3 Sampling and methods
3.5 Diffusion coefficients of iodide by the X-ray radiography method
14 rock core samples, vacuum sealed in polymer bags, were sent in coolers to Tom Al and his team at the University of New Brunswick (UNB). Upon arrival they were stored in a refrigerator prior to preparation for radiography measurements.
Measurements were conducted using a non-destructive X-ray radiography technique developed for the quantitative measurement of diffusion properties of rocks (Cavé et al. 2009). Samples were 11 mm in diameter and 12 – 16 mm in length. Additional analyses have been conducted in support of diffusion measurements, including water-loss porosity (WL) by gravimetric methods, and iodide accessible porosity (I) by radiography. Estimates of the porewater chemical com-position were provided by the Rock-Water Interaction group at Uni Bern.
Water-loss porosity
All cutting and drilling of samples was done dry, in air. Determination of water-loss porosity (WL) from gravimetric and pycnometric measurements provide a measure of the bulk porosity of the sample and are useful for comparison with iodide-accessible porosity determinations from the radiography experiments. The water-loss porosity method is based on the water imbi-bition technique presented by Emerson (1990) and is consistent with that of Blum (1997) in that the measurements account for the salinity of the natural porewater.
Water-loss porosity determinations were conducted from the cut-blocks remaining after sub-cores drilled for radiography measurements. Some porewater evaporation may have occurred during handling so samples were initially re-saturated in synthetic porewater (SPW) (Tab. 3-8).
Following re-saturation, the submerged mass (Msub) of each sample was determined with the sample suspended in SPW. The beaker of SPW was then removed and the mass of the sus-pended sample was weighed repeatedly over time to plot a surface drying curve. The mass of the saturated surface-dry sample (Msat) was determined at the critical point of slope change (indicating a change from surface evaporation to porewater evaporation). The samples were then oven-dried at 105 °C and the masses were monitored over 1 – 2 weeks. The final dry mass (Mdry) was recorded when a constant mass was attained.
Tab. 3-8: List of samples used for diffusion measurements and corresponding synthetic porewaters.
Sample ID Unit Synthetic porewater recipe
[mol/l] Tracer NaI [mol/l]
SLA 735.22 Effingen Member NaCl: 0.0724
0.46 SLA 741.60 Effingen Member Na2SO4: 0.1214
SLA 762.56 Variansmergel Fm. CaSO4: 0.0045 SLA 780.53 Parkinsoni-Württembergica Beds "
0.22 SLA 795.95 Humphriesioolith Fm. NaCl: 0.0992
SLA 808.89 Wedelsandstein Fm. Na2SO4: 0.0382 SLA 825.53 Wedelsandstein Fm. CaSO4: 0.0016
SLA 857.80 Opalinuston NaCl: 0.212
0.39 SLA 857.80 repl. Opalinuston "
SLA 896.43 Opalinuston KCl: 0.002
SLA 916.82 Opalinuston MgCl2: 0.017
SLA 929.22 Opalinuston CaCl2: 0.026
SLA 954.35 Posidonienschiefer SrCl2: 0.001 SLA 954.35 repl. Posidonienschiefer Na2SO4: 0.014 SLA 963.70 Numismalis-Amaltheen Beds NaHCO3: 0.005
SLA 977.64 Obtusus Beds "
In this procedure, SPW solutions were formulated based on porewater composition data provided by the Rock-Water Interaction group at Uni Bern. The density of the SPW solution is taken into account in porosity calculations, although the effect is minor for applied ionic strengths. To obtain an accurate mass for a dry rock sample, the mass of the salts retained in voids after drying is subtracted from Mdry. The equations for the determination of porosity by this method are:
where Msat is the mass of the saturated, surface-dry sample weighed in air (g); Msub is the mass of the saturated sample weighed when suspended in SPW (g); Mdry is the mass of the oven-dried sample (including salts retained in voids) weighed in air (g); ρSPW is the density of the SPW solution (assumed to have the same salinity and density as the natural porewater; g/ml) and x is the mass fraction of the salts in the synthetic porewater.
Diffusion coefficient and iodide-accessible porosity measurements – radiography
Cylindrical subsamples (nominal 11 mm diameter, and 12 to 16 mm length) were drilled (dry) from the larger core slices. The surface of the samples was brushed with a thin coat of silicone and immediately enclosed in heat-shrink tubing (3M FP-301). An 11 mm diameter piece of felt and a non-porous ceramic disc (11 mm diameter, 3 mm height; McMaster-Carr Mykroy/Mycalex ceramic) were placed on top of each subsample inside the heat shrink tubing and the tubing was gently heated. The samples were then attached to the reservoirs (Fig. 3-5) and sealed in place with silicone. The ceramic disc is used as an internal standard to correct for variability in the X-ray source. Rectangular ceramic bars (3 3 mm, 10 – 13 mm length) were glued upright on the reservoir on each side of the sample using silicone. These bars function as addi-tional internal standards and also as alignment guides for positioning the cell in the instrument.
