Clay plays a prominent role as barrier material in the geosphere. The small
particle sizes cause extremely small pore sizes and induce low permeability
and high sorption capacity. Transport of dissolved species by molecular
diffusion, driven only by a concentration gradient, is less sensitive to the
pore size. Heterogeneous structures on the centimetre scale could cause
heterogeneous effects, like preferential transport zones, which are difficult
to assess. Laboratory measurements with diffusion cells yield limited
information on heterogeneity, and pore space imaging methods have to consider
scale effects. We established positron emission tomography (PET), applying a
high-resolution PET scanner as a spatially resolved quantitative method for
direct laboratory observation of the molecular diffusion process of a PET
tracer on the prominent scale of 1–100 mm. Although PET is rather insensitive to bulk effects,
quantification required significant improvements of the image reconstruction
procedure with respect to Compton scatter and attenuation. The experiments
were conducted with
Natural clay typically has a heterogeneous composition and a spatially variant anisotropic structure. Due to grain sizes of the clay fraction in the micrometre range, pore sizes are extremely small. This effectively inhibits advective flow and causes high internal surface area, forming natural geological barriers. However, natural sediments have to be considered as heterogeneous material. In particular, in Opalinus Clay (OPA) we not only observe heterogeneity on the micrometre scale (Keller et al., 2011), but also laminations and concretions on the millimetre scale (Fig. 1) which potentially provide either preferential diffusion pathways or specific sorption sites, respectively. Therefore, standard millimetre-sized samples in diffusion cell experiments cannot be considered as homogeneous. As smallest possible size of the representative elementary volume (REV), we consider the size of standard drill cores because their size is just above the largest observed heterogeneities. It still is an unanswered question as to whether a REV exists beyond which the material may be considered as homogeneous, or whether analogical heterogeneities exist on larger scales.
Left: OPA drill core before it is embedded in resin (“plug size”
refers to the dimensions of the
Global result of the MC simulations. Left: line source in Opalinus
Clay, filled with
This question is relevant for a number of safety cases because clay layers are generally considered as a geological barrier for the safe enclosure of hazardous substances. Preferential zones with higher diffusion rates generally are less tortuous, which also means a smaller effective internal surface area. Therefore, these zones delimit the barrier function both by increased diffusion rate and decreased retention, which have to be considered as a worst case scenario.
Determination of these heterogeneous parameters with common diffusion-cell
experiments is one possible approach, but it is laborious and requires a
large number of studies in order to match these delimiting zones (Van Loon et
al., 2004). Another approach is based on the detailed characterization of the
pore space using multiscale imaging, applying X-ray
We introduced a method for quantitative visualization of the diffusing species (Kulenkampff et al., 2015), which can serve as an experimental complement and for the verification of structural models. We applied positron emission tomography (PET) as a totally selective and the most sensitive imaging method for positron-emitting radionuclides. PET responds to the spatial distribution of positron decay events, which are detected as coinciding antiparallel photons with energy of 511 keV. The mass attenuation is at a minimum in this energy range, which allows the reconstruction of the spatial distribution of positron decay events in rock samples up to diameters of 100 mm.
Since the introduction of PET as clinical imaging modality, a number of PET studies have been published on fluid flow in rocks, including dispersion phenomena (e.g. Kulenkampff et al, this issue). These studies have been conducted generally with short-living PET tracers and clinical PET scanners with rather low spatial resolution. Our application of non-standard long-living PET tracers and a high-resolution scanner, which was originally designed for biomedical research, is a means for long-term studies at higher spatial resolution. This is a prerequisite for monitoring slow molecular diffusion processes without other driving forces than the concentration gradient of the tracer.
However, strong blurring effects of Compton scattering and attenuation of the 511-keV-radiation have to be considered, which could delimitate the significance of the method. Earlier, we identified these effects as an issue that must be considered with regard to quantification of the tracer concentration (Zakhnini et al., 2013); the resulting images rather had to be considered as qualitative. Scattering and some deficiencies of the reconstruction procedure had caused blurring and imaging artefacts, and the fit of a conceptual diffusion model to these data had produced unexplainable high-diffusion coefficients (Kulenkampff et al., 2012). These issues could be solved to a large extent with a proper scatter correction procedure that is outlined in this article, and we are now able to make quantitative use of it.
An OPA horizontal drill core (diameter 100 mm, length 80 mm) from Mont Terri was cast in epoxy resin (Fig. 1). The sample is not considered to be undisturbed because fracturing due to the stress release and drying during storage is probable. This situation is representative rather of the excavation damage zone than of undisturbed host rock in the far field.
