \n',pfile);
fprintf(fiddis,# %s \n,date);
fprintf(fiddis,'%10d %9d %9d %9d %9d %9d\n',l,nrow,ncol,nstress,l,2);
fprintf(fiddis,' 0 \n');
fprintf(fiddis,'CONSTANT %f \n',dx);
fprintf(fiddis,'CONSTANT %f\n',dy);
fprintf(fiddis,'CONSTANT %f \n',elev( 1));
fprintf(fiddis,'CONSTANT %f \n',elev(2));
for i=l:nstress
for j=ntstep(i)
fprintf(fiddis,' 86400 %d 1.0 TR\n',j);
end
end
45


fclose(fiddis);
fprintf(fidnam,DIS 7 %s.dis \n',ftiame);
% Create .bas file
fidbas=fopen(strcat(fhame,'.bas'),'w');
fprintf(fidnam,'BAS6 8 %s.bas \n',fname);
fprintf(fidbas,'# MODFLOW Simulation set up using %s \n',pfile);
fprintf(fidbas,'# %s W',date);
fprintf(fidbas,'FREE, SHOWPROGRESS, PRINTTIME \n');
Q)rintf(fidbas,'CONSTANT 1 \n');
fgetl(fid);
fgetl(fid);
fgetl(fid);
fgetl(fid);
fgetl(fid);
fprintf(fidbas,' -999.99 \n');
fprintf(fidbas,'CONSTANT 200 \n');
fclose(fidbas);
% Create .oc file
fidoc=fopen(strcat(fhame,'. oc') ,'w');
fprintf(fidnam,'OC 22 %s.oc \n',fiiame);
fprintf(fidoc,'HEAD PRINT FORMAT 12 \n');
fprintf(fidoc/HEAD SAVE FORMAT (10(1X1PE13.5)) LABEL \n');
fprintf(fidoc,'HEAD SAVE UNIT 51\n');
fprintf(fidoc,'COMPACT BUDGET FILES \n\n');
for i=l :nstress
for j=l:(ntstep(i))
fprintf(fidoc,'PERIOD %d STEP %d \n',i,j);
fprintf(fidoc,' PRINT HEAD\n');
fprintf(fidoc, PRINT BUDGETW);
f)irintf(fidoc,' SAVE HEAD\n');
fprintf(fidoc,' SAVE BUDGETW);
end
end
fclose(fidoc);
46


% Create .bcf file
fidbcf=fopen(strcat(fname,'.bcf),'w');
fprintf(fidnam,'BCF6 11 %s.bcf \n',fname);
fprintf(fidbcf,'50 -2.00000000000000E+0020 0 5.00000000000000E-0001 1 1
\n');
ltype=fscanf(fid,'%d',l);
fgetl(fid);
k=fscanf(fid,'%f, 1);
fgetl(fid);
hetero=fscanf(fid,'%d', 1);
fgetl(fid);
fprintf(fidbcf,'%2d\n',ltype);
fprintf(fidbcf,'CONSTANT 1.0\n);
S=fscanf(fid,%f, 1);
fgetl(fid);
fprintf(fidbcf,CONSTANT %12.6g W,S*abs(elev(2)-elev(l)));
fprintf(fidbcf,CONSTANT %12.6g W,k*(l-ltype)*abs(elev(2)-
elev(l))+k*ltype);
fclose(fidbcf);
% Create .wel file
nwells=fscanf(fid,'%d, 1);
fgetl(fid);
fidwel=fopen(strcat(fhame,'.wer),'w');
fprintf(fidnam,'WEL 12 %s.wel W,fname);
fprintf(fidwel,'% 1 Od 50 W,nwells);
for i=l:nwells
Z=fscanf(fid,'%f,3);
fgetl(fid);
cw(i)=Z(l);
rw(i)=Z(2);
qw(i)=Z(3);
end
for j=l:nstress/2
for i=l:nwells
fprintf(fidwel,'l 0 W);
fprintf(fidwel,' 1 %9d %9d %9g W,rw(i),cw(i),qw(i));
47


end
end
fclose(fidwel);
fgetl(fid);
% Create .peg file
fidpcg=fopen(strcat(fhame,'.pcg'),'w');
fprintf(fidnam,'PCG 23 %s.pcg \n',fname);
fprintf(fidpcg,' 50 30 l\n');
fj)rintf(fidpcg,' .001 .001 1 1 1
fclose(fidpcg);
por=fscanf(fid,'%f, 1);
fgetl(fid);
nlines=fscanf(fid,'%d', 1);
fgetl(fid);
xl=zeros(nlines, 1);
yl=zeros(nlines,l);
xu=zeros(nlines, 1);
yu=xu;
for i=l:nlines
Z=fscanf(fid,'%f,4);
fgetl(fid);
xl(i)=Z(l);
yl(i)=Z(2);
xu(i)=Z(3);
yu(i)=Z(4);
xl(i)=max(min(xx),xl(i));
yl(i)=max(min(yy),yl(i));
xu(i)=min(max(xx),xu(i));
yu(i)=min(max(yy),yu(i));
end
ncirc=fscanf(fid,'%d', 1);
fgetl(fid);
colc=zeros(nlines, 1);
rowc=zeros(nlines, 1);
rc=zeros(nlines, 1);
ptsc=xu;
0 IV)
48


for i=l:ncirc
Z=fscanf(fid,'%f,5);
fgetl(fid);
colc(i)=Z(l);
rowc(i)=Z(2);
rc(i)=Z(3);
ptsc(i)=Z(4);
trelease(i)=Z(5);
end
tpart=fscanf(fid,'%f, 1);
fgetl(fid);
trackdir=fscanf(fid,'%d', 1);
fgetl(fid);
fclose(fid);
fprintf(fidnam,'DATA(BINARY) 50 %s.bud \n',fname);
fprintf(fidnam,'DATA 51 %s.hed \n',fname);
fclose(fidnam);
fid=fopen('modflow.bf,'w');
fprintf(fid,'%s.nam \n',fname);
fclose(fid);
% Externally run Modflow simulation using Modflow 2000
fid=fopen('modflow. bat','w');
fprintf(fid,'mf2k.exe /wait \n');
fprintf(fid,'pause \n');
fclose(fid);
eval('! modflow.bat');
% Read in output heads
fid=fopen(strcat(fname,' .hed') ,'r');
fgetl(fid);
temp=fscanf(fid,'%f,ncol*nrow);
fclose(fid);
head=reshape(temp,ncol,nrow)';
49


