EPA/600/A-96/022
AIR SPARGING EXPERIMENTS ON A TWO DIMENSIONAL SAND BOX WITH
DNAPLS: MULTIPHASE INVESTIGATION WITH ELECTRICAL IMPEDANCE
TOMOGRAPHY
Jong Soo Cho
US Environmental Protection Agency
National Risk Management Research Laboratory
Subsurface Processes and Remediation Division, Ada, Oklahoma
ABSTRACT
Electrical impedance tomography (EIT) applications in detection of organic chemical
sources and monitoring subsurface environments during air-sparging were studied. The
development of an inverse solution program and experimental tests in the laboratory were
included in this study. The inverse solution model used the Newton-Raphson method with the
Marquadt regularization technique. A multiphase flow and transport model was utilized to test
the EIT inverse modeling. Tetrachloroethylene (PCE) infiltration was simulated with a
multiphase flow model and the ability of EIT to trace the PCE distribution was tested.
Computational progress of the inverse solution was presented with a graphical display of
electrical conductivity distributions. The inverse program for EIT was used to obtain the
electrical conductivity distribution in a 2-D sand box. The experiments included a spillage of
dense non-aqueous phase liquid (DNAPL) dyed with a hydrophobic dye at the top of the sand
box filled with water and air sparging from the bottom. Electrical conductivity changed in the
soil as water was replaced water with DNAPL or air. This made the tomographic pictures of
electrical conductivity. The vapor concentration of DNAPL in the extracted air was measured
1
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with a GC to estimate the removal rate during air sparging. The tomographic images from the
EIT were compared with photographic images of dyed PCE in the water filled space.
INTRODUCTION
The Electrical Impedance Tomography has been used widely by geophysicists (Tripp et
al, 1984) to detect geological anomalies in the subsurface and by mining engineers (Shima,
1992) to locate mineral cores. Recently, biomedical engineers (Yorkey et al, 1985) started the
application of this technique to monitor their patients. The major advantage of EIT in medical
application is that it is much less harmful than X-ray or any isotope intake methods. In
environmental areas, this technique has been applied to locate the leakage from lined wastewater
treatment ponds (Van et al, 1991), to monitor the infiltration of water through subsurface (Daily
et al, 1992), and to trace the steam propagation during remediation with steam injection
(Ramirez et al, 1993). Due to electrical impedance differences of various phases of fluids in the
subsurface, i.e. air, water, and NAPLs, it was possible to monitor the movement of the separate
phases of fluid in the subsurface.
The basic principle of the EIT is that the electrical current passes through the less
resistive section bypassing the more resistive locations. By measuring the potential/current
distribution in space, differences in the conductivity distribution can be detected by inverting the
measured potential/current distribution with the computer programs. The electrical conductivity
of pure water is 4.2x10'2 Scm"1 at 25 °C and commonly available distilled water has electrical
conductivities in the range of 0.5 to 5 Scm'. The electrical conductivity of fresh ground water is
in the range of 30 to 2000 Scm"1; for PCE, a nonelectrolytic organic solvent, it is lxl 0'9 Scm"1.
Air is a very good insulator. The relationship between the resistivity and soil moisture content
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can be expressed with Archies' law (Archies, 1942):
p = apw4>M
(i)
where p is the bulk resistivity, pw is the resistivity of the pore water, $ is the volume fraction
porosity, and a and m are fitting parameters (a=l, m = 1.3 -1.5 for unconsolidated sand, Barber
et al. 1991). The following modification can be applied to the partially saturated media:
where S is the fraction water saturation and n is empirically determined but is usually 2 ± 0.5
(Hearst and Nelson, 1985). The electrical resistivity of a sandy aquifer material partially filled
with DNAPL was reported by Annan et al. (1991) and Schneider and Greenhouse (1994).
The estimated electrical resistivity in the sand partially filled with PCE and water is listed in
table 1. The parameters used for the estimation were: soil porosity, 0.4; electrical resistivity of
PCE, «>; water resistivity, 20 Dm; constants in the Archies' law equation, a=l .0, n=2.0, and
P = S"(apw"')
(2)
INVERSE MODEL FOR EIT
The electrical field in conductive media can be described by a Poisson's equation
V-kVV = -/
(3)
with boundary conditions
V =V.
on dA
(4)
O
3
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on BA
(5)
where k, V,, and /are the conductivity, voltage, and impressed current source distribution, and V
is the Laplacian operator, and A is the boundary. The forward solution of the above equation is to
find the internal voltages and current densities with known conductivity distribution and
boundary conditions. The inverse solution is to find the conductivity distribution which can
produce measured voltage and current density distribution on the boundaries and internal space.