Perpendicular to the bedding, an axillar blind hole (diameter 5 mm,
length 50 mm) was drilled into the core and filled with synthetic OPA
porewater (Pearson et al., 2003). After an equilibration period, which
included observations using
We applied a ClearPET scanner manufactured by Raytest (Sempere Roldan et
al., 2007). This is a high-resolution PET scanner, designated for biomedical
research on small animals, that was originally developed by the Crystal Clear
Collaboration (
The raw PET data are projections of the spatial tracer distribution. These projections correspond to lines of response (LORs) connecting the detection points of the antiparallel photon pair that was transmitted by the annihilating positron–electron pair. These photons undergo attenuation and Compton scattering, which are both controlled by the mass attenuation coefficient, which depends directly on material density. Because the density of geomaterials is considerably higher than of biological tissue, we have to consider corrections for these effects more thoroughly than in common biomedical or clinical PET applications. Details of the method are reported in Kulenkampff et al. (2016). Here, we focus on the implementation and calibration of the scatter correction procedure, which showed significant impact on the experimental results.
In Zakhnini et al. (2013), we applied a Monte Carlo (MC) simulation
procedure for determining the impact of scattered events and for developing
a tentative correction procedure. This procedure is extremely demanding with
respect to computing resources and takes at least several hours for each
image. The MC simulations were conducted with the open-source simulation
platform GATE (Jan et al., 2004). Input parameters are scanner geometry,
sample geometry (“phantom”), material parameters, and source parameters.
The source parameters include geometry, activity, and the significant
contributions of the decay spectrum of the particular nuclides. In addition
to the experimentally applied nuclides
In contrast to the real physical world, MC provides a means to study the
history of all recorded events, from the positron decay to the detection.
This includes a comprehensive parametrization of scattering, taking into
account the magnitude and origins of scatter, and the distributions of
energy, the order of scatter, and scattering angles. We also studied the
effects of different potential PET nuclides because different initial
positron energies and additional gamma radiation have different impacts on
the recorded data. We have to distinguish
The global MC results with respect to the nuclides are depicted in Fig. 2.
It should be noted that all parameters are functions of both PET nuclide
and matrix material. Comparison of the data sets with a
The mean order of scattering (number of Compton interactions per registered
coincidence) is more than 3; therefore the premises for single-scatter
modelling as a basis for a scatter correction procedure are not satisfied, and
the applicability has to be verified. However, the mean scatter angle is in
the range of small-angle scattering (below 10
Relative number of scatter corrected coincidences
In contrast to the preceding paper (Zakhnini et al., 2013), we abandoned the version 1.4 of STIR, which was the originally supplied image reconstruction library, and switched to the recent version 3.0 (Thielemans et al., 2012). As before, we applied corrections for random coincidences and attenuation. The normalization process was improved according to Weber et al. (2006) in order to better consider the effect of void bins in the projections caused by the gaps between the detectors.
The most recent version of the reconstruction software, since STIR 2.1 (Tsoumpas et al., 2004), supplies a simpler and faster analytical scatter modelling method than MC that is based on Watson et al. (1996). It is an approximation of the deviations of the coincidences along each LOR according to the Klein–Nishina equation for Compton scatter. Scatter correction of multiple time frames becomes practicable with an optimized procedure that typically requires 30 min on a standard CPU for each frame.
This single scatter simulation algorithm (SSS) does not account for multiple scattered events and scatter from sources and scatter points outside the field of view (FOV). It requires the distribution of mass attenuation coefficients, as a measure of the scatter cross section, and an estimate of the source, usually an uncorrected image, as input data. Multiple scattering is approximately considered by scaling of the scatter estimate and by iterative application of the procedure (Polycarpou et al., 2011). The customary calibration of the SSS correction is then conducted by fitting the simulated scatter events to the measured events outside the region of the source distribution. Because of the large number of void bins in this marginal region of the FOV of the ClearPET scanner, this method is unreliable. We therefore take advantage of the results of the MC simulations, with which we are able to determine the scatter fraction SF quantitatively, and vary the scaling factor of the SSS iteratively until the scatter fraction from the MC simulation is matched (Fig. 3). In order to avoid overcompensation of the scatter, we assume a target value which is 10 % lower than the simulated scatter fraction because the simulation includes additional sources of scatter (e.g. in the detector crystals and in material outside the FOV).
Intensity
20 PET frames of
Maximum, 99.9, and 90 % quantiles of the amplitude vs. frame time of Fig. 5. The colour scale in Fig. 5 refers to the maximum value.
Vertical slices and axial projection of selected frames of Fig. 5,
with uniform colour scale. At
In order to calibrate the scatter correction model, we thus either need an estimate of the scatter fraction, which is the result of one single MC simulation of a rough model, or we consider a standard calibration factor of 5 for our scanner as a conservative estimation.
The outcome of the SSS is in general accordance with the result of the
MC simulation. We reconstructed images from the MC data sets:
all true coincidences tot (no scatter correction) unscattered unsc (reference image) only scattered coincidences sc SSS-corrected with scaling factor 5 and 10.
In Fig. 4 we computed the circular mean values of the axial projections of
these images, yielding the intensity vs. the radial distance from the
central line source in clay. The impact of scattering becomes clear at
distances above 5 mm, and without scatter correction, the intensity becomes
dominated by scatter (tot and sc). The SSS correction scaled with a factor 10,
which is the intersection point in Fig. 3, yields data below the line of the
reference image, which therefore are overcorrected. With a factor 5 they are
undercorrected, and scatter effects dominate in regions far from the
source. We assume that this is the region of high scattering angles and
multiple scatter that is not considered by the SSS algorithm. It should be
noted that the ordinate of Fig. 4 is scaled logarithmically, and that these
deviations are more than 2 orders below the source intensity. We recommend
slight undercorrection to avoid the creation of additional void bins.
