Yoshito Nakashima

Mathematica Programs for the Analysis of Three-Dimensional Pore Connectivity and Anisotropic Tortuosity of Porous Rocks using X-ray Computed Tomography Image Data

Understanding of the transport properties of porous rocks is important for safe nuclear waste disposal because harmful contaminated groundwater can migrate along pore spaces over long distances. We developed three original Mathematica® version 5.2 programs to calculate the transport properties (porosity, pore connectivity, surface-to-volume ratio of the pore space, and anisotropic tortuosity of the pore structure) of porous rocks using three-dimensional (3-D) 8-bit TIFF or BMP X-ray computed tomography (CT) images. The pre-processing program Itrimming.nb extracts a 3-D rectangular region of interest (ROI) from the raw CT images. The program Clabel.nb performs cluster-labeling processing of the pore voxels in the ROI to export volume, surface area, and the center of gravity of each pore cluster, which are essential for the analysis of pore connectivity. The random walk program Rwalk.nb simulates diffusion of non-sorbing species by performing discrete lattice walks on the largest (i.e., percolated) pore cluster in the ROI and exports the mean-square displacement of the non-sorbing walkers, which is needed to estimate the geometrical tortuosity and surface-to-volume ratio of the pore. We applied the programs to microfocus X-ray CT images of a rhyolitic lava sample having an anisotropic pore structure. The programs are available at http://www.jstage.jst.go.jp/browse/jnst/44/9/ and http://staff.aist.go.jp/nakashima.yoshito/progeng.htm to facilitate the X-ray CT approach to groundwater hydrology.

Three-dimensional study on the interconnection and shape of crystals in a graphic granite by X-ray CT and image analysis

Abstract The technique of investigating 3-dimensional interconnections and the shapes of crystals in a rock by X-ray computerized tomography (CT) and image analysis was developed using a graphic granite specimen as an example. Fifty 2-dimensional tomographic images (slices) of the graphic granite were obtained ‘non-destructively’ using a medical X-ray CT scanner. Since a CT value of the specimen was decreased with increasing cross-sectional sample area by the effect of beam-hardening, the CT value was corrected using the area of each slice. Binary images of the slices were made comparing one of them with a thin-section of the slice. Using the binary images, connection analysis of quartz rods in the graphic granite specimen was performed on the basis of percolation theory (cluster labelling). This analysis showed that at least 89.9% of the quartz rods were connected in three dimensions. Furthermore, the 3-dimensional shape of the quartz rods was analysed using the 2-point correlation function calculated from the binary images. The average shape of the quartz rods was obtained by fitting an ellipsoid to the high-value region of the 2-point correlation function. The elongation axis of the ellipsoid agreed well with the crystallographic c-axes of the quartz rods.

Pulsed field gradient proton NMR study of the self-diffusion of H2O in montmorillonite gel: Effects of temperature and water fraction

Abstract Self-diffusion coefficients of water molecules (H2O) in Na-montmorillonite gel were measured as a function of water fraction (54.8 to 100 wt%) and temperature (30.4 to 60.0 °C) using proton nuclear magnetic resonance (NMR). Spin-echo pulse sequences with magnetic field gradient pulses for the diffusion measurement were applied to the montmorillonite gel at the Larmor frequency of 20 MHz. The self-diffusion coefficient, D, of H2O in the clay gel is expressed phenomenologically by ln(D/D0) = 1.77{exp[0.0798(w − 100)] − 1}, where D0 is the water diffusivity in bulk water and w is the water fraction of the gel (wt%). The data for w > 84.7 wt% can be explained by a theoretical diffusion model for the randomly distributed clay grains. The activation energy of the water diffusivity in the montmorillonite gel was nearly equal to that in bulk water, so the normalized diffusivity, D/D0, obeys the temperature-independent master curve. The transition from the free diffusion to the restricted diffusion was not observed for gradient pulse intervals ranging from 5 to 120 ms. This indicates that the average pore size of the gel is much smaller than a few tens of micrometers, so the random walk trajectory of water molecules in the gel is geometrically restricted by the packing of clay mineral grains. Water diffusivity higher than that of the present NMR study was found by computer simulations and neutron scattering experiments in which effects of bound water were considered but those of the tortuosity of the grain packing were neglected. Thus, the predominant factor controlling the diffusivity in the NMR experiments is not the bound water near the clay surface but the geometrical tortuosity of the packing of clay mineral grains.

