Three-Dimensional Nickel Ion Transport through Porous Media
Using Magnetic Resonance Imaging
K.-H. Herrmann,* A. Pohlmeier, S. Wiese, N. J. Shah, O. Nitzsche, and H. Vereecken
ABSTRACT
dimensional flow fields (see below). Besides others,
one versatile approach for modeling three-dimensional
The transport of Ni2 ions in a column, filled with porous media,
transport processes is the use of particle tracking. Parti-
was observed in three dimensions and time by magnetic resonance
imaging (MRI) in a clinical scanner. For porous media we used glass cle tracking models like PARTRACE (Neuendorf,
beads or quartz sand in a saturated continuous flow mode. The mag- 1997) use a divergence-free heterogenous flow velocity
1
netic moment of Ni2 decreased the T1 relaxation time of H in aqueous
field as input for transport modeling. The local flow
solution. This concentration-dependent effect was used by a fast low
properties have to be determined by either a modeling
angle shot (FLASH) MRI sequence for imaging the concentration of
program like TRACE (Seidemann, 1997) or by direct
the dissolved ions. Since Ni2 behaves as a conservative tracer under
measurement of the local flow velocities, which can be
the chosen conditions, the tracer motion was representative for the
achieved by the presented MRI experiments. PAR-
water flow in the porous medium. Currently, we can achieve an iso-
TRACE then will divide the total tracer mass in little
tropic spatial resolution of 1.5 mm and a temporal resolution of 170 s.
particles, each representing a fraction of the total tracer
The transport observation gives direct access to hydraulic flow proper-
mass, which are tracked on their way through the mod-
ties of the porous media. The fluid flow velocity field was calculated
by a fronttracking method and the statistical properties of the veloci- eled porous medium according to the local flow veloci-
ties were investigated. We also compared the experimental data with
ties. At each timestep, new local free and sorbed concen-
the three-dimensional particle tracking model PARTRACE, which
trations are calculated from the particle positions.
uses the experimental flow field as input.
Models like PARTRACE are quite capable of de-
scribing even very complex interactions between flow
and chemical heterogeneity but have high demands on
nvestigation and modeling of transport processes
computing resources. To achieve accurate modeling of
Iin heterogenous porous media are of great interest
experimentally observed transport it is most important
(Roth et al., 1999) in environmental science. Very-well
to have a good understanding of the underlying pro-
explored and popular methods to describe the solute
cesses and the heterogenous structure of the medium.
transport through a porous structure are models like the
This process understanding, and at least the statistical
one-dimensional convection dispersion equation (CDE)
distribution and geostatistical correlations of the struc-
and the one-dimensional Richards equation (Adler,
tural information, enable flow models like TRACE to cal-
1992). These formulate the transport of nonreactive and
culate accurate flow fields. The presented MRI method
reactive tracers employing average values of the soil
provides access to the local heterogenous flow velocities
parameters: porosity, flow velocity, hydraulic conductiv-
in transport direction at a sufficiently high resolution.
ity, and dispersivity. The averaging process can either
To benefit from the full potential of three-dimen-
be done in space by finding a representative elementary
sional modeling it is desirable to conceive adequate
volume (REV) or by ensemble averaging (Dagan, 1986).
three-dimensional experiments with a fine spatial reso-
The determination of the averaged model parameters is
lution. Another profit from such three-dimensional ex-
only possible by performing experiments on the respec-
periments is the knowledge of processes on a pore scale,
tive scale. A deeper understanding of the basic processes
which will serve as the basis for statistical analysis. One
leading to the mentioned averaged parameters on the
very promising technique is the (nuclear) magnetic reso-
laboratory scale is only possible by modeling and corre-
nance imaging (MRI, see Callaghan, 1991), which has
sponding experimental investigations with a fine spatial
been developed in the last two decades mainly for medi-
resolution (Roth et al., 1999; Feyen and Wiyo, 1999).
cal applications. It allows nondestructive and nonintru-
Promising novel approaches, which are available by
sive three-dimensional studies in aqueous media. Due to
high-speed computing, are three-dimensional models
the increased availability of MRI systems, it has become
that take into account the heterogenous structure of
possible to utilize this method for studying porous media
porosity, water flow, and possible chemical reactions.