head=flipud(head);
%[c,h]=contour(xx(l :ncol)+dx/2,yy(l :nrow)+dy/2,head);
%clabcl(c,h);
axis equal
axis([xmin,xmax,ymin,ymax]);
xlabel('x');
ylabel('y');
hold on
hold off
if (nlines+ncirc > 0)
fid=fopen(strcat(fhame,'.pnm'),'w');
fprintf(fid,'LIST 47 %s.mli \n',fname);
fprintf(fid,'MAIN 10 %s.mpa \n',fname);
fprintf(fid,'BUDGET 33 %s.bud \n',fname);
fprintf(fid,'DIS 71 %s.dis \n',fname);
fprintf(fid,'HEAD 23 %s.hed \n',fname);
fprintf(fid,'LOCATIONS 43 %s.prt \n',fname);
Iprintf(fid,'TIME 44 %s.tim \n',fname);
fprintf(fid,''ENDPOINT 46 %s.end \n',fname);
fprintf(fid,'PATHLINE 48 %s.lin \n',fname);
fclose(fid);
end
% Create the *.mpa file
fidmpa=fopen(strcat(fhame,'.mpa'),'w');
fprintf(fidmpa,'%8d% 10.0g%10.0g%8d%8d%8d\n\n',500000,-999.99,-
2.00000000000000E+0020,0,0,0);
fprintf(fidmpa,'%2d\n',ltype);
ibound=ones(nrow,ncol);
fprintf(fidmpa,'INTERNAL 1 (FREE) 5 V);
for i=l:nrow
fprintf(fidmpa,'%3 d%3 d%3 d%3 d%3 d%3 d%3 d%3 d%3 d%3 d%3 d%3 d%3 d%3 d%
3 d%3 d%3 d%3 d%3 d%3 d \n', ibound( i,:));
if mod(ncol,20)
50


fprintf(fidmpa,'\n');
end
end
fprintf(fidmpa,'CON ST ANT %f \n',por);
fprintf(fidmpa,0. \n');
%for i=l:nstress
%for j=ntstep(i)
%fprintf(fidmpa,' 86400 %d 1 \n',j);
%end
%end
fprintf(fidmpa,T 1 %d 1 \n',nstress);
fclose(fidmpa);
% Create .prt file
fidprt=fopen(strcat(fhame,'.prt'),'w');
for i=l:nlines
xl(i)=max(min(xx),xl(i));
yl(i)=max(min(yy),yl(i));
xu(i)=min(max(xx),xu(i));
yu(i)=min(max(yy),yu(i));
lcol=max(find(xx<=xl(i)));
lrow=nrow-max(find(yy<=y l(i)))+1;
ucol=max(fmd(xx<=xu(i)));
urow=nrow-max(find(yy<=yu(i)))+1;
npts=max(abs(ucol-lcol)+l,abs(urow-lrow)+l);
icol=floor(linspace(lcol,ucol,npts));
irow=floor(linspace(lrow,urow,npts));
for j=l:npts
fprintf(fidprt;%8d%8d%8d%8.2P/o8.2f%8.2f\n',icol(j),irow(j),1,0.5,0.5,0.5);
end
end
for i=l:ncirc
theta=linspace(0,2*pi,ptsc(i)+1);
theta=theta( 1: length(theta)-1);
51


xxc=0.5+(rc(i)*cos(theta))/dx;
yyc=0.5+(rc(i)*sin(theta))/dy;
for j=l :length(xxc)
%icol=max(find(xx<=xxc(j)));
%irow=nrow-max(find(yy<=yyc(j)))+1;
fprintf(fidprt,'%8d%8d%8d%8.2f%8.2f%8.2f 0 0 0
%d\n',colc(i),rowc(i), 1 ,xxc(j),yyc(j),0.5,trelease(i));
end
end
fclose(fidprt);
% Create .tim file
fidtim=fopen(strcat(fhame,'.tim'),'w');
fprintf(fidtim,' 1 l\n');
fprintf(fidtim,'% 10.4f \n',tpart);
fclose(fidtim);
fidrsp=fopen(strcat(fhame,'.rsp'),'w');
fprintf(fidrsp,'\n%s.pnm \n2\nO.\nl\nN\nl\n%s.cbf \n2\nY\nl\n43200 \nl
\n%d\n 1 \n 1 \n l\nN\n 1 \nN\nN\nY\n',fname,fname,nstress*2);
fclose(fidrsp);
% Run MODPATH externally
cmd=sprintf('! mpathr4_3.exe < %s.rsp',fname);
eval(cmd);
% Plot the particle paths
fid=fopen(strcat(fhame,'.lin'),'r');
fgetl(fid);
temp=fscanf(fid,'%f);
nn=length(temp)/10;
temp=reshape(temp, 10,nn)';
fclose(fid);
% Plot all particle paths as solid lines
nparts=max(temp(:, 1));
for i= Imparts
list=find(temp(:, 1 )==i);
52


hold on
plot(temp(list,2)+xmin,temp(list,3)+yniin,'-');
plot(temp(list( 1 ),2)+xmin,temp(list( 1 ),3)+ymin,'-');
%title('Plot 1)
xlabel('X [meters]')
ylabel('Y [meters]')
end
% Plot half of particle paths as solid lines, half as dotted lines
%for i=l :nparts/2
% list=find(temp(:, 1 )==i);
% hold on
% plot(temp(list,2)+xmin,temp(list,3)+ymin,'-');
% plot(temp(list( 1 ),2)+xmin,temp(list( 1 ),3)+ymin,'-');
% xlabel('X [meters]')
% ylabel('Y [meters]')
%end
%for i=nparts/2:nparts
% list=fmd(temp(:, 1 )==i);
% hold on
% plot(temp(list,2)+xmin,temp(list,3 )+ymin,':');
% plot(temp(list( 1),2)+xmin,temp(list( 1),3)+ymin,':');
% xlabel('X [meters]')
% ylabel('Y [meters]')
%end
hold off
pause
close
% The following command makes Matlab skip the remaining code.
%retum
% CALCULATE SEPARATION DISTANCE
% Define simulation parameters,
dt = 86400;
SD = [];
53