Nondestructive three-dimensional element-concentration mapping of a Cs-doped partially molten granite by X-ray computed tomography using synchrotron radiation

Abstract Nondestructive, three-dimensional (3-D) element-concentration mapping was performed and high spatial resolution and quantitative applicability were demonstrated. X-ray computed tomography using synchrotron radiation developed at SPring-8 (SP-μCT) enabled us to acquire high-resolution tomographic images with X-ray energies just above and below the absorption edge of an element. Concentration of the element could be calculated from the difference of these images with a correction using standard material. A 3-D Cs concentration map of a partially molten granite was obtained by this technique and compared with a 2-D element map produced by an electron-probe X-ray microanalyzer (EPMA), with respect to spatial and compositional resolution. A spatial resolution of about 20 μm was achieved by SP-μCT. The compositional resolution of ± 2.5 wt% was achieved using the following two calibration processes of linear attenuation coefficients (LAC): (1) calibration based on the empirical relationship between theoretical LACs and observed CT values, and (2) the calibration of spatial variation of observed mass attenuation coefficients (MAC) due to X-ray energy shift using a standard material (Cs-bearing solution). Using the Cs2O map obtained by SP-μCT, 3-D image analysis was demonstrated, for example, connectivity of melt was calculated and it was found that 88 vol% of melt was connected in three dimensions in the sample. Furthermore, the possibility of 3-D diffusion studies by SP-μCT was discussed based on the spatial and compositional resolutions. This “nondestructive” and “3-D” mapping technique can reveal the internal compositional distribution of precious samples such as extraterrestrial materials and cultural assets, and can solve many 3-D issues such as material transport in geological and industrial materials.

Nuclear Magnetic Resonance Properties of Water-Rich Gels of Kunigel-V1 Bentonite

Kunigel-V1 bentonite was analyzed by proton nuclear magnetic resonance (NMR) spectroscopy over a wide range of water content and temperature at 0.47 T. Kunigel-V1 is a bentonite clay consisting of ~50 wt% Na-rich montmorillonite from Yamagata, Japan, and represents a candidate for engineered barriers of underground nuclear waste disposal sites in Japan. The NMR-related properties of bentonite are also important with respect to application of the material as a mud in boreholes for NMR well logging in the geophysical exploration of disposal sites. The proton relaxation times, surface relaxivity of montmorillonite, and H2O self-diffusion coefficient, were determined in this study for water-rich gel samples of bentonite at 11.0 to 70.0°C and for bentonite weight fractions of 0 to 37.7 wt%. The proton relaxation times (T1 and T2) were measured by the inversion recovery method and Carr-Purcell-Meiboom-Gill method, respectively, and the self-diffusion coefficient of H2O molecules (D) was measured by the pulsed-gradient spin-echo method. The results showed that T1, T2, and D increased with increasing temperature, and decreased with increasing bentonite weight fraction (w). The T1 and T2 surface-relaxivities were on the order of 10–7 m/s and also decreased with temperature. The activation energies of the T1 and T2 relaxation for the bentonite gels were significantly lower than those for bulk water (i.e., about 50 to 70%), whereas the activation energy of the diffusion process for the gels was nearly equal to that for bulk water. As a result, the normalized H2O self-diffusivity, D/D 0, obeys a temperature-independent master curve described by In(D/D 0)=1.54[exp(—0.0377w)— 1], where D 0 is D in bulk water and w is in wt%.

Diffusivity measurement of heavy ions in Wyoming montmorillonite gels by X-ray computed tomography.