in a stationary state as well as for monitoring their flow
These models may be based either on simple statistical
properties (Oswald et al., 1997). These experiments pro-
properties (mean value, higher moments), geostatistics
vide both the possibility of determining the proton den-
describing their temporal and spatial correlation on frac-
sity (e.g., of H2O) directly, and determining the concen-
tal models according to the soil model in question
tration of suitable tracer substances by their influence
1
(Nitzsche and Merkel, 1999), or directly measured three-
on the magnetic resonance properties of H. It is also
Abbreviations: CDE, convection dispersion equation; FLASH, fast low
K.-H. Herrmann and A. Pohlmeier, MOD; S. Wiese and N.J. Shah,
angle shot (a specific magnetic resonance imaging sequence); MRI,
IME; and O. Nitzsche and H. Vereecken, ICG-4, Research Center
Juelich, D-52425 Juelich, Germany. Received 26 June 2000. *Corre- magnetic resonance imaging; PARTRACE, particle tracking computer
program; RF, radio frequency; TRACE, computer program for solving
sponding author (k.-h.herrmann@fz-juelich.de).
the Richards equation for heterogenous conductivity; voxel, one pixel
Published in J. Environ. Qual. 31:506 514 (2002). representing a volume element in magnetic resonance imaging.
506
HERRMANN ET AL.: THREE-DIMENSIONAL TRACER TRANSPORT BY MRI 507
possible to study the movement (convection, dispersion)
of the protons (respectively the water molecules) as
shown, for example, by Sedermann et al. (1997).
The objective of this study is firstly to visualize the
motion of a tracer in porous media of two different pore
sizes (quartz sand and glass beads) on the laboratory
scale with high spatial and temporal resolution using
MRI. Secondly, the three-dimensional flow field is ob-
tained from the tracer motion and thirdly statistical
properties of the flow field are calculated and used to
determine mean flow properties. The validity of the
approach is checked by three-dimensional modeling us-
ing PARTRACE, based on the obtained velocity field.
EXPERIMENTAL SETUP
The experimental setup is shown in Fig. 1. A polymethyl
methacrylate column (18 5 cm) was used. It was filled with
Fig. 1. Schema of the experimental setup. The metal-free column is
the porous medium, with the flow passing from the bottom
located inside the nuclear magnetic resonance (NMR) scanner. A
to the top to guarantee saturation. At the intake a small mixing
chromatography pump generates a constant flow rate through a
space was followed by a glass filter plate to create a homoge- degasser and the porous medium. A 20-mL pulse of Ni2 tracer
can be injected into the flow and for monitoring breakthrough
nous flow into the porous medium. A constant flow rate was
curves a fractional collector is available at the outflow.
produced by a chromatography pump. To remove small air
bubbles, which tend to collect at the filter plates and in the
(RF) pulse of frequency and circular polarization in the y z
matrix, the water was routed through a degasser, as shown in
plane (perpendicular to the external B0 field), they will be
the schematic overview (Fig. 1). A 20-mL pulse of Ni2 tracer
turned synchronously away from the x axis towards the y z
can be injected into the flow and for recording breakthrough
plane. The angle by which the magnetization is rotated is
curves a fractional collector was available at the outflow. The
usually called the flip angle. Once flipped away from the x
column, located in the MRI scanner, was connected by 10 m
axis, the nuclear spins will precess synchronously and in phase
of Teflon tubing (1/163 inner diameter) to the pump and to
with the Larmor frequency . This is a macroscopic rotating
the fractional collector.
magnetization of the sample, which can be detected by a radio
The porous media we used included: (i) fine grained quartz
antenna as the magnetic resonance response signal (after de-
sand (Teco-Sil Fused Silica, 50 100, approximately 80%
modulation also known as free induction decay). Once the
100 mesh (150 m) and 15% 140 mesh (100 m); C-E Minerals,
radio signal is switched off, the x component Mx of the sample
Greeneville, NC), which was carefully cleaned by subsequent
magnetization will relax back to the equilibrium state along
washing in diluted acid and water, and (ii) regular glass beads
the x axis (for a 90 flip angle) according to:
of 2 mm diameter, which were also carefully cleaned in water.