delT = 1;
% Create vector of times
times = [0:dt:dt*nstress];
% Create matrix of separation distances (SD) size = nparts wide
% by nparts tall times nstress+1
for i = l:nstress+l
index = fmd(temp(:,6) == -times(i));
x = NaN(nparts,l);
y = NaN(nparts,l);
x(temp(index,l)) = temp(index,2);
y(temp(index,l)) = temp(index,3);
I = ones(l,nparts);
Xa = x I;
Xb = I' x';
Xc = Xa Xb;
Ya = y I;
Yb = I' y';
Yc = Ya Yb;
D1 = (Xc.A2 + Yc.A2);
D2 = D1.A0.5;
SD = [SD; D2] ; %Appends data into one large matrix %of separation
distances
end
SD2 = [];
a=7; %Particle A (change to input value)
d=9; %Particle B (change to input value)
delT=l; %Duration of stress periods in days
for i=l :nstress+l %Create matrix of SD of particles at each stress period
SDl=SD(a,d); %Create vector SD1 during stress period 1
SD2 = [SD2; SD1]; %Vector of all separation distance for Particles A and D
a=a+nparts; %Move down by number of particles
54


end
time = (Omstress); %Create vector for stress period
T2 = transpose(time)*delT ; %Transpose vector and multiply by %duration of
stress period
SD3 = [T2,SD2]
distance
%Combine into one matrix of time and separation
xl= SD3(:,1);
yl = SD3(:,2);
plot(xl,yi;b-')
xlabel('time [d]')
ylabel('separation distance [m]')
pause
close
%Create vector xl, all rows, column %1 (elapsed time)
%Create vector yl, all rows, column 2 %(separation
distance)
%Plot of xl vs yl (particle position)
% The following command makes Matlab skip the remaining code.
%retum
% CALCULATE DILUTION INDEX WITH KITANIDIS.M
% Calculations limited by maximum number of particles = number of grid blocks
b/c of Emax
% Define simulation parameters,
dt = 86400;
% Create vector of times
times = [0:dt:dt*nstress];
% For each time, extract (x,y) data, then calculate dilution index,
for i = l:nstress+l
index = find(temp(:,6) = -times(i));
x = temp(index,2);
y = temp(index,3);
[dilution(i),N(i)] = kitanidis(x,y,dx,dy,ncol,nrow);
Emax(i)=miin(dx*dy*N(i),ncol*nrow*dx*dy);
end
% Plot dilution index versus time step.
plot(times/dt,dilution)
55


%title(['Dilution Index' datestr(now)])
xlabel('time [days]')
ylabel('dilution index [mA2]')
pause
close
% Plot E/Emax versus time step.
plot(times/dt,dilution./(Emax))
title(['Dilution Index datestr(now)])
xlabel('time [days]')
ylabel('E/Emax')
pause
close
56


APPENDIX C
Dilution Index Function
kitanidis.m
function [E,N] = kitanidis(x,y,dx,dy,nx,ny)
% E = kitanidis(x,y,dx,dy,nx,ny)
%
% This function file calculates the dilution index using equation
% (6) in Kitanidis, P.K. (1994), The concept of the dilution
% index, Water Resources Research, 30(7), 2011-2026. A 2D model
% is assumed. Inputs:
%
% x = lxN vector of particle x-positions [L]
% y = lxN vector of particle y-positions [L]
% dx = x-dimension of MODFLOW grid block [L]
% dy = y-dimension of MODFLOW grid block [L]
% nx = number of grid blocks in x-direction [-]
% ny = number of grid blocks in y-direction [-]
%
% where N is the number of particles being tracked. Output:
%
% E = dilution index [A]
%
% where A means "area", the dimensions of Kitanidis's "dV" in 2D.
%
% Rev. 1, CRR 6/29/09, modified from David Mays 5/6/09, MATLAB
% 7.1.0.246 (R14) Service Pack 3
dV = dx*dy;
count = zeros(nx,ny);
N = length(x);
for k = 1 :N
i = ceil(x(k)/dx);
j = ceil(y(k)/dy);
count(i,j) = count(i,j) + 1;
end
57


P = count/N; %DCM 5/6/09
index = find(P);
H = -sum(sum(P(index).*log(P(index))));
E = dV*exp(H);
58


APPENDIX D
MODPATH output
chaos, lin
The MODPATH output file, containing the locations of tracked particles as they
cross into a new grid block and at the end of a time step, is automatically saved in
a fname.lin, where fname corresponds to the root name of the input parameter file.
A printout of the *.lin file for 10 particles follows this descriptive page. At the
end of the file particularly one can see how the number of values reported for
each particle is the not the same due to the data reporting when crossing into new
grid blocks.
The file contains 10 columns of data, which are described below.
Column 1:
Column 2:
Column 3:
Column 4:
Column 5:
Column 6:
Column 7:
Column 8:
Column 9:
Column 10:
particle number
global coordinate in x direction
global coordinate in y direction
local coordinate within cell in z direction
global coordinate in z direction
cumulative particle tracking time (negative values indicate the end of
MODFLOW time step)
i coordinate within model
j coordinate within model
z coordinate (layer) within model
cumulative time step
1500
1000
500

