PROCEEDINGS, Thirty-Seventh Workshop on Geothermal Reservoir Engineering
Stanford University, Stanford, California, January 30 - February 1, 2012
SGP-TR-194
USE OF TRACERS TO INTERROGATE FRACTURE SURFACE AREA IN SINGLEWELL TRACER TESTS IN EGS SYSTEMS
Paul Reimus1, Mark Williams2, Vince Vermeul2, Peter Rose3, Kevin Leecaster3, Bridget Ayling3,
Raphael Sanjuan3, Morgan Ames3, Cynthia Dean1 and Dick Benoit4
1
Los Alamos National Laboratory
P.O. Box 1663, Mail Stop J966
Los Alamos, NM 87545
e-mail: [email protected]
2
Pacific Northwest National Laboratory
3
Energy and Geoscience Institute at the University of Utah
4
Magma Energy Corporation
ABSTRACT
Based on the thermal decay and sorption behavior of
Safranin T observed in laboratory tests and in an
interwell field tracer test (Leecaster et al. and Rose et
al., these proceedings), we use numerical models to
demonstrate how this tracer could be employed to
interrogate fracture surface area in a single-well
tracer test in an Engineered Geothermal System
(EGS) reservoir. We also show how lithium ion,
which adsorbs to fracture surfaces but does not
thermally decay (Dean et al., these proceedings),
could be used in single-well tracer tests to
accomplish the same objective. The interrogation of
surface area in single-well tracer tests could be a very
useful tool in the development of EGS reservoirs, as
the effectiveness of a fracture stimulation could be
evaluated before additional wells are drilled.
INTRODUCTION
Rose et al. (these proceedings) describe a tracer test
involving both a thermally-stable conservative tracer
(1,6-Naphthalene Disulfonate, or NDS) and a
thermally-degrading sorbing tracer (Safranin-T, or
Saf-T) conducted in a geothermal field at Soda Lake,
NV. In this paper, we provide both semi-analytical
and numerical modeling interpretations of the tracer
breakthrough curves from that experiment, and we
use the deduced sorption parameters in numerical
simulations of single-well injection-withdrawal tracer
tests to show how the sorbing tracer could be used to
estimate fracture surface area in such tests. We
similarly use the laboratory data generated by Dean
et al (these proceedings) for the cation-exchanging
tracer lithium ion to demonstrate how this tracer
might be used in single-well injection-withdrawal
tests for surface area interrogation.
INTERPRETATIONS OF SODA LAKE TEST
Semi-Analytical Model
The semi-analytical RELAP (Reactive Transport
LAPlace Transform Inversion) model, which was
developed to interpret multiple tracer breakthrough
curves in interwell tracer tests in either single- or
dual-porosity media (Reimus et al., 2003), was used
to provide an initial interpretation of the Soda Lake
tracer test.
RELAP uses a relatively simple
retardation approach to model reactive transport.
Laboratory testing with Saf-T (Leecaster et al., these
proceedings) suggested that this approach should be
adequate for modeling the transport of this reactive
tracer. The thermal decay corrections described by
Rose et al. (these proceedings), in which an average
reservoir temperature of C was assumed, were
applied to the Saf-T field data. The concentrations of
both the 1,6-NDS and the Safranin-T were
normalized by dividing their observed concentrations
in the production well (decay corrected in the case of
Saf-T) by their injection masses prior to analysis by
RELAP.
The 1,6-NDS curve was first matched by adjusting
the mean residence time and Peclet number (travel
distance divided by longitudinal dispersivity)
assuming both a single-porosity system (no matrix
diffusion) and a dual-porosity system. In the dualporosity case, both a nominally high and a nominally
low amount of matrix diffusion was assumed to occur
(using diffusive mass transfer coefficients,
,
equal to 9e-4 sec-1/2 and 1e-4 sec-1/2, respectively;
After obtaining reasonable matches to the 1,6-NDS
breakthrough curve for each of the three matrix
diffusion cases, the best-fitting parameters in each
case (mean residence time, Peclet number, and mass
fraction) were assumed to apply to the corrected SafT breakthrough data, and the data were fitted by
adjusting either a retardation factor in the flowing
porosity and/or a retardation factor in the matrix
porosity. The resulting fits to both the 1,6-NDS data
and the corrected Saf-T data are shown in Figure 1,
and the best-fitting parameters are listed in Table 1.