We chose Ni(NO3)2, at a concentration of 4 mmol L 1, for
t
the nonreactive tracer. Due to its strong paramagnetism, Ni2
Mx M0 1 exp [1]
1
T1
has a sufficiently strong influence on the H magnetic reso-
nance relaxation properties at these relatively low concentra-
where M0 is the equilibrium magnetization in x direction and
tions and was thus very convenient for monitoring the water
T1 is the spin-lattice relaxation time.
flow. The column was conditioned with a solution of Mg(NO3)2 To monitor the water motion the protons (1H) of the water
with an adjusted pH 5.0 and a density close to the one of
molecules are probed by MRI. The presence of the paramag-
the Ni2 solution. We used a Siemens Magnetom Vision 1.5T
netic Ni2 ions decreases T1 of the water protons inversely
(Siemens AG, Erlangen, Germany) MRI scanner with a static
proportional to the Ni2 concentration (Grant and Harris,
magnetic field of B 1.5 Tesla, in which the column was
1996). To detect this change in T1 a specialized T1 weighted
placed inside a head coil.
fast low angle shot (FLASH) sequence was used. The main
concept of FLASH is a fast repetition (TR 14 ms in our
case) of RF pulses, which rotate the magnetization only by a
MAGNETIC RESONANCE IMAGING
small flip angle (we use 10 ), followed by a fast readout of
TECHNIQUE AND DATA ANALYSIS
data. Some preparation RF pulses (inversion recovery), which
Magnetic Resonance Imaging Sequence cause the sample magnetization M to approximately vanish
for pure water, are used to achieve the T1 weighting before
The tracer experiments used the nuclear magnetic reso-
the 10 FLASH RF pulses; see Haase et al. (1986) for a detailed
nance effect of nuclei, which are subjected to a strong magnetic
description. For this short repetition time TR 14 ms the data
field B0 along the x axis (see Callaghan [1991] for a general
acquisition time is even shorter and the signal loss due to
introduction). (In MRI the convention is to use z as the B0 dephasing of the spins as well as to spin-lattice relaxation can
direction, but we wanted to stay consistent with the soil science
be neglected. The response signal I to each of these 10 RF
convention, where the flow is along the z axis.) Since all nuclei
pulses is then approximately proportional to the magnetiza-
have a small magnetic moment (spin angular momentum),
tion Mx directly before the RF pulse:
they act as a gyroscope under the force of the external field
B0 with the precession or Larmor frequency B0, where
TR
I I0 1 exp [2]
is the gyromagnetic moment of a given nucleus. After a
T1
certain relaxation time the nuclei are in an equilibrium parallel
to the x axis. If the nuclei are subjected to a radio frequency With the proportionality:
508 J. ENVIRON. QUAL., VOL. 31, MARCH APRIL 2002
constant
T1 [3]
CNi
we find:
TR CNi
ln(I0 I) ln(I0) [4]
constant
The logarithm ln(I0 I) of the intensity of the response
signal is therefore linearly dependent on the Ni2 concentra-
tion CNi. The constant parameter is an empirical constant ob-
tained from the calibration curve (not shown). This calibration
curve also shows the linear relation according to Eq. [4] down
to a concentration of CNi 0.02 mmol L 1. The detection limit
is below 0.01 mmol L 1.
Calculated breakthrough curves (Fig. 2, bottom) for trans-
versal slices of the column at different axial (z) positions show
a slight loss of total integrated logarithmic signal intensity
Fig. 3. Fronttracking algorithm: From the front positions at time t
(i.e., the total detected amount of nickel) with transport dis-
and t t the front position difference per timestep t allows
tance. This indicates that with increasing transport distance
calculation of a velocity at the front position between times t and
an increasing small amount of Ni2 is lost to observation by
t t.
dilution below the detection limit. However, the change of
the total integrated logarithmic signal intensity inside the col-
umn is less than 10%. This small signal loss has no significant
effect on the detected front position, because the applied front
detection algorithm (see below and Fig. 3) is sensitive to the
sharp rise of the concentration above the background noise.
Figure 2 (top) shows the mean of the detected tracer front
position at time t. Since the transport at the chosen pore
velocity of 0.0158 mm s 1 is dominated by convective flow
(Peclet number [Pe] 100), the expected mean tracer move-
ment is close to the convective pore velocity. This again shows
the vanishing effect of the detection limit on the front-
tracking results.
The data acquisition for the complete column volume takes
170 s at a spatial resolution of 1.56 1.0 1.56 mm (128
60 128 voxels, where a voxel one pixel representing a
volume element in MRI).
Data Analysis
Fronttracking
The obtained data from the nuclear magnetic resonance
(NMR) scanner are intensity values corresponding to Ni2
concentration in real space. These can be used directly for
two-dimensional (sections) or three-dimensional (isosurfaces)
graphical visualization of the tracer distribution and motion.