>
0
0
500 1000 1500
X (meters]
59


@ [ MODPATH Version 4.00 (V4, Release 3, 7-2003) (TREF= 0.000000E+00) ]
1 7.17450E+02 9.22500E+02 5.00000E-01 5.00000E+00 0.00000E+00 48 39 1 1
1 7.20000E+02 9.22488E+02 5.00000E-01 5.00000E+00 4.36080E+02 49 39 1 1
1 7.35000E+02 9.22372E+02 5.00000E-01 5.00000E+00 3.47462E+03 50 39 1 1
1 7.50000E+02 9.22112E+02 5.00000E-01 5.00000E+00 9.44065E+03 51 39 1 1
1 7.65000E+02 9.21699E+02 5.00000E-01 5.00000E+00 1.88154E+04 52 39 1 1
1 7.80000E+02 9.21139E+02 5.00000E-01 5.00000E+00 3.16877E+04 53 39 1 1
1 7.90876E+02 9.20659E+02 5.00000E-01 5.00000E+00 -4.32000E+04 53 39 1 1
2 7.16550E+02 9.25500E+02 5.00000E-01 5.00000E+00 0.00000E+00 48 39 1 1
2 7.20000E+02 9.28033E+02 5.00000E-01 5.00000E+00 6.46628E+02 49 39 1 1
2 7.27290E+02 9.30000E+02 5.00000E-01 5.00000E+00 1.83260E+03 49 38 1 1
2 7.35000E+02 9.37611E+02 5.00000E-01 5.00000E+00 5.78326E+03 50 38 1 1
2 7.48676E+02 9.45000E+02 5.00000E-01 5.00000E+00 1.35852E+04 50 37 1 1
2 7.50000E+02 9.46294E+02 5.00000E-01 5.00000E+00 1.48156E+04 51 37 1 1
2 7.65000E+02 9.55756E+02 5.00000E-01 5.00000E+00 2.95792E+04 52 37 1 1
2 7.73392E+02 9.60000E+02 5.00000E-01 5.00000E+00 3.86846E+04 52 36 1 1
2 7.76556E+02 9.62198E+02 5.00000E-01 5.00000E+00 -4.32000E+04 52 36 1 1
3 7.14000E+02 9.27300E+02 5.00000E-01 5.00000E+00 0.00000E+00 48 39 1 1
3 7.14851E+02 9.30000E+02 5.00000E-01 5.00000E+00 4.70591E+02 48 38 1 1
3 7.17724E+02 9.45000E+02 5.00000E-01 5.00000E+00 3.52667E+03 48 37 1 1
3 7.20000E+02 9.55950E+02 5.00000E-01 5.00000E+00 7.58809E+03 49 37 1 1
3 7.21794E+02 9.60000E+02 5.00000E-01 5.00000E+00 1.01832E+04 49 36 1 1
3 7.26042E+02 9.75000E+02 5.00000E-01 5.00000E+00 2.14755E+04 49 35 1 1
3 7.30066E+02 9.90000E+02 5.00000E-01 5.00000E+00 3.58450E+04 49 34 1 1
3 7.31645E+02 9.96572E+02 5.00000E-01 5.00000E+00 -4.32000E+04 49 34 1 1
4 7.11000E+02 9.27300E+02 5.00000E-01 5.00000E+00 0.00000E+00 48 39 1 1
4 7.10155E+02 9.30000E+02 5.00000E-01 5.00000E+00 4.70591E+02 48 38 1 1
4 7.07332E+02 9.45000E+02 5.00000E-01 5.00000E+00 3.52667E+03 48 37 1 1
4 7.05000E+02 9.56382E+02 5.00000E-01 5.00000E+00 7.78254E+03 47 37 1 1
4 7.03420E+02 9.60000E+02 5.00000E-01 5.00000E+00 1.01099E+04 47 36 1 1
4 6.99355E+02 9.75000E+02 5.00000E-01 5.00000E+00 2.14027E+04 47 35 1 1
4 6.95583E+02 9.90000E+02 5.00000E-01 5.00000E+00 3.57726E+04 47 34 1 1
4 6.94116E+02 9.96634E+02 5.00000E-01 5.00000E+00 -4.32000E+04 47 34 1 1
5 7.08450E+02 9.25500E+02 5.00000E-01 5.00000E+00 0.00000E+00 48 39 1 1
5 7.05000E+02 9.28039E+02 5.00000E-01 5.00000E+00 6.47817E+02 47 39 1 1
5 6.97743E+02 9.30000E+02 5.00000E-01 5.00000E+00 1.82931E+03 47 38 1 1
5 6.90000E+02 9.37681E+02 5.00000E-01 5.00000E+00 5.81626E+03 46 38 1 1
5 6.76520E+02 9.45000E+02 5.00000E-01 5.00000E+00 1.35360E+04 46 37 1 1
5 6.75000E+02 9.46499E+02 5.00000E-01 5.00000E+00 1.49611E+04 45 37 1 1
5 6.60000E+02 9.56080E+02 5.00000E-01 5.00000E+00 2.98658E+04 44 37 1 1
5 6.52322E+02 9.60000E+02 5.00000E-01 5.00000E+00 3.82550E+04 44 36 1 1
5 6.48896E+02 9.62408E+02 5.00000E-01 5.00000E+00 -4.32000E+04 44 36 1 1
6 7.07550E+02 9.22500E+02 5.00000E-01 5.00000E+00 0.00000E+00 48 39 1 1
6 7.05000E+02 9.22488E+02 5.00000E-01 5.00000E+00 4.36799E+02 47 39 1 1
6 6.90000E+02 9.22373E+02 5.00000E-01 5.00000E+00 3.48150E+03 46 39 1 1
6 6.75000E+02 9.22111E+02 5.00000E-01 5.00000E+00 9.47070E+03 45 39 1 1
6 6.60000E+02 9.21694E+02 5.00000E-01 5.00000E+00 1.89021E+04 44 39 1 1
6 6.45000E+02 9.21125E+02 5.00000E-01 5.00000E+00 3.18813E+04 43 39 1 1
6 6.34394E+02 9.20649E+02 5.00000E-01 5.00000E+00 -4.32000E+04 43 39 1 1
7 7.08450E+02 9.19500E+02 5.00000E-01 5.00000E+00 0.00000E+00 48 39 1 1
60


