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
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.
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.
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)
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
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).
⎛ ⎞⎜ ⎟⎝ ⎠∫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
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
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
Detector:Planar x-ray-sensitive scintillating detector;provides instantaneous 2D radiographic image,that is recorded by CCD camera
Detector Plane
Source
CCD Camera
mirror
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
Example of CMT for nondestructive 3D plant root measurements
Experimental Setup
3D Root Image, showing isolines of attenuation
Heeraman, Hopmans andClausnitzer
Plant &Soil, 1997
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
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
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
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
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
POTENTIAL FOR WITHIN PORE CONCENTRATION MEASUREMENT
500 micrometer
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
( , ) ( )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
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
ADVANCED PHOTON SOURCE OF ANL, CHICAGO, IL
,
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
GeoSoilEnviroCARS-CAT (13) BeamlineAdvanced Photon Source
Argonne National Laboratory
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
Separate solid from water and air phase, and
estimate interfacial areas
IMAGE PROCESSING
6 mm
Solid Grain
Pore Space
LATTICE BOLTZMANN SIMULATIONS
(Don Zhang et al, Geophys Res Letters, 2000)
• 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
Neutron Radiography& Computed Tomography
Gadolinium control rods
2.0 x2.0 cm triangular aluminum sample holders
Increasing water saturation
Increasing thickness
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
Fast Neutron Tomography
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 ! ! ! ! ! ! !