It is known that Ni2 is subject to sorptive retardation in
glass and quartz sand media depending on pH. Typically the
pH-dependent sorption of hydrolizable metal ions like Ni2
at dispersed oxides show a s-shaped isotherm. For example,
Kosmulski et al. (1999) found that for the binding of Ni2 to
silica, whose reactive surface is chemically similar to that of
quartz and glass, this s-shaped adsorption edge started at pH
7. Therefore, we performed these experiments at pH 5 to
prevent sorption. Figure 2 (top) shows that the actual detected
front movement has the same mean flow velocity (0.0158 mm
s 1) as is imposed on the system by the chromatography pump
Fig. 2. The top graph shows the detected mean tracer front positions (0.0150 mm s 1). This indicates that no significant retardation
....
( front edge, back edge). The slope (0.0158 mm s 1 ) is within
of the tracer substance Ni2 occurs and that the detected tracer
the experimental error and in good agreement with the known
movement is a valid observation for determining the water
mean pore velocity (0.0150 mm s 1 ). The bottom graph shows
flow velocity at pH 5.
breakthrough curves calculated for x y slices at the specified z
To obtain the velocity information of the water flow by
positions. The decreasing maximum Ni2 concentration is mostly
tracer monitoring a fronttracking algorithm is used (Fig. 3).
due to dispersive broadening of the breakthrough curves. The total
The actual front position is found by searching for a signal rise
integrated concentrations exhibit a slight decrease with transport
at each x y position above a threshold, which is approximately
distance. The concentration loss due to detection limits is less
50% above the background noise. To exclude artifacts, the
than 10%.
second criterium for the front position is that this increase of
HERRMANN ET AL.: THREE-DIMENSIONAL TRACER TRANSPORT BY MRI 509
the intensity persists for more than three voxels. For a flow
in z direction the z positions zt and zt t of the tracer front
at times t and t t are calculated from the raw data for each
point in the x y plane. This allows us to define the z component
vz of the velocity v at the position (x, y, zt) as:
zt t zt z
vz(t) [5]
t t
where t is chosen so that z 5 mm (3 voxels). If we assume
further a stationary flow field for a constant overall flow, the
velocity vz is not dependent on time. Repeating this for all
positions (x,y,z) leads to complete three-dimensional informa-
tion on the z component of the velocity field.
For the usage of the flow field in PARTRACE simulations,
all three components of the flow in each voxel are needed
and the flow velocity field has to be free of divergence, which
Fig. 4. Calculating the vx and vy velocity components: First the flow
can be derived from the continuity equation: through every x y plane is scaled to the overall flow. Then the
flow balance into the subvolume (voxel) is calculated according
to the boundaries and the already calculated neighboring voxels,
( v ) [6]
starting at the corner ix iy 1. From this the unknown flows in
t
vx vy are determined (see text for details).
where is the fluid density. Since in saturated conditions the
water in the column is incompressible this simplifies to:
sponding to a Peclet number of Pe 110. The immobile
v 0 [7]
water fraction is approximately 5%.
or, integrated over a volume (slab) according to Gauss law:
Figure 5 shows sections and isoconcentration surfaces
for the Ni2 ions in the quartz sand column at three
v dr v ds 0 [8]
different timesteps. (The isoconcentration surface is de-
slab slab surface
fined at all volume elements with identical nickel con-
this requires an identical flow through every x y plane in
centrations. This three-dimensional surface encloses the
the column. Since this is an ill-posed problem, an additional
higher concentration.) One can see a rather smooth
constraint is needed inside the column where no boundary
transport pattern with only small wall effects. A closer
conditions (wall) are available. The axial symmetry suggests
look at an animation of all timesteps shows small fluctu-
that we assume identical x and y components inside the box
ations in the front movement, which tend to average
as an approximation.
out over time, so the tracer front stays quite smooth;
With this constraint a quite simple scheme will lead to a
velocity field that satisfies Eq. [8]. To avoid edge problems
with the cylindrical geometry of the column, a box-shaped
part of the column, nx ny nz data points, is chosen and
in a first step the flow through every x y plane is calculated
and all vz values of that plane are scaled so that the plane
average is the same as the overall flow average to enforce Eq.
[8]. Then the first plane (iz 1) is chosen, and starting in one
of the corners (ix iy 1), the known boundaries and the
already known flows from and to the neighboring volumina
are calculated (Fig. 4). This, for each voxel, results in a flow
balance ix,iy,iz from which the two unknown border flow veloci-
ties vx vy are calculated. At the end of every row the flow
in x direction is known from the wall boundary and the voxel
flow balance nx,iy,iz will be ascribed to the flow in y direction.