7 7.05000E+02 9.16922E+02 5.00000E-01
7 6.98045E+02 9.15000E+02 5.00000E-01
7 6.90000E+02 9.06839E+02 5.00000E-01
7 6.77905E+02 9.00000E+02 5.00000E-01
7 6.75000E+02 8.97017E+02 5.00000E-01
7 6.60000E+02 8.86570E+02 5.00000E-01
7 6.57179E+02 8.85000E+02 5.00000E-01
7 6.50290E+02 8.79757E+02 5.00000E-01
8 7.11000E+02 9.17700E+02 5.00000E-01
8 7.10163E+02 9.15000E+02 5.00000E-01
8 7.07388E+02 9.00000E+02 5.00000E-01
8 7.05000E+02 8.88185E+02 5.00000E-01
8 7.03648E+02 8.85000E+02 5.00000E-01
8 6.99792E+02 8.70000E+02 5.00000E-01
8 6.96293E+02 8.55000E+02 5.00000E-01
8 6.94649E+02 8.46997E+02 5.00000E-01
9 7.14000E+02 9.17700E+02 5.00000E-01
9 7.14843E+02 9.15000E+02 5.00000E-01
9 7.17668E+02 9.00000E+02 5.00000E-01
9 7.20000E+02 8.88627E+02 5.00000E-01
9 7.21561E+02 8.85000E+02 5.00000E-01
9 7.25591E+02 8.70000E+02 5.00000E-01
9 7.29325E+02 8.55000E+02 5.00000E-01
9 7.31096E+02 8.47061E+02 5.00000E-01
10 7.16550E+02 9.19500E+02 5.00000E-01
10 7.20000E+02 9.16928E+02 5.00000E-01
10 7.26986E+02 9.15000E+02 5.00000E-01
10 7.35000E+02 9.06909E+02 5.00000E-01
10 7.47279E+02 9.00000E+02 5.00000E-01
10 7.50000E+02 8.97231E+02 5.00000E-01
10 7.65000E+02 8.86913E+02 5.00000E-01
10 7.68473E+02 8.85000E+02 5.00000E-01
10 7.75166E+02 8.79966E+02 5.00000E-01
1 7.90876E+02 9.20659E+02 5.00000E-01
1 7.95000E+02 9.20391E+02 5.00000E-01
1 8.10000E+02 9.19345E+02 5.00000E-01
1 8.22444E+02 9.18337E+02 5.00000E-01
2 7.76556E+02 9.62198E+02 5.00000E-01
2 7.80000E+02 9.64607E+02 5.00000E-01
2 7.95000E+02 9.72905E+02 5.00000E-01
2 7.99495E+02 9.75000E+02 5.00000E-01
2 8.03896E+02 9.77508E+02 5.00000E-01
3 7.31645E+02 9.96572E+02 5.00000E-01
3 7.34152E+02 1.00500E+03 5.00000E-01
3 7.35000E+02 1.00844E+03 5.00000E-01
3 7.38636E+02 1.02000E+03 5.00000E-01
3 7.40242E+02 1.02577E+03 5.00000E-01
4 6.94116E+02 9.96634E+02 5.00000E-01
4 6.91871E+02 1.00500E+03 5.00000E-01
4 6.90000E+02 1.01320E+03 5.00000E-01
5.00000E+00 6.47817E+02 47 39 1 1
5.00000E+00 1.77209E+03 47 40 1 1
5.00000E+00 5.91445E+03 46 40 1 1
5.00000E+00 1.27595E+04 46 41 1 1
5.00000E+00 1.54821E+04 45 41 1 1
5.00000E+00 3.03866E+04 44 41 1 1
5.00000E+00 3.33996E+04 44 42 1 1
5.00000E+00 -4.32000E+04 44 42 1 1
5.00000E+00 0.00000E+00 48 39 1 1
5.00000E+00 4.66969E+02 48 40 1 1
5.00000E+00 3.49459E+03 48 41 1 1
5.00000E+00 7.87556E+03 47 41 1 1
5.00000E+00 9.87552E+03 47 42 1 1
5.00000E+00 2.08047E+04 47 43 1 1
5.00000E+00 3.45905E+04 47 44 1 1
5.00000E+00 -4.32000E+04 47 44 1 1
5.00000E+00 0.00000E+00 48 39 1 1
5.00000E+00 4.66969E+02 48 40 1 1
5.00000E+00 3.49459E+03 48 41 1 1
5.00000E+00 7.67693E+03 49 41 1 1
5.00000E+00 9.94607E+03 49 42 1 1
5.00000E+00 2.08757E+04 49 43 1 1
5.00000E+00 3.46621E+04 49 44 1 1
5.00000E+00 -4.32000E+04 49 44 1 1
5.00000E+00 0.00000E+00 48 39 1 1
5.00000E+00 6.46628E+02 49 39 1 1
5.00000E+00 1.77510E+03 49 40 1 1
5.00000E+00 5.88153E+03 50 40 1 1
5.00000E+00 1.28047E+04 50 41 1 1
5.00000E+00 1.53323E+04 51 41 1 1
5.00000E+00 3.00986E+04 52 41 1 1
5.00000E+00 3.37820E+04 52 42 1 1
5.00000E+00 -4.32000E+04 52 42 1 1
5.00000E+00 4.32000E+04 53 39 1 2
5.00000E+00 4.79947E+04 54 39 1 2
5.00000E+00 6.75772E+04 55 39 1 2
5.00000E+00 -8.64000E+04 55 39 1 2
5.00000E+00 4.32000E+04 52 36 1 2
5.00000E+00 4.81274E+04 53 36 1 2
5.00000E+00 7.07609E+04 54 36 1 2
5.00000E+00 7.79660E+04 54 35 1 2
5.00000E+00 -8.64000E+04 54 35 1 2
5.00000E+00 4.32000E+04 49 34 1 2
5.00000E+00 5.36121E+04 49 33 1 2
5.00000E+00 5.81993E+04 50 33 1 2
5.00000E+00 7.64931E+04 50 32 1 2
5.00000E+00 -8.64000E+04 50 32 1 2
5.00000E+00 4.32000E+04 47 34 1 2
5.00000E+00 5.35405E+04 47 33 1 2
5.00000E+00 6.47613E+04 46 33 1 2
61