It is noteworthy that the best-fitting Saf-T retardation
factors in the flowing and matrix porosity are nearly
identical regardless of how much (or whether) matrix
diffusion is assumed. The fits were not very sensitive
to the matrix retardation factor, but the retardation
factor in the flowing porosity was tightly constrained
by the timing of the Saf-T arrival relative to the 1,6NDS.
In principle, the retardation factor in the flowing
porosity of a fractured system can be used to estimate
fracture surface area to volume ratio if the surfacearea-based distribution coefficient is known:
SA/V = 1/b = (R-1)/Ka
(1)
Where SA = surface area, m2, V = volume, m3, b =
fracture half-aperture (assuming parallel plates), cm,
R = retardation factor, and Ka = surface-area-based
distribution coefficient, m3/m2. The volume of the
system can be estimated reasonably well by
multiplying the mean residence time of a
conservative tracer by the production flow rate, and
for the Soda Lake tracer test, the volume is estimated
to be 10-12 Mgal or 38,000-46000 m3.
The
retardation factor is obtained directly from the
sorbing tracer breakthrough curve, and the Ka value
must be estimated from laboratory experiments.
100
Normalized Concentration (mg/L per kg injected)
where  = matrix porosity, b = fracture half aperture,
cm, and Dm = matrix diffusion coefficient, cm2/sec).
It can be shown that it is generally possible to fit
single conservative tracer breakthrough curves almost
equally well assuming a wide range of matrix
diffusion mass transfer coefficients, including no
matrix diffusion. The tracer mass assumed to be
participating in the test was also treated as an
adjustable parameter, as the overall 1,6-NDS
recovery was on the order of 30% when the test
concluded. It was also assumed that 26.5% of any
tracer mass recovered was recirculated to the
injection well, reflecting reinjection and production
flow rates as well as dilution of the production water
with untraced water from other wells prior to
reinjection.
RELAP can robustly account for
recirculated tracer mass.
10
1
1,6 NDS
1,6 NDS no matrix diffusion Model
0.1
1,6 NDS high matrix diff. Model
1,6 NDS low matrix diff. Model
Safranin-T corrected
0.01
Saf-T no matrix diffusion Model
Saf-T high matrix diff. Model
Saf-T low matrix diff. Model
0.001
0
100
200
300
400
Time (hr)
500
600
700
Figure 1: RELAP matches to 1,6-NDS and corrected
Safranin-T normalized concentrations at
Soda Lake.
Table 1: RELAP Soda Lake parameter estimates for
different matrix diffusion assumptions.
Parameter
No matrix
diffusion
=
0.0001 sec-1/2
=
0.0009 sec-1/2
Res. time, hrs
258
248
174
Peclet number
4
4.2
6.7
Mass fraction
0.27
0.28
0.35
Fracture Ret. Fac.
3.4
3.4
3.7
Matrix Ret. Fac.
N/A
3.5
3.5
Based on the laboratory data of Leecaster et al. (these
proceedings), the inferred value of Ka for Saf-T on
quartz sand surfaces is on the order of 1e-6 to 2e-6
m3/m2 at temperatures above C. Insertion of
these values into equation (1), and using the
retardation factor of 3.5 observed at Soda Lake yields
unrealistically high surface area to volume ratios of a
few million m2/m3, or fracture half-apertures on the
order of a micron. A more reasonable value of halfaperture would be in the mm to cm range. Clearly, a
site-specific value of Ka is needed to obtain a
reasonable estimate of surface area in the Soda Lake
system. We would expect a much larger Ka value for
the Soda Lake mineral surfaces than quartz sand.
It is also important to recognize that the surface area
interrogated by a sorbing tracer is likely to be much
larger than the effective surface area for heat transfer.
The former includes all the accessible microporosity
and roughness at the fracture surfaces, which can
exceed the bulk surface area (used for heat transfer)
by orders of magnitude (Figure 2). The relationship
between these two surface areas should be estimated
if a sorbing tracer breakthrough curve is used to
estimate surface area for heat transfer calculations.
Figure 2: Illustration of difference between sorption
surface area and heat transfer surface area
at a fracture surface.
Numerical Model
A numerical model was developed using the
ToughReact code (Xu et al. 2006) to simulate the
Soda Lake tracer test and for investigation of the
efficacy of using single-well injection/withdrawal
tests at the site for reservoir characterization. Site
characterization and tracer parameters from fitting the
two-well tracer test data are used for the single-well
injection-withdrawal test models. The ToughReact
code was selected to take advantage of the MINC
(Mulitple INteracting Continua, Pruess 1983) option
for simulating a fractured reservoir and options for
simulating sorbing and thermally decay of tracers.