The inverse solution is actually an iteration of forward solutions with assumed conductivity
distributions. The forward solution is repeated until the objective function, usually the
summation of squared errors, meets the criteria. At each iteration, the parameters, here the
conductivity distribution, are adjusted in the direction of reducing errors. The direction of the
parameter adjustment is searched by the non-linear parameter optimization method. In this
effort, the Newton-Raphson method (Hua and Woo, 1990) is used (Figure 1).
Newton-Raphson Method
The objective function is defined as
where V0 is the measured voltage, V(k) the computed voltage for a conductivity distribution k. To
find the k which minimizes the objective function, its derivative is expressed as
*(*) = \/2{V{k) - Vf(V{k) - Vo)
(6)
•'(*) = [kW(*t*) - ya) = o
(7)
Taylor series expansion yields
4
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fc'CJfc**1) = + d>"{kk)Lkk (8)
where &*+/ = k* +Akk. The term " is called the Hessian matrix,
" = (VfV' + (V'Y [I <8> (V - v0)] (9)
Truncating the second derivative term, it becomes
= (vfv' (10)
Substitution of equations yields,
[(VyV>]Akk = -(Vfl V - VJ (11)
Regularization
Due to the ill-posed condition on the Hessian matrix, the Marquadt method (Marquadt,
1963) was adopted. The equation (11) is written in a matrix/vector form as
[tf][A*]=fe] (12)
where [g] represents the right hand side of the equation (11). By adding a stabilization term
after scaling the matrix and vectors, it becomes
[ff' +kl][ A**] = [g>] (13)
where X is an arbitrary positive constant, /, the identity matrix. Hessian matrix and vectors are
scaled as:
5
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H..
"V M
b'] = [-5=]
Vs.
(14)
(15)
and
k'
[At) = [-J-] (16)
Finite Difference Formulation
A five-point finite difference approximation of the Poisson's equation in the 2D
rectangular space is
1 k +k V -V k +k V -V
I rx*lj, rx? _ Kxj>Kx-lj> Vxy +
A* 2 Ax 2 Ax
l k +k V -V k +k V -V ('')
1 xy rxp> _ Kxq> *xy 1 ¥xy rxj>-K = r
A/ 2 Ay 2 Ay ~J*>
which is in a matrix format
iAw\ = m (is)
where [A] is the coefficient matrix, and [ V] and [5] are the vectors of potentials and impressed
currents.
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Sensitivity Matrix
The relationship between changes in model parameters and results of the model
(MeGillivray and Oldenburg, 1990) is expressed by
/
y, - (i9)
Differentiation of the difference equation on both sides with Aj yields
I A ]' [V} + [ A ][Ff = 0 (20)
which becomes
I A m' = - [ A ]'[F] (21)
The equation (21) has the identical coefficient matrix [ A ] with the matrix difference equation
(18). Once the coefficient matrix [ A ] is obtained, then the same solution process can be
repeated to obtain the [F]'. For the five- point difference formulation, only thirteen elements in
[ A ]' have non-zero values for differentiation with kr
NUMERICAL TESTING
An aquifer highly contaminated by nonaqueous phase liquid has four primary phases: a
stationary phase composed primarily of mineral soil and organic matter, an aqueous phase
consisting of water and dissolved ions, a vapor phase consisting primarily of air, and a non-
aqueous phase normally consisting of organic liquids. It is assumed that the electrical properties
of the aqueous phase are not significantly changed as the organic components of limited
7
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solubilities are dissolved. The observed change is assumed to be a result of the volume fraction
occupied by each phase. Tetrachloroethylene (PCE) has been used as a solvent in machine shops
and dry cleaning facilities. Since PCE is a chlorinated hydrocarbon which is heavier and less
viscose than water with a specific gravity, 1.63 and relative viscosity, 0.9, it can infiltrate below
the water table and serve as a long-term source for ground-water contamination. From the
bottom of the aquifer, detection and removal of PCE become very difficult.
