X-RAY MICRO-TOMOGRAPHY OF PORE-SCALE FLOW AND TRANSPORT. University of California Davis. Dorthe Wildenschild & Annette Mortensen

Transcription

1 X-RAY MICRO-TOMOGRAPHY OF PORE-SCALE FLOW AND TRANSPORT Jan W. Hopmans University of California Davis Volker Clausnitzer Dorthe Wildenschild & Annette Mortensen

2 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.

3 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.

4 X-ray computed micro-tomography (CMT) provides three-dimensional nondestructive and noninvasive measurements of fluid saturation and concentration at the micro-scale AS OPPOSED TO RADIOGRAPHY Source (2-dimensional) Detector Plane Pore-scale measurements are being developed so that fundamental processes of flow & transport can be studied at pertinent micro-scale range

5 I o (x-rays): Intensity (photons/sec) produced by electron ray tube Characteristic energy levels (Tungsten target) Specific Beam Intensity [photons sec -1 ev -1 ] 1.E+1 1.E+0 1.E-1 1.E-2 1.E-3 POLYCHROMATIC 1.E-4 1.E-5 at Source after 3.2 mm Plexiglas after 3.2 mm Plexiglas + 2 mm H2O + 3 mm Glass Photon Energy [kev] Bremstrahlung

6 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). Source Detector Plane

7 I=Iexp - µ(x)dx o L I I o L 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

8 I = I oexp - µ(x)dx L Attenuation coefficient is a linear function of electron density. In practice: Conduct a priori calibration to estimate soil density, water content, or soil solution concentration µ [cm -1 ] kev 60 kev R 2 = kev 80 kev c NaI [mg/ml]

9 BEAM HARDENING 3 60 Effective Linear Attenuation Coefficient [cm -1 ] [cm -1 ] [kev] Equivalent Monochromatic Beam Energy [kev] Object Depth [cm] 0 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

10 Detector: Planar x-ray-sensitive scintillating detector; provides instantaneous 2D radiographic image, that is recorded by CCD camera Source Detector Plane mirror CCD Camera

11 Beam Geometry: Fan beam (2D) Cone beam (3D) Parallel beam (3D- synchrotron Source Detector Plane Voxel size controlled by: source and detector size photon flux acquisition time

12 Example of CMT for nondestructive 3D plant root measurements 3D Root Image, showing isolines of attenuation Experimental Setup Heeraman, Hopmans and Clausnitzer Plant &Soil, 1997

13 Representative Elementary Volume (REV) of glass beads Clausnitzer et al (1999) Noninvasive measurement of 3D material attenuation; Glass bead diameter is 0.5 mm Spatial resolution: 20 micrometer Source Detector Plane

14 f(α) = φ air f air (α) + φ glass f glass (α) + φ mix f mix (α) 25 φ air fair ( α) fdα= 1 Relative Frequency Air Glass φ glass fglass ( α) 5 0 φ mixed mixed f ( α) α [mm -1 ]

15 Representative Elementary Volume (REV) of glass beads (Clausnitzer et al 1999) centered in pore 0.50 Porosity centered in solid REV REV REV L /d p

16 Pore-scale measurements of solute breakthrough (Clausnitzer et al 2000) 5 cm long and 4.76 mm diameter plexiglas flow cell 2cm After saturation and steady flow rate, 90- minute pulse of 0.1 ml/hr NaI solution was applied 0.44mm 5cm 3-dimensional scans of 0.44 mm thick slice, about 20 mm below inflow end, were obtained during breakthrough 4.76 mm

17 CT SCAN of iodide transport Spatial resolution: 20 µm Nr. of voxels: about 2 million 15 scans for a total of 5 hrs iodide e 4.76 mm

18 POTENTIAL FOR WITHIN PORE CONCENTRATION MEASUREMENT 500 micrometer

19 SPATIAL DISTRIBUTION OF PORE WATER VELOCITY c NaI [mg/ml] b c Elapsed Time [min] 40 c NaI [mg/ml] Elapsed Time [min] Computed from time to peak concentration to pass through each of 17x17 segments

20 Spatial distribution of total mass breakthrough, with decreasing segment size cnai [mg/ml] c Elapsed Time [min] Mass = c( x, t) v( x) dadt T A pore 17 x 17 segments, with 4100 voxels per segment Mass balance error: 5%

21 Synchrotron-produced x-rays High photon flux fluence rate (photons mm -2 sec -1 ); Although beam is filtered (monochromator), the fluence rate remains very high; Thereby allowing high spatial resolutions (micrometer); And fast transient measurements; Furthermore, monochromatic beam eliminates beamhardening; Experimental results can be compared with Lattice- Boltzmann simulations

22 ADVANCED PHOTON SOURCE OF ANL, CHICAGO, IL

23 , 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

24 GeoSoilEnviroCARS-CAT (13) Beamline Advanced Photon Source Argonne National Laboratory

25 Drainage and inhibition of fine sand (median particle size is about 200 micrometer) 1.5 mm Study of Flow Rate Effects on Water Distribution

26 6 mm IMAGE PROCESSING Separate solid from water and air phase, and estimate interfacial areas

27 LATTICE BOLTZMANN SIMULATIONS (Don Zhang et al, Geophys Res Letters, 2000) Pore Space Solid Grain

28 LATTICE BOLTZMANN SIMULATIONS 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 macroscale processes

29 Neutron Radiography & Computed Tomography Gadolinium control rods

30

31 Increasing thickness Increasing water saturation 2.0 x2.0 cm triangular aluminum sample holders

32 2 cm thick 0.35 Attenuation - Saturation Volumetric Water Content Saturation [v/v%] Attenuation Attenuation 1 cm thick soil sample 12.3 mm 15.4 mm 25.4 mm 30.7 mm 20.1 mm 6.8 mm 9.0 mm 11.0 mm

33 Fast Neutron Tomography

34 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!!!!!!!