At the far corner (ix nx, iy ny), the flow balance nx,ny,iz
should be zero. This criterion is used to check the validity of
the procedure.
RESULTS AND DISCUSSION
Quartz Sand Column
The porosity, or the water content at saturation, re-
spectively, for the quartz sand column is determined by
weighing the dry and the fully saturated column as
Fig. 6. The velocity distribution of the quartz sand column calculated
0.4. The average pore velocity is Vpore 1.5 10 2 mm
s 1, and the dispersion coefficient (D 2.8 10 2 mm2 from the experimental data by the fronttracking algorithm. Gener-
ally, it shows a log-normal form but there is an accumulation at
s 1) is determined by fitting a mobile immobile CDE
very low velocities that correspond to stagnant (immobile) water
model to the experimental breakthrough curve, corre- in the column.
510 J. ENVIRON. QUAL., VOL. 31, MARCH APRIL 2002
Fig. 5. Isoconcentration surface and section of the quartz sand column at times t 4.6 103, 7.1 103, and 9.8 103 s. We see a rather smooth
flow pattern and only slight wall effects. By studying an animation of all timesteps we can recognize small fluctuations at the front, which
average out over time.
refer to http://www.fz-juelich.de/icg/icg-iv/ch/people/ 5% immobile water. This determined distribution is in
khherrmann/tracerfilms.html (verified 26 Sept. 2001) good agreement with results from other flow velocity
for more information. studies (Sedermann et al., 1997, 1998).
The probability distribution of the calculated veloci- For the simulation with PARTRACE the whole col-
ties, using the fronttracking algorithm described in Data umn is not used, only a box-shaped part located com-
Analysis, above, corresponds with a log-normal distribu- pletely inside the column. The result of the tracer trans-
tion with an accumulation of very low velocities (Fig. port simulation (Fig. 7) resembles strongly the monitored
6). This indicates stagnant or immobile water, which transport pattern. This indicates the validity of the simu-
was already detected by fitting a mobile immobile CDE lation approach as well as the validity of the extraction
model to the breakthrough curve, yielding a fraction of of flow parameters by the fronttracking algorithm.
HERRMANN ET AL.: THREE-DIMENSIONAL TRACER TRANSPORT BY MRI 511
Fig. 7. Isoconcentration surface and section of the PARTRACE simulation. As input the experimental velocities of the quartz sand column are
used. The area is not the complete cylindric column but a box-shaped part from the column core due to the calculation method for the vx
and vy components of the velocity field.
Statistical Analysis proportional to the concentration (see Eq. [4]), is taken.
By calculating the variance of the concentration plume
Another access to the dispersion coefficient D is given
for every timestep, and taking the slope as the time de-
by analyzing the statistical moments of the tracer con-
rivative, we find that for the quartz sand column Deff
z
centration (Freyberg, 1986; Kabala and Sposito, 1991,
2.0 10 2 mm2 s 1. Since the CDE model is in this
1994):
parameter range insensitive to small variations of D, there
1 d 2 1 d C()
x
Deff (z z0)2 [9] is a very good accordance between the laboratory scale
z
2 dt 2 dt C0
x column
D, determined by the CDE model, and the one calculated
from the mm-scale tracer concentration variance.
where z0 is the center of the tracer plume and C0 the
total tracer concentration. To calculate the concentra- For further statistical description of the flow proper-
tions, the logarithm of the MRI intensities, which is ties, covariograms are used and correlation lengths are
512 J. ENVIRON. QUAL., VOL. 31, MARCH APRIL 2002
calculated. The covariance is calculated by using the pro-
gram GSLIB (Deutsch and Journel, 1992) according to:
N( h )
1
C(h) z() z( h ) z zh [10]
ui ui
N(h)
i 1
using the expectation values:
N( h )
1
z z() [11]
ui
N(h )
i 1
N( h )
1
zh z( h ) [12]
ui
N( h )
i 1
where h is the difference vector between two positions,
z() is the observable value at that position, and z(ui
ui
h) is the observable value at the position ui h. N(h)
is the total number of possible differences for a given
vector h.