4 6.88020E+02 1.02000E+03 5.00000E-01
4 6.86533E+02 1.02618E+03 5.00000E-01
5 6.48896E+02 9.62408E+02 5.00000E-01
5 6.45000E+02 9.65191E+02 5.00000E-01
5 6.30000E+02 9.73726E+02 5.00000E-01
5 6.27325E+02 9.75000E+02 5.00000E-01
5 6.22199E+02 9.77985E+02 5.00000E-01
6 6.34394E+02 9.20649E+02 5.00000E-01
6 6.30000E+02 9.20356E+02 5.00000E-01
6 6.15000E+02 9.19275E+02 5.00000E-01
6 6.03261E+02 9.18293E+02 5.00000E-01
7 6.50290E+02 8.79757E+02 5.00000E-01
7 6.45000E+02 8.75425E+02 5.00000E-01
7 6.36878E+02 8.70000E+02 5.00000E-01
7 6.30000E+02 8.64041E+02 5.00000E-01
7 6.24714E+02 8.60222E+02 5.00000E-01
8 6.94649E+02 8.46997E+02 5.00000E-01
8 6.92961E+02 8.40000E+02 5.00000E-01
8 6.90000E+02 8.25979E+02 5.00000E-01
8 6.89742E+02 8.25000E+02 5.00000E-01
8 6.87689E+02 8.15199E+02 5.00000E-01
9 7.31096E+02 8.47061E+02 5.00000E-01
9 7.32984E+02 8.40000E+02 5.00000E-01
9 7.35000E+02 8.31132E+02 5.00000E-01
9 7.36743E+02 8.25000E+02 5.00000E-01
9 7.39022E+02 8.15586E+02 5.00000E-01
10 7.75166E+02 8.79966E+02 5.00000E-01
10 7.80000E+02 8.76091E+02 5.00000E-01
10 7.89308E+02 8.70000E+02 5.00000E-01
10 7.95000E+02 8.65196E+02 5.00000E-01
10 8.01332E+02 8.60755E+02 5.00000E-01
1 8.22444E+02 9.18337E+02 5.00000E-01
1 8.21621E+02 9.15000E+02 5.00000E-01
1 8.20434E+02 9.10564E+02 5.00000E-01
2 8.03896E+02 9.77508E+02 5.00000E-01
2 8.03455E+02 9.75000E+02 5.00000E-01
2 8.02702E+02 9.71021E+02 5.00000E-01
3 7.40242E+02 1.02577E+03 5.00000E-01
3 7.39874E+02 1.02008E+03 5.00000E-01
4 6.86533E+02 1.02618E+03 5.00000E-01
4 6.86615E+02 1.02049E+03 5.00000E-01
5 6.22199E+02 9.77985E+02 5.00000E-01
5 6.22583E+02 9.75000E+02 5.00000E-01
5 6.23082E+02 9.71484E+02 5.00000E-01
6 6.03261E+02 9.18293E+02 5.00000E-01
6 6.03937E+02 9.15000E+02 5.00000E-01
6 6.04956E+02 9.10489E+02 5.00000E-01
7 6.24714E+02 8.60222E+02 5.00000E-01
7 6.25861E+02 8.55000E+02 5.00000E-01
7 6.26974E+02 8.50432E+02 5.00000E-01
5.00000E+00 7.57694E+04 46 32 1 2
5.00000E+00 -8.64000E+04 46 32 1 2
5.00000E+00 4.32000E+04 44 36 1 2
5.00000E+00 4.88819E+04 43 36 1 2
5.00000E+00 7.20057E+04 42 36 1 2
5.00000E+00 7.63670E+04 42 35 1 2
5.00000E+00 -8.64000E+04 42 35 1 2
5.00000E+00 4.32000E+04 43 39 1 2
5.00000E+00 4.83827E+04 42 39 1 2
5.00000E+00 6.83283E+04 41 39 1 2
5.00000E+00 -8.64000E+04 41 39 1 2
5.00000E+00 4.32000E+04 44 42 1 2
5.00000E+00 5.08908E+04 43 42 1 2
5.00000E+00 6.31433E+04 43 43 1 2
5.00000E+00 7.61678E+04 42 43 1 2
5.00000E+00 -8.64000E+04 42 43 1 2
5.00000E+00 4.32000E+04 47 44 1 2
5.00000E+00 5.12918E+04 47 45 1 2
5.00000E+00 6.95080E+04 46 45 1 2
5.00000E+00 7.09841E+04 46 46 1 2
5.00000E+00 -8.64000E+04 46 46 1 2
5.00000E+00 4.32000E+04 49 44 1 2
5.00000E+00 5.13633E+04 49 45 1 2
5.00000E+00 6.25743E+04 50 45 1 2
5.00000E+00 7.16114E+04 50 46 1 2
5.00000E+00 -8.64000E+04 50 46 1 2
5.00000E+00 4.32000E+04 52 42 1 2
5.00000E+00 5.00981E+04 53 42 1 2
5.00000E+00 6.39058E+04 53 43 1 2
5.00000E+00 7.44309E+04 54 43 1 2
5.00000E+00 -8.64000E+04 54 43 1 2
5.00000E+00 8.64000E+04 55 39 1 3
5.00000E+00 1.05081E+05 55 40 1 3
5.00000E+00 -1.29600E+05 55 40 1 3
5.00000E+00 8.64000E+04 54 35 1 3
5.00000E+00 1.03215E+05 54 36 1 3
5.00000E+00 -1.29600E+05 54 36 1 3
5.00000E+00 8.64000E+04 50 32 1 3
5.00000E+00 -1.29600E+05 50 32 1 3
5.00000E+00 8.64000E+04 46 32 1 3
5.00000E+00 -1.29600E+05 46 32 1 3
5.00000E+00 8.64000E+04 42 35 1 3
5.00000E+00 1.06354E+05 42 36 1 3
5.00000E+00 -1.29600E+05 42 36 1 3
5.00000E+00 8.64000E+04 41 39 1 3
5.00000E+00 1.04767E+05 41 40 1 3
5.00000E+00 -1.29600E+05 41 40 1 3
5.00000E+00 8.64000E+04 42 43 1 3
5.00000E+00 1.09625E+05 42 44 1 3
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62


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5.00000E+00 -3.88800E+05 50 54 1 6
5.00000E+00 3.45600E+05 55 48 1 6
5.00000E+00 3.63251E+05 55 49 1 6
5.00000E+00 -3.88800E+05 55 49 1 6
5.00000E+00 3.88800E+05 59 43 1 6
5.00000E+00 4.25897E+05 60 43 1 6
5.00000E+00 -4.32000E+05 60 43 1 6
66