Medical X-ray computed tomography (CT) was applied to the measurement of the diffusion coefficients of heavy ions in an artificial barrier material for the disposal of nuclear wastes. Cs(+), Sr(2+), I(-), and Br(-) are the heavy ions measured and the barrier used is the water-rich gel of Wyoming montmorillonite (86.5-100 wt.% H(2)O). X-ray CT yields an inevitable artifact (beam-hardening) in the obtained images. Before the diffusion experiments, the polychromatic primary X-ray spectrum of the CT scanner was measured by a CdZnTe detector, and the effects of the artifact were examined for an aqueous CsCl solution sample. The results show that the beam-hardening artifact derived from the polychromatic photon energy distribution can be suppressed by applying a special image reconstruction method assuming the chemical composition of samples. The transient one-dimensional diffusion of heavy ions in a plastic container filled with the gel was imaged nondestructively by the X-ray CT scanner with an in-plane resolution of 0.31 mm and slice thickness of 2 mm. The results show that diffusivities decrease with increasing clay weight fraction. The degree of the diffusivity decrease was high for cations (Cs(+) and Sr(2+)) and low for anions (I(-) and Br(-)). The quantitative decomposition of the contribution of the geometrical tortuosity and of the sorption to the diffusivity was performed by subtracting the diffusivity of nonsorbing I(-) from the measured diffusivities. The results show that the contribution of the sorption is large for Cs(+), Sr(2+) and small for Br(-). Because X-ray CT allows nondestructive and quick measurements of diffusivities, the technique would be useful particularly for measuring the diffusive migration of harmful radioactive elements.

Effects of clay fraction and temperature on the H2O self-diffusivity in hectorite gel : A pulsed-field-gradient spin-echo nuclear magnetic resonance study

Self-diffusion coefficients of H2O molecules in Na-rich hectorite gel were measured by ’H nuclear magnetic resonance (NMR), Spin-echo pulse sequences with magnetic field gradient pulses for the translational diffusion measurement were applied to the hectorite gel at the Larmor frequency of 20 MHz. Effects of clay fraction (0-51.2 wt. %) and temperature (20.0-60.3°C) were studied. The results show: (1) Phenomenologically, the self-diffusion coefficient, D, of 1H2O in the clay gel is expressed by the normalized diffusivity, D/D0 = exp(−0.0257w), where D0 is the water self-diffusivity in bulk water at temperature and w is the weight fraction of the hectorite (wt. %). (2) The activation energy of H2O diffusivity in the hectorite gel is nearly equal to that in bulk water. Hence, the normalized diffusivity, D/D0, obeys a temperature-independent curve. (3) The exponential dependence of D/D0 on w for w <30 wt. % is explained by a random-walk model, in which free or unbound H2O molecules migrate in the geometrically complex and tortuous pore structure of randomly scattered clay-mineral grains.

DIFFUSION OF H2O IN SMECTITE GELS: OBSTRUCTION EFFECTS OF BOUND H2O LAYERS

In water-rich smectite gels, bound or less mobile H2O layers exist near negatively-charged clay platelets. These bound H2O layers are obstacles to the diffusion of unbound H2O molecules in the porespace, and therefore reduce the H2O self-diffusion coefficient, D, in the gel system as a whole. In this study, the self-diffusion coefficients of H2O molecules in water-rich gels of Na-rich smectites (montmorillonite, stevensite and hectorite) were measured by pulsed-gradient spin-echo proton nuclear magnetic resonance (NMR) to evaluate the effects of obstruction on D. The NMR results were interpreted using random-walk computer simulations which show that unbound H2O diffuses in the gels while avoiding randomly-placed obstacles (clay platelets sandwiched in immobilized bound H2O layers). A ratio (volume of the clay platelets and immobilized H2O layers)/(volume of clay platelets) was estimated for each water-rich gel. The results showed that the ratio was 8.92, 16.9, 3.32, 3.73 and 3.92 for Wyoming montmorillonite (⩽ 5.74 wt.% clay), Tsukinuno montmorillonite (⩽ 3.73 wt.% clay), synthetic stevensite (⩽ 8.97 wt.% clay), and two synthetic hectorite samples (⩽ 11.0 wt.% clay), respectively. The ratios suggest that the thickness of the immobilized H2O layers in the gels is 4.0, 8.0, 1.2, 1.4 and 1.5 nm, respectively, assuming that each clay particle in the gels consists of a single 1 nm-thick platelet. The present study confirmed that the obstruction effects of immobilized H2O layers near the clay surfaces are important in restricting the self-diffusion of unbound H2O in water-rich smectite gels.

