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 ! ! ! ! ! ! !