2 8.60009E+02 9.72898E+02 5.00000E-01
2 8.68879E+02 9.75000E+02 5.00000E-01
2 8.70000E+02 9.75299E+02 5.00000E-01
2 8.76324E+02 9.76646E+02 5.00000E-01
3 7.59798E+02 1.06416E+03 5.00000E-01
3 7.60146E+02 1.06500E+03 5.00000E-01
3 7.65000E+02 1.07787E+03 5.00000E-01
3 7.65742E+02 1.07954E+03 5.00000E-01
4 6.68238E+02 1.06489E+03 5.00000E-01
4 6.68195E+02 1.06500E+03 5.00000E-01
4 6.63231E+02 1.08000E+03 5.00000E-01
4 6.63138E+02 1.08031E+03 5.00000E-01
5 5.65998E+02 9.73803E+02 5.00000E-01
5 5.61011E+02 9.75000E+02 5.00000E-01
5 5.55000E+02 9.76638E+02 5.00000E-01
5 5.50243E+02 9.77695E+02 5.00000E-01
6 5.53334E+02 8.66940E+02 5.00000E-01
6 5.40000E+02 8.60431E+02 5.00000E-01
6 5.38918E+02 8.59929E+02 5.00000E-01
7 6.01396E+02 7.70665E+02 5.00000E-01
7 6.00000E+02 7.68365E+02 5.00000E-01
7 5.97753E+02 7.65000E+02 5.00000E-01
7 5.93502E+02 7.57808E+02 5.00000E-01
8 6.88792E+02 6.96747E+02 5.00000E-01
8 6.88262E+02 6.90000E+02 5.00000E-01
8 6.87830E+02 6.83773E+02 5.00000E-01
9 7.37637E+02 6.97214E+02 5.00000E-01
9 7.38447E+02 6.90000E+02 5.00000E-01
9 7.39046E+02 6.84222E+02 5.00000E-01
10 8.24851E+02 7.71631E+02 5.00000E-01
10 8.25000E+02 7.71396E+02 5.00000E-01
10 8.29474E+02 7.65000E+02 5.00000E-01
10 8.33259E+02 7.58949E+02 5.00000E-01
1 8.87020E+02 8.60535E+02 5.00000E-01
1 8.85000E+02 8.56400E+02 5.00000E-01
1 8.84353E+02 8.55000E+02 5.00000E-01
1 8.83204E+02 8.52725E+02 5.00000E-01
2 8.76324E+02 9.76646E+02 5.00000E-01
2 8.75825E+02 9.75000E+02 5.00000E-01
2 8.74452E+02 9.70792E+02 5.00000E-01
3 7.65742E+02 1.07954E+03 5.00000E-01
3 7.65252E+02 1.07485E+03 5.00000E-01
4 6.63138E+02 1.08031E+03 5.00000E-01
4 6.63148E+02 1.08000E+03 5.00000E-01
4 6.63311E+02 1.07558E+03 5.00000E-01
5 5.50243E+02 9.77695E+02 5.00000E-01
5 5.50900E+02 9.75000E+02 5.00000E-01
5 5.51751E+02 9.71808E+02 5.00000E-01
6 5.38918E+02 8.59929E+02 5.00000E-01
6 5.40000E+02 8.57457E+02 5.00000E-01
5.00000E+00 3.88800E+05 58 36 1 6
5.00000E+00 4.11136E+05 58 35 1 6
5.00000E+00 4.14227E+05 59 35 1 6
5.00000E+00 -4.32000E+05 59 35 1 6
5.00000E+00 3.88800E+05 51 30 1 6
5.00000E+00 3.91015E+05 51 29 1 6
5.00000E+00 4.26768E+05 52 29 1 6
5.00000E+00 -4.32000E+05 52 29 1 6
5.00000E+00 3.88800E+05 45 30 1 6
5.00000E+00 3.89104E+05 45 29 1 6
5.00000E+00 4.31097E+05 45 28 1 6
5.00000E+00 -4.32000E+05 45 28 1 6
5.00000E+00 3.88800E+05 38 36 1 6
5.00000E+00 4.01455E+05 38 35 1 6
5.00000E+00 4.18285E+05 37 35 1 6
5.00000E+00 -4.32000E+05 37 35 1 6
5.00000E+00 3.88800E+05 37 43 1 6
5.00000E+00 4.28640E+05 36 43 1 6
5.00000E+00 -4.32000E+05 36 43 1 6
5.00000E+00 3.88800E+05 41 49 1 6
5.00000E+00 3.95917E+05 40 49 1 6
5.00000E+00 4.07336E+05 40 50 1 6
5.00000E+00 -4.32000E+05 40 50 1 6
5.00000E+00 3.88800E+05 46 54 1 6
5.00000E+00 4.10954E+05 46 55 1 6
5.00000E+00 -4.32000E+05 46 55 1 6
5.00000E+00 3.88800E+05 50 54 1 6
5.00000E+00 4.12478E+05 50 55 1 6
5.00000E+00 -4.32000E+05 50 55 1 6
5.00000E+00 3.88800E+05 55 49 1 6
5.00000E+00 3.89525E+05 56 49 1 6
5.00000E+00 4.11224E+05 56 50 1 6
5.00000E+00 -4.32000E+05 56 50 1 6
5.00000E+00 4.32000E+05 60 43 1 7
5.00000E+00 4.55469E+05 59 43 1 7
5.00000E+00 4.63005E+05 59 44 1 7
5.00000E+00 -4.75200E+05 59 44 1 7
5.00000E+00 4.32000E+05 59 35 1 7
5.00000E+00 4.44220E+05 59 36 1 7
5.00000E+00 -4.75200E+05 59 36 1 7
5.00000E+00 4.32000E+05 52 29 1 7
5.00000E+00 -4.75200E+05 52 29 1 7
5.00000E+00 4.32000E+05 45 28 1 7
5.00000E+00 4.34820E+05 45 29 1 7
5.00000E+00 -4.75200E+05 45 29 1 7
5.00000E+00 4.32000E+05 37 35 1 7
5.00000E+00 4.51866E+05 37 36 1 7
5.00000E+00 -4.75200E+05 37 36 1 7
5.00000E+00 4.32000E+05 36 43 1 7
5.00000E+00 4.4593 8E+05 37 43 1 7
67


