x-ray micro-tomography of pore-scale flow and...
TRANSCRIPT
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X-RAY MICRO-TOMOGRAPHY OF PORE-SCALE FLOW AND TRANSPORT
X-RAY MICRO-TOMOGRAPHY OF PORE-SCALE FLOW AND TRANSPORT
Jan W. Hopmans Volker ClausnitzerUniversity of California
Davis
Dorthe Wildenschild &
Annette Mortensen
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ISSUES:
• Measurements and modeling of water flow and contaminant transport in soils and groundwater are generally macroscopic (spatial scale range of 1 cm to 1 m or larger);
• Fundamental mechanisms occur at microscopic scales ( micrometer or smaller);
• Improved understanding and model predictions require microscopic approach.
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WE HAVE COME AT CROSS ROADS WITHIN PORE-SCALE FLUID
CONTINUUM,
FOR WHICH MEASUREMENTS AND MODELING APPLY TO IDENTICAL
SPATIAL SCALES
Note: It was Bear (1972) that presumed that any attempt to describe in an exact manner the geometry of pores and solid surfaces inside a porous medium is hopeless.
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Detector Plane
Source
X-ray computed micro-tomography (CMT) provides three-dimensional nondestructive and noninvasive measurements of fluid saturation
and concentration at the micro-scale
Pore-scale measurements are being developed so that fundamental processes of flow & transport can be studied at pertinent micro-scale range
AS OPPOSED TO RADIOGRAPHY
(2-dimensional)
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Io (x-rays): Intensity (photons/sec) produced by electron ray tube
Bremstrahlung
Characteristic energy levels (Tungsten target)
1.E-5
1.E-4
1.E-3
1.E-2
1.E-1
1.E+0
1.E+1
0 20 40 60 80 100 120
Photon Energy [keV]
Spec
ific
Bea
m In
tens
ity [p
hoto
ns s
ec-1
eV-1
]
at Source
after 3.2 mm Plexiglas
after 3.2 mm Plexiglas + 2 mm H2O + 3 mm GlassPOLYCHROMATIC
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Detector Plane
Source
Procedure for 3-D imaging:Cone beam with planar Detector Array;Scan object from many different beam directions;By rotating scanning object;Use reconstruction algorithm to solve for µ(x).
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⎛ ⎞⎜ ⎟⎝ ⎠∫oL
I = I exp - µ(x)dx
µ : linear attenuation coefficient, and is equal to the probability that photon is removed from the beam (by either scattering or absorption). It is a function of energy of x-ray
source
Io
I
L
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R2 = 0.9992
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 20 40 60 80 100
c NaI [mg/ml]
µ [c
m-1
]50 keV
60 keV
70 keV80 keV
⎛ ⎞⎜ ⎟⎝ ⎠∫oL
I = I exp - µ(x)dxAttenuation coefficient is a linear function of
electron density.
In practice:
Conduct a priori calibration to estimate soil
density, water content, or soil
solution concentration
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0
0.5
1
1.5
2
2.5
3
0 0.2 0.4 0.6 0.8 1
Object Depth [cm]
Effe
ctiv
e Li
near
Att
enua
tion
Coe
ffic
ient
[cm-1
]
0
10
20
30
40
50
60
Equi
vale
nt M
onoc
hrom
atic
Bea
m E
nerg
y [k
eV]
[keV]
[cm-1]
BEAM HARDENING
For polychromatic radiation, attenuation decreases with penetration depth, due to selected removal of photons of the more strongly attenuated energy levels, hence variations in
attenuation are biased
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Detector:Planar x-ray-sensitive scintillating detector;provides instantaneous 2D radiographic image,that is recorded by CCD camera
Detector Plane
Source
CCD Camera
mirror
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Detector Plane
Source
Beam Geometry: Fan beam (2D)Cone beam (3D)Parallel beam (3D- synchrotron
Voxel size controlled by: source and detector sizephoton fluxacquisition time
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Example of CMT for nondestructive 3D plant root measurements
Experimental Setup
3D Root Image, showing isolines of attenuation
Heeraman, Hopmans andClausnitzer
Plant &Soil, 1997
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Representative Elementary Volume (REV) of glass beads Clausnitzer et al (1999)
Detector Plane
Source
Noninvasive measurement of 3D material attenuation;
Glass bead diameter is 0.5 mm
Spatial resolution: 20 micrometer
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f(α) = φairfair(α) + φglass fglass(α) + φmix fmix(α)
1f dα∞
−∞
=∫
0
5
10
15
20
25
-0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1
α [mm-1]
Rel
ativ
e Fr
eque
ncy
Air Glass
( )air airfφ α
( )glass glassfφ α
( )mixed mixedfφ α
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REV
Representative Elementary Volume (REV) of glass beads (Clausnitzer et al 1999)