As an example, one resulting covariogram in the y
direction for the vz component (transport direction) of
the flow velocity for the quartz sand column is shown
Fig. 8. Covariogram in y direction for the quartz sand column of the
in Fig. 8. The correlation length in y direction of the vz vz velocity component. The correlation length is determined to be
component was determined to be 1 mm; the correlation
1 mm in the transversal directions and 2 mm in transport direction.
length in the other transversal direction x (not shown)
was also 1 mm. The correlation length in transport di-
rection z was found to be 2 mm (also not shown). As
expected, the correlation length was 10 to 15 times greater
in a porous medium. The spatial resolution and concen-
than the mean particle size of the porous medium.
tration sensitivity is quite sufficient to monitor the flow
even for highly diffusive or dispersive flows, which cause
Glass Bead Column
a high dilution of the tracer. For sufficiently regular flows
the fronttracking algorithm is capable of extracting the
The porosity, or the water content at saturation, for
z component of the velocities from the tracer motion.
the glass bead column was 0.4. The average pore
The statistical properties, a log-normal distribution with
velocity was Vpore 1.5 10 2 mm s 1. A section and
some additional stagnant water, are sensible and in ac-
isoconcentration surface of the glass bead column is
cordance with other velocity-determining experiments.
shown in Fig. 9. A large difference for the finer grained
The simple algorithm to calculate the x and y compo-
quartz sand column is immediately obvious: The flow
nents of the velocities proves to be sufficient to use
pattern in the glass bead column is highly irregular and
dispersive, showing pronounced preferential flow as well the v field as input for the three-dimensional particle
as stagnant areas. The center part of the column shows tracking model PARTRACE. The obtained results for
almost no tracer, which indicates that flow predomi- a flow simulation with PARTRACE are in good agree-
nantly takes place in the finger-like structures of the outer
ment with the original experimental data.
parts of the column. There also develop three finger- By statistical momentum analysis of the concentra-
like areas of stagnant water (tracer). See http://www.
tion, a laboratory scale quantity (Deff) could be related
z
fz-juelich.de/icg/icg-iv/ch/people/khherrmann/tracerfilms.
directly to the mm-scale flow properties for the porous
html (verified 26 Sept. 2001) for an animation of the
media used in this experiment. The strong divergence
transport.
of the glass bead column, which can already be seen in
An analysis with the fronttracking algorithm is not
the flow pattern, is quantified by the momentum analysis.
possible, since a large area of the column (center area)
Geostatistical correlation analysis leads to correlation
does not show a discernible front line at all times. For
lengths that characterize the spatial structure of the po-
this reason, neither the velocity field nor the statistical
rous medium. The correlation lengths can be used for
properties of the velocity are calculable. However, by
a better statistical generation of porous media in com-
an analysis of the spatial moments (Eq. [9]), we find
puter models.
the dispersion coefficient to be Deff 9.3 10 2 mm2
z
s 1 and therefore considerably larger then the one found
Future Plans
for the fine-grained quartz sand. This results in a Peclet
number of Pe 23.6.
The fronttracking algorithm shows poor velocity reso-
lution for low values ( 1 voxel per timestep, i.e., 0.01
mm s 1). A new tracer experiment with higher temporal
CONCLUSIONS
resolution, which can be achieved by sacrificing spatial
Achievements
resolution, could prove advantageous. Also, an MRI
We could prove the MRI FLASH technique to be a technique that can measure all three velocity compo-
very convenient tool for visualizing the motion of Ni2 nents directly would make the crude scheme to gain the
HERRMANN ET AL.: THREE-DIMENSIONAL TRACER TRANSPORT BY MRI 513
Fig. 9. Isoconcentration surface and section of the glass bead column at times t 2.5 103, 5.0 103 , and 1.2 104 s. The isoconcentration
surface is defined as a surface with an identical signal intensity where the higher intensities are enclosed by the surface. This surface is then
displayed by a three-dimensional shading algorithm. The flow shows preferential flow paths as well as stagnant areas.
vx and vy components dispensable. This will be achieved differences between the reactive and the nonreactive
by using diffusion-sensitive sequences and phase-encod- system. Also, the influence of adsorbed nickel on the
ing sequences parallel to the tracer experiments. Further T1 relaxation time of the water hydrogen nucleus would
insight in transport processes could be gained by re- give direct access to sorption processes and their effect
peating the same tracer experiment at a higher pH value on the nickel transport. The nickel quartz system is
(pH 7) at which the nickel should have a strong very suitable for this comparison experiment, since the
adsorption to the quartz sand or glass matrix. Important reactivity of the system can be adjusted by simply chang-
further transport properties can be derived from the ing the solution pH.
514 J. ENVIRON. QUAL., VOL. 31, MARCH APRIL 2002
solute concentration in a heterogenous aquifer. Water Resour.
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