6 5.41019E+02 8.55000E+02 5.00000E-01 5.00000E+00 4.59101E+05 37 44 1
6 5.42398E+02 8.51975E+02 5.00000E-01 5.00000E+00 -4.75200E+05 37 44 1
7 5.93502E+02 7.57808E+02 5.00000E-01 5.00000E+00 4.32000E+05 40 50 1
7 5.97676E+02 7.50000E+02 5.00000E-01 5.00000E+00 4.59698E+05 40 51 1
7 6.00000E+02 7.46121E+02 5.00000E-01 5.00000E+00 4.73273E+05 41 51 1
7 6.00329E+02 7.45523E+02 5.00000E-01 5.00000E+00 -4.75200E+05 41 51 1
8 6.87830E+02 6.83773E+02 5.00000E-01 5.00000E+00 4.32000E+05 46 55 1
8 6.89648E+02 6.75000E+02 5.00000E-01 5.00000E+00 4.45619E+05 46 56 1
8 6.90000E+02 6.73659E+02 5.00000E-01 5.00000E+00 4.47621E+05 47 56 1
8 6.92873E+02 6.60000E+02 5.00000E-01 5.00000E+00 4.65196E+05 47 57 1
8 6.94954E+02 6.51191E+02 5.00000E-01 5.00000E+00 -4.75200E+05 47 57 1
9 7.39046E+02 6.84222E+02 5.00000E-01 5.00000E+00 4.32000E+05 50 55 1
9 7.36885E+02 6.75000E+02 5.00000E-01 5.00000E+00 4.46345E+05 50 56 1
9 7.35000E+02 6.68171E+02 5.00000E-01 5.00000E+00 4.56292E+05 49 56 1
9 7.33192E+02 6.60000E+02 5.00000E-01 5.00000E+00 4.66507E+05 49 57 1
9 7.31198E+02 6.52402E+02 5.00000E-01 5.00000E+00 -4.75200E+05 49 57 1
10 8.33259E+02 7.58949E+02 5.00000E-01 5.00000E+00 4.32000E+05 56 50 1
10 8.28153E+02 7.50000E+02 5.00000E-01 5.00000E+00 4.63874E+05 56 51 1
10 8.26107E+02 7.46774E+02 5.00000E-01 5.00000E+00 -4.75200E+05 56 51 1
1 8.83204E+02 8.52725E+02 5.00000E-01 5.00000E+00 4.75200E+05 59 44 1
1 8.79155E+02 8.44567E+02 5.00000E-01 5.00000E+00 -5.18400E+05 59 44 1
2 8.74452E+02 9.70792E+02 5.00000E-01 5.00000E+00 4.75200E+05 59 36 1
2 8.72550E+02 9.64837E+02 5.00000E-01 5.00000E+00 -5.18400E+05 59 36 1
3 7.65252E+02 1.07485E+03 5.00000E-01 5.00000E+00 4.75200E+05 52 29 1
3 7.65000E+02 1.07239E+03 5.00000E-01 5.00000E+00 4.97559E+05 51 29 1
3 7.64766E+02 1.07006E+03 5.00000E-01 5.00000E+00 -5.18400E+05 51 29 1
4 6.63311E+02 1.07558E+03 5.00000E-01 5.00000E+00 4.75200E+05 45 29 1
4 6.63483E+02 1.07078E+03 5.00000E-01 5.00000E+00 -5.18400E+05 45 29 1
5 5.51751E+02 9.71808E+02 5.00000E-01 5.00000E+00 4.75200E+05 37 36 1
5 5.53318E+02 9.65820E+02 5.00000E-01 5.00000E+00 -5.18400E+05 37 36 1
6 5.42398E+02 8.51975E+02 5.00000E-01 5.00000E+00 4.75200E+05 37 44 1
6 5.46075E+02 8.43754E+02 5.00000E-01 5.00000E+00 -5.18400E+05 37 44 1
7 6.00329E+02 7.45523E+02 5.00000E-01 5.00000E+00 4.75200E+05 41 51 1
7 6.05973E+02 7.35000E+02 5.00000E-01 5.00000E+00 5.08617E+05 41 52 1
7 6.07858E+02 7.31862E+02 5.00000E-01 5.00000E+00 -5.18400E+05 41 52 1
8 6.94954E+02 6.51191E+02 5.00000E-01 5.00000E+00 4.75200E+05 47 57 1
8 6.96179E+02 6.45000E+02 5.00000E-01 5.00000E+00 4.81626E+05 47 58 1
8 6.99640E+02 6.30000E+02 5.00000E-01 5.00000E+00 4.95123E+05 47 59 1
8 7.03477E+02 6.15000E+02 5.00000E-01 5.00000E+00 5.05875E+05 47 60 1
8 7.05000E+02 6.11363E+02 5.00000E-01 5.00000E+00 5.08119E+05 48 60 1
8 7.07283E+02 6.00000E+02 5.00000E-01 5.00000E+00 5.12264E+05 48 61 1
8 7.10107E+02 5.85000E+02 5.00000E-01 5.00000E+00 5.15278E+05 48 62 1
9 7.31198E+02 6.52402E+02 5.00000E-01 5.00000E+00 4.75200E+05 49 57 1
9 7.29573E+02 6.45000E+02 5.00000E-01 5.00000E+00 4.82939E+05 49 58 1
9 7.25856E+02 6.30000E+02 5.00000E-01 5.00000E+00 4.96436E+05 49 59 1
9 7.21822E+02 6.15000E+02 5.00000E-01 5.00000E+00 5.07189E+05 49 60 1
9 7.20000E+02 6.10709E+02 5.00000E-01 5.00000E+00 5.09822E+05 48 60 1
9 7.17817E+02 6.00000E+02 5.00000E-01 5.00000E+00 5.13682E+05 48 61 1
9 7.14918E+02 5.85000E+02 5.00000E-01 5.00000E+00 5.16696E+05 48 62 1
10 8.26107E+02 7.46774E+02 5.00000E-01 5.00000E+00 4.75200E+05 56 51 1
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
68


10 8.25000E+02 7.45015E+02 5.00000E-01 5.00000E+00 4.81345E+05 55 51 1 7
10 8.19327E+02 7.35000E+02 5.00000E-01 5.00000E+00 5.13188E+05 55 52 1 7
10 8.18273E+02 7.33334E+02 5.00000E-01 5.00000E+00 -5.18400E+05 55 52 1 7
69


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