The initial model has a two dimensional plan view
grid (x,y) with a constant thickness (z) of 300 m. The
grid spacing in the x,y is 10 m between and near the
injection and production wells and then increases to a
final 1 km spacing near the edges (overall domain
size is 5.47 km x 2.59 km). The wells are spaced 550
m apart. We used ½ symmetry for the problem with
the corresponding reductions in injection and
withdrawal rates (full values were 800 gpm injection
and 885 gpm production) and tracer mass. Boundary
conditions are no-flow along the top, bottom, and line
of symmetry (e.g. y=0) with dirichlet conditions
specified along the other boundaries. The MINC
option in ToughReact is used for simulating the
fractured reservoir. In initial simulations divided the
domain into 5 continua (1 for the fracture network
and 4 for the matrix).
Thermal decay of Saf-T was directly simulated in the
model based on parameters measured in the
laboratory (Rose et al., these proceedings). This
approach is in contrast to the RELAP modeling
approach where heat transfer was not included in the
model and thermal decay was corrected for in
advance of the model interpretations. Initial sorption
properties of Saf-T (partition coefficients) are based
on fitting the tracer test data from the Soda Lake twowell tracer test as discussed below. Results from
ongoing laboratory studies of Saf-T transport with
site materials will be incorporated in this modeling
effort when they become available.
Initial reservoir temperatures were set to C and
the temperature of the injection fluid was set at 71 C.
A manual calibration process was used for this initial
model. Parameters were varied based on visual
comparison of simulated results with the tracer
concentration measurements from the production
well. The parameters varied during this fitting
process included fracture and matrix volumes, matrix
porosity, matrix diffusion coefficient, and Saf-T
partition coefficients (different values for fractures
and matrix). An initial fracture spacing of 10 m was
used but was not varied. The impact of this
parameter will be investigated in further sensitivity
studies.
Figure 3 shows a comparison of the simulated 1,6NDS and Safranin-T concentrations at the production
well with the measured values. Maximum simulated
Saf-T concentrations were approximately 2X the
measured values during the peak for this case.
Simulated 1,6-NDS and Saf-T plumes within the
fractures at 4 days are plotted in Figure 4.
1000
100
100
10
1,6-NDS (ppb)
Simulated 1,6-NDS
Safranin T
Simulated Safranin T
10
1
1
Safranin T (ppb)
Sorption Surface Area
Injection and withdrawal started at time = 0 and ran
for 28 days (800 gpm for the injection well and 885
gpm for the production well, scaled to the model
symmetry). For simplicity in this initial model, the
tracers were injected during the first hour of the test
followed by fresh water injection for the duration of
the simulation period (50 kg of 1,6-NDS and 90 kg of
Saf-T, scaled to the model symmetry). During the
field test the 1,6-NDS was injected in about ½ hr at
the start of the test and the Safranin-T was injected
afterward over a period of about 3 hours due to
injection difficulties. Additionally for these initial
simulations, re-injection of the partial mass recovered
from the production well was not included.
1,6-NDS (ppb)
Heat Transfer Surface Area
0.1
0.1
0.01
0.01
0
5
10
15
Time (days)
20
25
30
Figure 3: Comparison of simulated and measured
production well tracer concentrations in
the Soda Lake tracer test.
Two grids were developed during these initial
scoping simulations to investigate grid effects on the
results, a two-dimensional plan view grid (similar
spacing as used in the two-well tracer test) and a onedimensional radially-symmetric grid. Both grids
used 10-m spacing near the injection-withdrawal
well. Results were similar for the two models
therefore the results of the one-dimensional radially
symmetric model are reported here, as it was more
computationally efficient.
Figure 4: Simulated 1,6-NDS(top) and Safranin-T
(bottom) plumes in the fracture domain at
4 days. Length scale is m.
Although it is difficult to make a direct visual
comparison of the RELAP model results shown in
Figure 1 and the ToughReact results of Figure 3
(because of the vast differences in uncorrected and
corrected Saf-T concentration differences), the results
are nonetheless in good agreement. The agreement
between the Saf-T simulations is most readily
apparent in the overprediction of the concentrations
from about 7 to 12 days and the significant
underprediction of the last two data points.