Axial maximum projection of frame 9 (27 days), when the tracer distribution reached the circumference.
15 PET frames of
As example, we report the measurements on one sample (BLT 137/3): Beginning
daily, with increasing time lag, we produced a sequence of 20 PET images
over a period of 150 days until the tracer was roughly equally distributed
over the core (Fig. 5) (
Figure 8 is an enlargement of the maximum projection of frame 9, after 1
month and just before the spreading reaches the circumference of the sample.
The shape of this distribution appears as a roughly 10 mm thick rectangular
block, rather than as a smooth anisotropy ellipsoid, notwithstanding
remaining indications of circular artefacts. This type of shape could be
interpreted as an indication of diffusion along fine layering, rather than
homogenous transversal anisotropic behaviour. However, these findings should
be confirmed by additional investigations (e.g.
Prior to the investigations with
In the past we have experienced problems with the correction methods that had been supplied with the scanner because these had been designed for material with low attenuation and scatter. Attenuation model and scatter correction had been derived from measured data, a procedure that increased the noise level unacceptably. Instead, we implemented a method which is based upon attenuation and scatter modelling. Their establishment is simple because of the plain geometry of the samples. The expedience of the STIR-SSS for scatter modelling has been proven with MC simulations, and calibration factors have been found.
With these corrections we could reconstruct clear and sharpened images which
retained a minimum scatter component. Features became visible that had been
covered by blurring effects, and new levels of detail were identified. A gas
bubble became clearly distinguishable. The extension of the tracer cloud,
which had been apparently widespread due to scatter effects, became
localized and bounded. An optimum fit of an updated finite-element model now
yields anisotropic diffusion coefficients in the range of literature results
(
Maximum, 99.9, and 90 % quantiles of the amplitude of Fig. 9 vs. frame time of Fig. 9. The colour scale in Fig. 9 refers to the maximum value.
We fitted anisotropy ellipses to the axial projections of the data in order
to determine direct experimental anisotropy parameters and to estimate the
propagation velocity of the tracer front. The position of this front was
defined as the location of the FWHM line (full width half maximum). From
Fig. 11 we read a propagation velocity of 0.5 and 2 mm d
We also computed the ratio
Lengths of the major axes of the FWHM vs. frame time (red: fast
axis, green: slow axis) of the
Left: axial projection of the activity distribution with elliptical fit of the FWHM curve of the ninth frame after 27 days (see Fig. 8). Right: temporal evolution of the ratio of the major anisotropy axis.
Figure 8 may explain this situation. Here, the amplitude distribution appears as a roughly rectangular region with a thickness of about 2 cm, rather than as a lineament. Therefore the anisotropic behaviour could be caused by a thin layer with elevated diffusion properties.
It is not yet possible to compare these findings with structural
As heterogeneous effects are controlled by the topology of the pathways, they are only observable on sufficiently large samples. Nevertheless, these effects should be taken into account for transport simulations on the field scale because preferential diffusion zones could accelerate diffusional transport, not only by increased directional transport. Zones which are not effectively taking part in the diffusional transport process are inefficient with respect to sorption as well. Therefore, the retention parameters decrease simultaneously with the increasing diffusional transport through preferred zones. This could further amplify the acceleration of the diffusional propagation. We therefore recommend conducting diffusion experiments on the decimetre scale, where these heterogeneous effects emerge, preferably with PET.
In the past it was shown that PET is applicable as a non-destructive method for quantitative determination of the spatio-temporal tracer distribution in order to observe flow phenomena in complete drill cores. We have now established PET as a tomographic method for the imaging of molecular diffusion. We take advantage of the extreme sensitive detection of decay radiation, which is a beneficial characteristic of radiometric methods in general. In particular, we applied long-living PET tracers, a high-resolution PET scanner, and specially adapted correction methods of the raw data, in order to gain suitable quantitative tomograms of the temporal evolution of the tracer distribution. From these data, integral anisotropic diffusion coefficients can be computed that are comparable to the results of a large set of single one-dimensional diffusion-cell experiments on small specimens. Beyond that, it is presently the only quantitative method which enables the effects of heterogeneities to be studied on the centimetre scale, in particular preferential diffusion zones. Such zones could have a significant impact on the diffusional propagation of chemical species on the field scale.
The voluminous spatio-temporal image data were archived at the HZDR data
repository which is currently prepared for open access. The HZDR has
registered at datacite.org to provide open access data. Using the short name
of the HZDR (TIB.HZDR) – data will be accessible via the datacite search
(
The authors thank the Federal Ministry for Economic Affairs and Energy for financial support of this study (grant no. 02E10971) and the Project Management Agency Karlsruhe (Water Technology and Waste Management Division) for administration. Reference Opalinus drill samples were supplied courtesy of Nagra. The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association. Edited by: M. Halisch Reviewed by: two anonymous referees