A simulation of PCE infiltration in a 2D sand box was conducted with a multiphase fluid
flow model (MOFAT, 1991) and detection of electrical conductivity change using the EIT
inverse was examined. The parameters used in the simulation are in Table 2. The initial water
and electrical conductivity distribution are seen in Figure 2. These were used as the baseline
information. The water table located at 15 cm below the surface. The electrical conductivity
shows a very similar pattern. Water saturation at 0.4 hr after a PCE spill at the top of the sand
box shows tremendous changes due to PCE infiltration (Figure 3). PCE started to touch the
bottom of the sand box and both side walls at this moment. Electrical conductivity distribution
followed very closely the pattern of water saturation. The EIT inverse model was tested to see
whether it could trace the conductivity pattern. Five electrical nodes were located on both sides
of the sand box at a depth of 5,10,15,20, and 25 cm. The total number of voltage measurement
at the electrodes was three hundred fifteen with 169 unknown values of conductivities. Uniform
distribution of conductivity was used as the initial guess in the inverse model. After 10
iterations, the sum of squared errors reduced from 1.16 to 8.73x10"3 and became 3.9x10"5 after
the 27th iteration (Figure 4). Most of the computation time was spent on sensitivity matrix
calculations at each iteration.
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SAND BOX EXPERIMENTS
A 2D sand box was built of Teflon® square bars, glass, and plexiglass plates (Figure 5).
The size of the sand box was 70 cm x 50 cm with 2.5 cm thickness. It was mounted on wooden
brackets inside a ventilation hood in the laboratory. To make tight seals between glass plates
and frame bars, Teflon® joint sealant and vise grips were used. Seven !4 inch holes were drilled
and threaded to install the Teflon® compression fittings on both side frames. One hole was
drilled at the bottom bar for the air-sparging tubing and the Teflon® compression fittings were
installed. Five electrodes made of 1/4 inch copper coated carbon rods were inserted through the
fittings. One hole on each side was used as the water intake and outlet port. The sand box was
initially filled with sand and tap water. Later the spill of PCE from the top and the air-sparging
from the bottom were initiated.
Experimental data were obtained using electrodes and the multimeter connected through
rotary switches. The four-electrode method was used to eliminate the electrical noise caused by
the electrochemical reaction around the current electrodes. A constant current (0.33 mA) was
passed through two electrodes. The third electrode was used as the reference electrode for the
potential measurement. This setting yields n(n-l)/2 independent voltage measurements sets
with n electrodes. All of the measurements were done with a multimeter and manual rotary
switches. Three hundred fifteen voltage measurements for an individual cycle were expected.
The electrical parts used in the experiment were as follows: ten carbon electrodes, five on
the each side of the sandbox; a 15 V power supply; a low distortion oscillator; a constant current
circuit board to supply 0.33 mA current; a switch board connected to the power supply,
oscillator, circuit and electrodes, complete with four different adjustments (injection node,
9
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reference node, extraction node, and voltage node); and a multimeter. The physical
measurement components were a rotameter and a pressure gauge for air flow.
Data are being collected at the present time under various sand box conditions with PCE
and air. They will be used as the input data files for the inverse model. Output generated from
the inverse model will be sent to a visualization software (Geomview, 1993) to produce
graphical outputs.
RESULTS AND DISCUSSION
From the comparison of conductivity distribution before and after the PCE spill, very
distinctive differences could be found. This difference allowed EIT to trace the separate phase
liquid movement. Testing of the EIT inverse model showed that the model could minimize the
object function by several orders of magnitude, but the model still needs further tuning for
accurate tracing and reduction of noise expected during the potential measurement. Next step is
the actual application of the EIT in the laboratory experiment with a sand box. Measurement
noises in the experiments are expected and the robustness of the EIT inverse model should be
tested against them. The images of the electrical conductivity distribution generated from the
EIT inverse mode will be compared with the photographic images from dyed chemical
distribution inside the sand box.
CONCLUSIONS
1. Change of electrical resistivity could be found during the PCE infiltration in the simulation
with a multiphase flow model,
2. The EIT tests with the simulation results showed its ability to detect the anomalies of
electrical conductivities. The developed program showed its ability to locate the anomalies even
10
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though the absolute values of conductivity estimated showed marginal errors, especially at the
boundaries. The inverse model still needs further adjustments.
3. The most computation time in the inverse modeling was spent in the calculation of sensitivity
matrices. Other methods such as the compensation theory method will significantly reduce the
computational time.
3. The Newton-Raphson method with the Marquadt regularization showed a good computational
efficiency and stability. With significant measurement noise, the regularization method will
help to reduce the instability problems.
4. The 2-D EIT inverse model will be used to investigate the DNAPL and air movement in the
laboratory experiments.
DISCLAIMER
Although the research reported in this paper has been funded wholly or in part by the
United States Environmental Protection Agency, it has not been subjected to the agency peer-
review and therefore does not necessarily reflect the view of the agency. No official
endorsement of the system design or trade names should be inferred.