SINGLE-WELL TRACER TEST NUMERICAL
SIMULATIONS
Saf-T Single-Well Tracer Test at Soda Lake
In previous numerical modeling studies, Pruess et al.
(2010) and Fayer et al. (2009) have demonstrated the
potential for using single-well injection-withdrawal
tests to characterize fracture surface area in
geothermal reservoirs. In this effort we are using the
site-specific parameters determined from the two
well tracer test conducted at the Soda Lake site to
investigate the potential responses of a single-well
injection/withdrawal test conducted at the site under
different operational conditions. The goals are to (1)
show sensitivity of the test results under different
operating conditions to help design a single-well
injection-withdrawal test at the Soda Lake site to
provide optimal responses for fracture surface area
characterization, (2) help identify beneficial reactive
tracer properties for such a test (e.g. thermal decay,
sorption), and (3) to address impacts of parameter
uncertainty.
Simulated single-well injection-withdrawal tracer test
results are shown in Figure 5 using the site
parameters from fitting the two-well tracer test,
shown in Figures 3 and 4. Given that one of the
goals for a single-well injection/withdrawal test is a
shorter operational time, the simulated test case
consisted of 3 days of injection, 3 days of shut-in (no
flow), and 3 days for withdrawal. Two different
operational cases are shown in Figure 5 with the first
case using an initial pulse of tracer during the first
hour of the test followed by fresh water injection for
the rest of the injection stage (as in the two-well
tracer test operation). The second case uses a
constant tracer injection concentration for the
duration of the injection stage but with the same
overall mass injected as the first case.
The simulated results in Figure 5 illustrate the
potential for using single-well tracer tests for surface
area interrogation. The differences between the 1,6
NDS and Saf-T concentrations are a function of the
surface area to volume ratio in the system, and the
volume in this case is simply the volume of water
injected (tracer pulse + fresh). Note that in a porous
medium, a fast and reversibly-sorbing tracer with
little sorption/desorption hysteresis, like Saf-T, would
be expected to have a response during the withdrawal
period very similar to that of a conservative tracer
because the transport of the Saf-T would be retarded
by the same amount going into and coming out of the
flow system. Such a response would not be very
useful for surface area interrogation. Figure 5 shows
significant differences between the 1,6-NDS and SafT because of Saf-T sorption in the matrix after
diffusion out of fractures and into the matrix. Under
these circumstances, the effective mass transfer
coefficient for matrix diffusion is
, where
Rm is the matrix retardation factor. The value of R m
for Saf-T is large enough that a considerable
difference is observed in the responses of the two
tracers, which can be exploited to estimate a surfacearea-to-volume ratio (1/b) provided reasonable
estimates of  and Dm for the tracers are available.
1000
180
900
170
800
160
150
600
500
1,6 NDS
400
Safranin T
140
130
Temperature
Temperature (C)
Concentration (ppb)
700
300
120
200
110
100
Withdrawal
Shut-in
Injection
0
100
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
Time (Days)
7000
180
6000
170
160
150
1,6 NDS
4000
140
Safranin T
3000
Temperature
130
Temperature (C)
Concentration (ppb)
5000
A test was simulated in which a tracer solution was
injected for 10 hours, followed by 2 hours of
untraced chase water and 20 hours of shut in (no
flow) prior to pumping back. Lithium was assumed
to be injected as LiBr, with the bromide serving as a
conservative tracer. Selectivity coefficients typical of
Li+, Na+, and Ca2+ (Appelo 1996) were used in
MULTRAN, with Na+ and Ca2+ assumed to be the
two primary resident cations in the reservoir
(dominant mono- and di-valent cations, respectively).
The injection concentration of LiBr was 0.01 M,
which was approximately a factor of 4 greater than
the combined concentrations of the Na+ and Ca2+ in
the system. 2-D radial flow was assumed in the
simulations.
Figure 6 shows how the Li+ breakthrough curve
depends on fracture SA/V ratio and assumed cation
exchange capacity in the simulated test. This figure
illustrates the following key points:
2000
120
1000
110
Withdrawal
Shut-in
Injection
0
100
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
Time (Days)
Figure 5: Single-well tracer test simulation results,
showing responses after injecting a 1-hr
tracer pulse followed by fresh water (top),
and after injecting a 3-day pulse of
constant tracer concentration with same
mass as 1-hr pulse (bottom).