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0 1 2 3 4 5 6
L /d p
Poro
sity
↓REV
centered in pore
centered in solid REV
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Pore-scale measurements of solute breakthrough (Clausnitzer et al 2000)
• 5 cm long and 4.76 mm diameter plexiglas flow cell
• After saturation and steady flow rate, 90-minute pulse of 0.1 ml/hr NaI solution was applied
• 3-dimensional scans of 0.44 mm thick slice, about 20 mm below inflow end, were obtained during breakthrough 4.76 mm
5cm
2cm
0.44mm
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CT SCAN of iodide transportSpatial resolution: 20 µm
Nr. of voxels: about 2 million15 scans for a total of 5 hrs
iodide
iodide
4.76 mm
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POTENTIAL FOR WITHIN PORE CONCENTRATION MEASUREMENT
500 micrometer
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SPATIAL DISTRIBUTION OF PORE WATER VELOCITY
Computed from time to peak concentration to pass through each of
17x17 segments
-10
0
10
20
30
40
50
60
0 60 120 180 240 300
Elapsed Time [min]
c NaI
[mg/
ml]
6789
b
-10
0
10
20
30
40
50
60
0 60 120 180 240 300
Elapsed Time [min]
c NaI
[mg/
ml]
310
c
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( , ) ( )poreT A
Mass c t v dAdt= ∫ ∫ x x
Spatial distribution of total mass breakthrough, with decreasing segment size
17 x 17 segments, with 4100 voxels per
segment
Mass balance error: 5%
-10
0
10
20
30
40
50
60
0 60 120 180 240 300
Elapsed Time [min]
c NaI [m
g/m
l]
310
c
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Synchrotron-produced x-rays
High photon flux fluence rate (photons mm-2 sec-1);
Although beam is filtered (monochromator), the fluencerate remains very high;
Thereby allowing high spatial resolutions (micrometer);
And fast transient measurements;
Furthermore, monochromatic beam eliminates beam-hardening;
Experimental results can be compared with Lattice-Boltzmann simulations
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ADVANCED PHOTON SOURCE OF ANL, CHICAGO, IL
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,
BOOSTER,elevating electron energy to 7 billion
electron volts (GeV), about equal to speed of light
Storage Ring of about 1,100 m
High brilliance, up to 100 keV
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GeoSoilEnviroCARS-CAT (13) BeamlineAdvanced Photon Source
Argonne National Laboratory
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Drainage and inhibition of fine sand (median particle size is about 200
micrometer)
1.5 mm
Study of Flow Rate Effects on Water Distribution
www.aps.a
nl.gov/ap
simage/poro
usmediamain.h
tml
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Separate solid from water and air phase, and
estimate interfacial areas
IMAGE PROCESSING
6 mm
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Solid Grain
Pore Space
LATTICE BOLTZMANN SIMULATIONS
(Don Zhang et al, Geophys Res Letters, 2000)
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• Unique capabilities (advantages):– Quantitatively incorporates pore-scale physical and
chemical processes– For arbitrarily complex pore space geometries– Allows direct computation of system characteristics
(e.g., permeability, dispersion)
• Unique capabilities (advantages):– Quantitatively incorporates pore-scale physical and
chemical processes– For arbitrarily complex pore space geometries– Allows direct computation of system characteristics
(e.g., permeability, dispersion)
• Links microscale physics to macroscaleprocesses
• Links microscale physics to macroscaleprocesses
LATTICE BOLTZMANN SIMULATIONS
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Neutron Radiography& Computed Tomography
Gadolinium control rods
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2.0 x2.0 cm triangular aluminum sample holders
Increasing water saturation
Increasing thickness
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Attenuation - Saturation
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0 20 40 60 80 100 120 140 160 180
Attenuation
Satu
ratio
n [v
/v%
]
12.3 mm15.4 mm25.4 mm30.7 mm20.1 mm6.8 mm9.0 mm11.0 mm
AttenuationVolumet
ric
Wat
er C
onte
nt 1 cm thick soil sample
2 cm thick
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Fast Neutron Tomography
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OPPORTUNITIES ? ? ? ? ?
Development of micro tomography capabilities is approaching spatial and time scales that control flow and transport;
Capabilities are becoming such that physical, chemical and biological processes at solid-liquid and liquid-gas interfaces can be measured;
This is especially true for high photon fluxes, such as provided by synchrotron;
THERE ARE PLENTY ! ! ! ! ! ! !