REFERENCES
Annan, A. P., P. Bauman, J.P. Greenhouse, and J.D. Redman, 1991, Geophysics and DNAPLS:
Groundwater Management #5, in Proc. of the Fifth Annual Outdoor Action Conference on
Aquifer Restoration, Groundwater Monitoring, and Geophysical Methods, Las Vegas, Nevada.
Archies, G.E., 1942, The Electrical Resistivity Log as an Aid in Determining Some Reservoir
Characteristics, Trans. Am. Inst. Min. Metall. Pet. Eng., 146, 54.
Barber, C., G.B. Davis. G. Buselli, and M. Height, 1991, Remote Monitoring of Groundwater
Pollution Using Geoelectric Techniques in Undulating Sandy Terrain, Western Australia,
International Journal of Environment and Pollution, IO/2), 97-112.
Daily, W., A.Ramirez, D.Labreque, and J.Nitao, 1992, Electrical Resistivity Tomography of
11
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Vadose Water Movement, Water Resources Research, 28(5), 1429-1442.
Geomview®, 1993, Geomview Manual, The Geometry Center, University of Minnesota,
Minneapolis, MN,
Hearst, J.R. and P.H. Nelson, 1985, Well Logging for Geophysical Properties, MacGraw-Hill,
New York, NY.
Hua, P. and E.J, Woo, 1990, Chapter 10, Reconstruction Algorithms, Electrical Impedance
Tomography, edited by J.G.Webster, Adam Hilger, Bristol and New York.
Marquadt, D.W., 1963, An Algorithm for Least-Squares Estimation of Nonlinear Parameters, J.
Soc. Indust. Appl. Math., 11(2), 431-441.
McGillivray, P.R. and D.W.Oldenburg, 1990, Methods for Calculating Frechet Derivatives and
Sensitivities for the Non-Linear Inverse Problem: A Comparative Study, Geophysical
Prospecting, 38,499-524.
MOFAT, A Two-Dimensional Finite Element Program for Multiphase Flow and
Multicomponent Transport, Program Documentation and User's Guide, EPA/600/2-91/020, US
EPA, RSKERL, Ada, OK, 1991.
Ramirez, A., W. Daily, D.Labreque, E.Owen, and D.Chesnut, 1993, Monitoring an Underground
Steam Injection Process Using Electrical Resistance Tomography, Water Resources Research,
29(1), 73-87.
Schneider, G.W. and J.P. Greenhouse, 1994, Geophysical Detection of Perchloroethylene in a
Sandy Aquifer Using Resistivity and Nuclear Logging Techniques, in Proc. of Symposium on
the Application of Geophysics to Engineering & Environmental Problems, Atlanta, GA.
Shima, H., 1992,2-D and 3-D Resistivity Image Reconstruction Using Crosshole Data,
Geophysics, 57(10), 1270-1281.
Tripp, A.C., G.W. Hohman, and C.M. Swift,Jr., 1984, Two Dimensional Resistivity Inversion,
Geophysics, 49(10), 1708-1717.
Van, G.P., S.K. Park, and P. Hamilton, 1991, Monitoring Leaks from Storage Ponds Using
Resistivity Methods, Geophysics, 56(8), 1267-1270.
Yorkey, T.J., J.G. Webster, and W.J. Tompkins, 1987, Comparing Reconstruction Algorithms
for Electrical Impedance Tomography, IEEE Transactions on Biomedical Engineering, BME-
34(11), 843-852.