Exchanging Cation Single-Well Tracer Test
Dean et al. (these proceedings) conducted laboratory
column experiments at elevated temperature and
pressure using lithium ion as a cation-exchanging
tracer to interrogate surface area. They used a
crushed amphibolite schist from Fenton Hill, NM that
had very low matrix porosity (~1%) and showed that
the lithium breakthrough curves could be simulated
using a dual-porosity, multicomponent numerical
model that explicitly accounted for lithium cation
exchange reactions in the column. It was somewhat
surprising that a dual-porosity model was needed to
match the lithium responses, but this result
underscores the importance of coupled diffusion and
sorption processes even in systems that would seem
to have all the characteristics of a porous medium.
We employed the same model used by Dean et al.
(these proceedings), i.e., MULTRAN (Sullivan et al.,
2003), or MULticomponent Reactive TRANsport, to
simulate single-well tracer tests involving lithium
ion. Diffusive mass transfer and cation exchange
parameters similar to those measured in the
laboratory experiments were used in the simulations.
1) The breakthrough curve of Li + is quite sensitive
to a difference of a factor of 2 in the SA/V ratio
in the system. It is apparent that the Li+
breakthrough curve could readily distinguish
between these two SA/V ratios in this
hypothetical system.
2) The Li+ breakthrough curve is surprisingly
insensitive to the CEC of the system, with a
factor of 10 difference in CEC, resulting in only
a minor change in the breakthrough curve. This
result is very encouraging because it suggests
that SA/V ratio estimates will not be highly
sensitive CEC values, which can be difficult to
estimate in fractured rock flow systems.
3) Conservative tracers with different diffusion
coefficients could not be used effectively in this
hypothetical system to interrogate surface area
because the differences in their breakthrough
curves (approximated by the differences in the
conservative tracer breakthrough curves at the
two different SA/V ratios) are too small to be
distinguished (especially when considering
typical analytical measurement errors).
A major advantage of using lithium ion over a
fluorescent tracer with a lower detection limit, such
as Saf-T, is that it is not susceptible to thermal decay.
The need to simultaneously account for both sorption
and thermal decay in a tracer test interpretation
introduces additional uncertainty to the interpretation
that is avoided if thermal decay can be neglected.
0.010
Conservative Tracer with SA/V = 10 and 20 cm-1
Molar Concentration
0.008
SA/V = 10 cm-1
SA/V = 20 cm-1 and 10 times smaller CEC
0.006
SA/V = 20 cm-1
0.004
Sodium
0.002
Calcium
0.000
20
30
40
50
60
70
Time, hr
Figure 6: Simulated differences in Li+ breakthrough
curves (brown and red) as a function of
SA/V and CEC in a single-well tracer test.
The sodium and calcium “breakthrough
curves” are a result of Na + and Ca2+ being
displaced by Li+ at cation exchange sites.
Note that the difference in conservative
tracer breakthrough curves at the two
different SA/V values roughly corresponds
to the differences that could be expected for
conservative tracers with a factor of 4
difference in diffusion coefficients at either
SA/V value.
DISCUSSION AND CONCLUSIONS
In this paper, we used numerical models to
demonstrate how adsorbing tracers can be used in
single-well tracer tests to interrogate surface area to
volume ratios in geothermal reservoirs. Rather than
using hypothetical tracer properties in the
simulations, we used transport parameters for Saf-T
deduced from the interpretation of an interwell tracer
test conducted at Soda Lake, NV and lithium ion
transport parameters derived from laboratory column
experiments conducted by Dean et al. (these
proceedings).
The interrogation of surface area in single-well tracer
tests could be a very useful tool in the development
of EGS reservoirs, as the effectiveness of a fracture
stimulation could be evaluated before additional
wells are drilled. Single-well tracer tests also offer
the advantage of yielding much higher return
concentrations (for a given tracer injection mass) than
typical interwell tests. Tracers such as lithium ion,
which
can
have
significant
background
concentrations in native groundwater and do not have
extremely low detection limits, may be very well
suited for surface area interrogation in single-well
tests even if they are not suitable for interwell tests.
80
In the future, we hope to develop a three-dimensional
numerical model of the Soda Lake site using a
recently developed detailed three-dimensional
conceptual model of the site (Echols et al. 2011).
The model will be exercised to determine the
increase in predictive capability for both single-well
and interwell tracer tests that can be achieved by
incorporating this more detailed site information.
REFERENCES
Appelo C.A.J.
1996.
“Multicomponent ion
exchange and chromatography in natural systems.”
In: Reactive Transport in Porous Media.