DIFFUSION OF H2O AND I− IN EXPANDABLE MICA AND MONTMORILLONITE GELS: CONTRIBUTION OF BOUND H2O

Self-diffusion coefficients of H2O molecules in water-rich gels of Na-rich expandable mica synthesized using natural talc were measured by pulsed-gradient spin-echo 1H nuclear magnetic resonance (NMR), and the dependence on mica fraction (0.00–43.8 wt.%) and temperature (30.0–60.9°C) was examined. On the basis of the NMR results, the self-diffusion coefficient of H2O, Dwater, in the gel can be expressed by ln(Dwater/D0water) = 1.64[exp( −0.0588w) - 1], where D0water is the self-diffusivity of bulk water at temperature and w is the weight fraction of the mica (wt.%). The activation energy of H2O diffusivity in mica gel is nearly equal to that in bulk water. These findings indicate that the normalized diffusivity, Dwater/D0water, is independent of temperature. The diffusivity of I−, Diodine, in the gels was examined by X-ray computed tomography (CT) at 22°C, and the influence of the mica fraction (0.00–24.8 wt.%) was studied to determine the contribution of bound H2O. The X-ray CT results show that the normalized I− diffusivity, Diodine/D0iodine, obeys the above-mentioned phenomenological curve where D0iodine is the I− diffusivity in bulk water. I− is non-sorbing, and thus its diffusion is restricted only by the geometrical complexity of the pore structure of gels. Therefore, the effect of bound H2O molecules on average H2O diffusivity is negligible for w <24.8 wt.%. Diffusivity is governed by free or unbound H2O molecules diffusing in the geometrically complex and tortuous pore structure of mica-mineral grains. This is a result of the large population of unbound H2O far from the grain surface compared to the small population of bound H2O near the grain surface. The diffusion of I− ions in montmorillonite gels was examined by X-ray CT for w <16.7 wt.% montmorillonite. The normalized iodine diffusivity, (Diodine/D0iodine) obtained is in reasonably close agreement with the literature data for the normalized diffusivity of H2O and is similar to the master curve of expandable mica. Therefore, bound H2O molecules near negatively charged clay surfaces do not play a major role in the H2O diffusivity for water-rich montmorillonite gels.

Three-dimensional miarolitic cavity distribution in the Kakkonda granite from borehole WD-1a using X-ray computerized tomography

Abstract Three-dimensional imaging of a granite core from the borehole WD-1a, drilled at the Kakkonda geothermal field, NE Japan, was performed by X-ray computerized tomography (CT). The CT images displayed miarolitic cavities (possible geothermal reservoir), felsic minerals, mafic minerals, and enclaves in the granite. Voxels with CT numbers less than 1500 were estimated to be the miarolitic cavities on the basis of (i) the CT imaging of the synthetic glass tubes, and (ii) the detailed comparison between the CT image and the cut surface of the rock sample. A three-dimensional distribution of miarolitic cavities was reconstructed from a set of contiguous two-dimensional CT images and showed a spatially heterogeneous distribution with a boundary that strikes N 20° E. This trend is probably important as the regional distribution of the geothermal reservoir, which demonstrates that X-ray CT is a powerful tool in geothermal studies. Chemical fluctuations of Na and K were found around the miarolitic cavity zone. This may be useful for finding miarolitic cavity zones without coring.