12
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Table 1. Electrical Resistivity in the Sand Partially Filled with PCE and Water
Saturation of PCE (%)
Resistivity (Qm)
0.0
72
10
89
20
113
50
289
75
1154
90
7200
100
CO
13
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Table 2. Parameters Used in the Multiphase Model Simulation and Inverse Model
PCE Properties
Density
1.63 g/cm3
Viscosity
0.9 cp
Soil Properties
Porosity
0.4
Hydraulic Conductivity
40 cm/hr
Van Genuchten Parameters
a
0.145 cm"1
n
2.8
0.1
**FOW
0.2
Sand Box Dimension
Size
30 x 30 x 1 cm
Initial Water Table
15 cm
Initial Water Volume
301 cm3
PCE Infiltration
Infiltration Mode
Constant Head
Infiltration Period
0.28 hr (17 min)
Total Volume
36 cm3
EIT Inverse Model
Nodes (Unknown Conductivities)
13 x 13(169)
Electric Nodes
10
Time of Measurement
0.4 hr (24 min)
14
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Guess initial
distribution k
i^VH
Solve forward
model
i
| Calculate error) Update k
No
"'error small?*
%
Yes
*a®>
Figure 1. Flow Chart of Inverse Solution algorithm for Electrical
Impedance Tomography
-------
(a) Initio) Woler Sofurolion (b) Boseline Conductivity (s/cm)
10 -
Figure 2. Initial Water Saturation and Electrical Conductivity Distribution in 2D
Sandbox From Multiphase Model Simulation
-------
Woter Soturotion ot t « 0.4 hr
(b) PCE Soturotion After Spill, t ¦ 0.4 hr
(c) Conductivity After PCE Sp;U ($/cm). t « 0.4 hr
Figure 3. (a) Water Saturation, (b) PCE Saturation, (c) Electrical
Conductivity Distribution at 0.4 hr After PCE Spill Started
-------
Figure 4. Progress ofEIT Inversion, (a) Original, (b) Initial
Guess, (c) After 10th Iteration, (d) After 27th Iteration
-------
water table
adjustment*^
1
7
sand -
and
, water
k •
*
* •*
>
sandbox
^electrodes
y
multimeter
oscillator
power
o o o o
switcvi board
air
supply
pressure
gauge
flow
meter
Figure 5. Schematic Diagram of 2D Sandbox Experimental System
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1!
HI || Hill 1 HI||HI HI II TECHNICAL REPORT DATA
PR9fi- 17 04 51
i. REPORT£j9A/600/A_96/022
2 .
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
AIR SPARGING EXPERIMENTS ON A TWO DIMENSIONAL SAND BOX WITH
DNAPLS: MULTIPHASE INVESTIGATION WITH ELECTRICAL IMPEDANCE TOMOGRAPHY
5. REPORT DATE
6. PERFORMING ORGANIZATION CODE
7. AUTHOR (S)
JONG SOO CHO
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
USEPA
NATIONAL RISK MANAGEMENT RESEARCH LABORATORY
SUBSURFACE PROCESSES AND REMEDIATION DIVISION
P.O. BOX 1198
ADA, OK 74820
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
IN-HOUSE RSJC3
12. SPONSORING AGENCY NAME AND ADDRESS
USEPA
NATIONAL RISK MANAGEMENT RESEARCH LABORATORY
SUBSURFACE PROCESSES AND REMEDIATION DIVISION
P.O. BOX 1198
ADA, OK 74820
13. TYPE OF REPORT AND PERIOD COVERED
14. SPONSORING AGENCY CODE
EPA/600/15
15. SUPPLEMENTARY NOTES
16. ABSTRACT
Electrical impedance tomography (EIT) applications in detection of organic chemical
sources and monitoring subsurface environments during air-sparging were studied. The
development of an inverse solution program and experimental tests in the laboratory were
included in this study. The inverse solution model used the Newton-Raphson method with
the Marquadt regularization technique. A multiphase flow and transport model was
utilized to test the EIT inverse modeling. Tetrachloroethylene(PCE)infiltration was
simulated with a multiphase flow model and the ability of EIT to trace the PCE
distribution was tested. Computational progress of the inverse solution was presented
with a graphical display of electrical conductivity distributions. The inverse program
for EIT was used to obtain the electrical conductivity distribution in a 2-D sand box.
The experiments included a spillage of dense non-aqueous phase liquid(DNAPL) dyed with a
hydrophobic dye at the top of the sand box filled with water and air sparging from the
bottom. Electrical conductivity changed in the soil as water was replaced with DNAPL or
air. This made the tomographic pictures of electrical conductivity. The vapor
concentration of DNAPL in the extracted air was measured with a GC to estimate the
removal rate during air sparging. The tomographic images from the EIT were compared with
photographic images of dyed PCE in the water filled space.
17. KEY WORDS AND DOCUMENT ANALYSIS
A. DESCRIPTORS
B. IDENTIFIERS/OPEN ENDED TERMS
C. COSATI FIELD, GROUP
DNAPL
MULTIPHASE FLOW
AIR-SPARGING
EIT
18. DISTRIBUTION STATEMENT
RELEASE TO THE PUBLIC
19. SECURITY CLASS(THIS REPORT!
UNCLASSIFIED
21. NO. OF PAGES
20
20. SECURITY CLASS(THIS PAGE)
UNCLASSIFIED
22. PRICE
EPA FORM 2220-1 (REV.4-77) PREVIOUS EDITION IS 0BS0LET3
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