PC
Lichtner, CI Steefel, and EH Oelkers (Editors).
Reviews in Mineralology 34:193–227.
Dean, C.A., Reimus, P., and Newell, D. “Evaluation
of a Cation Exchanging Tracer to Interrogate Fracture
Surface
Area
in EGS
Systems”
(2012)
PROCEEDINGS, Thirty-Seventh Workshop on
Geothermal
Reservoir
Engineering
Stanford
University, Stanford, California, January 30 February 1, 2012, SGP-TR-194.
Echols J., D. Benoit, M. Ohren, G. Oppliger, and T.
Van Gundy. 2011. Integration of a 3D-3C Reflection
Seismic Survey over a Known Geothermal Resource:
Soda Lake, Churchill County, Nevada.
GRC
Transactions, Vol. 35. 2011.
Fayer S., P. Rose, S. Petty, M.D. Deo, and T. Xu.
2009. A Computational Technique for Estimating the
Fracture Surface Area Adjacent to a Newly
Stimulated Well within an Engineered Geothermal
System. Proceeding Tough Symposium September
14-16, 2009.
Lawrence Berkeley Laboratory.
Berkeley, CA.
Leecaster, K., Ayling, B., Moffitt, G., Clausen, S. and
Rose, P.E. “Use of Safranin T as a Reactive Tracer
for Geothermal Reservoir Characterization” (2012)
PROCEEDINGS, Thirty-Seventh Workshop on
Geothermal
Reservoir
Engineering
Stanford
University, Stanford, California, January 30 February 1, 2012, SGP-TR-194.
Pruess K. 1983. GMINC – A Mesh Generator for
Flow Simulations in Fractured Reservoirs. Lawrence
Berkeley Laboratory Report LBL-15227, Berkeley
CA.
Pruess K., and C. Doughty. 2010. Thermal SingleWell Injection-Withdrawal Tracer Tests for
Determining Fracture-Matrix Heat Transfer Area.
Proceedings: Thirty-Fifth Workshop on Geothermal
Reservoir Engineering, Stanford University, Stanford
CA. Feb 1-3, 2010.
Reimus, P. W., G. Pohll, T. Mihevc, J. Chapman, L.
Papelis, B. Lyles, S. Kosinski, R. Niswonger, and P.
Sanders. 2003. “Testing and Parameterizing a
Conceptual Model for Radionuclide Transport in a
Fractured Granite using Multiple Tracers in a ForcedGradient Test”, Water Resources Research, 39(12),
1350, doi:10.1029/2002WR001597.
Rose, P.E., Leecaster, K., Clausen, S., Sanjuan, R.,
Ames, M., Reimus, P., Williams, M., Vermeul, V.,
and Benoit, D. “A Tracer Test at the Soda Lake,
Nevada Geothermal Field Using a Sorbing Tracer”
(2012) PROCEEDINGS, Thirty-Seventh Workshop
on Geothermal Reservoir Engineering Stanford
University, Stanford, California, January 30 February 1, 2012, SGP-TR-194.
Sullivan, E. J., Reimus, P. W., and Counce, D. A.,
2003, “Transport of a reactive tracer in saturated
alluvium described using a three-component cationexchange model,” Journal of Contaminant
Hydrology, v. 62/63, no. 0, p. 675-694.
Xu T, E. Sonnenthal, N. Spycher, and K. Pruess.
2006.
TOUGHREACT V1.2 User’s Guide: A
Simulation Program for Nonisothermal Multiphase
Reactive Geochemical Transport in Variably
Saturated Geologic Media. LBNL-55460, Lawrence
Berkeley Laboratory, Berkeley, California.
Acknowledgment: This material is based upon work
supported by the Department of Energy under Award
Numbers DE-GO18193 and DE-PS36-09GO99017.
Disclaimer: “This report was prepared as an account
of work sponsored by an agency of the United States
Government. Neither the United States Government
nor any agency thereof, nor any of their employees,
makes any warranty, express or implied, or assumes
any legal liability or responsibility for the accuracy,
completeness, or usefulness of any information,
apparatus, product, or process disclosed, or represents
that its use would not infringe privately owned
rights. Reference herein to any specific commercial
product, process, or service by trade name,
trademark, manufacturer, or otherwise does not
necessarily constitute or imply its endorsement,
recommendation, or favoring by the United States
Government or any agency thereof. The views and
opinions of authors expressed herein do not
necessarily state or reflect those of the United States
Government or any agency thereof.”