Fig. 3-5: Diagram of the cell used for diffusion experiments by X-ray radiography.
The reservoirs of the diffusion cells were filled with SPW. The samples were allowed to saturate in SPW for 5 to 7 days, during which time the cells were repeatedly placed under a vacuum for short periods and the SPW was refreshed in the reservoirs regularly.
Diffusion experiments were initiated by replacing the SPW in the reservoirs with a tracer solution containing NaI (Tab. 3-8). Replicate reference radiographs (time = 0) were collected immediately after the tracer solutions were introduced, and then time-series radiographs were collected at selected intervals as diffusion proceeded. After the time-series measurements were completed, the samples were saturated with iodide tracer from both ends by removing the nylon screw caps (Fig. 3-5) and immersing the top in tracer solution.
The progress of saturation was monitored by X-ray radiography until no changes were observed in X-ray attenuation between consecutive images. During this time, the tracer solutions in the reservoirs were refreshed periodically. The time required for complete saturation of the samples ranged between 15 to 27 days.
All data were collected as digital radiographs (16 bit greyscale TIFF files) using a Skyscan 1072 desktop microCT instrument. The instrumental settings used for data acquisition are shown in Tab. 3-9.
Ceramic disc internal standard
Injection
openings Positioning pin
Rock sample (11mm diameter, 12-16 mm height) mounted in shrink tubing
Tracer reservoir
Nylon screw with o-ring removable seal
Fabric disc
Ceramic bar internal standards, also alignment guides
Tab. 3-9: X-Ray radiography data acquisition parameters for diffusion tests using the SkyScan 1072 MicroCT.
Parameter Settings
Data collection 2 or 3 replicate reference images
Time-series images collected at intervals between 2 to 12 hr
Energy 60 kV
Current 162 μA
Acquisition time 9968 ms Frame-averaging 8
Filter 1 mm Al between source and sample Flat field correction On
Image settings 16-bit TIFF, 1024x1024 pixels, 2MB Sample alignment ceramic bars
Magnification 14
Stage height 0.5 – 4 mm (variable between samples but consistent for each sample)
The principles of the X-ray radiography technique, and the data processing procedures, are described in Cavé et al. (2009). Briefly, data are collected in the form of two-dimensional (2D) digital radiographs where the greyscale value at each pixel is a function of the X-ray intensity measured by the detector. The measured intensity represents the difference between the X-ray source intensity and the X-ray absorption in the sample:
I = I0 e -µd (3-30)
where I is the measured X-ray intensity (greyscale value); I0 is the source X-ray intensity; is the X-ray attenuation coefficient; and d is the thickness of the sample. Because of the cylindrical geometry of the sample, the X-ray path length through the sample varies from zero, at the edges, to 11 mm (the sample diameter) at the centre. Intensity measurements from 2D radiographs are integrated horizontally across the width of the sample thereby producing 1D profiles of X-ray intensity versus distance along the axis of the sample and removing the effects of lateral thick-ness variation.
The iodide tracer was selected for use with this method because iodide is generally a conser-vative tracer in most saturated porous media, and because iodide has a large X-ray attenuation coefficient compared to other common conservative tracers, thereby providing good contrast for radiographic imaging (Cavé et al. 2009). Using an approach in which the difference in X-ray attenuation between a reference image (Iref, time = 0) and a time-series image (It, time = t), the attenuation due to the presence of iodide is calculated as:
µd = [ln (Iref) – ln (It)] (3-31)
In this way, the background X-ray absorption due to the rock matrix is removed and only the net X-ray absorption due to the presence of the iodide is recorded. The thickness, d, of the samples is constant and µd is therefore represented by µ. As an example, Fig. 3-6a presents 1D µ profiles measured from sample SLA 857.8.
(a) (b)
Fig. 3-6: One-dimensional profiles of (a) and (b) C/C0 for sample SLA-857.8.
In (b), the discrete points represent measured data and the solid lines are the best-fit model profile. Note that there is a 0.0013 m gap in data near the influx boundary because the end of the sample is hidden within the top plate of the tracer reservoir.
The value of µ is a function of the concentration (C) of the iodide tracer present in the pores.
As described in Cavé et al. (2009), µ at time t is transformed to relative concentration profiles (C/C0) according to:
where µsat is obtained from the tracer-saturated sample. This transformation allows the calculation of relative concentration profiles (Fig. 3-6b).
The values in tracer-saturated samples (Fig. 3-6a) are proportional to I and these data are used to obtain quantitative spatially-resolved porosity data (I):
std I ∆μsat
∆μ
(3-33)
where µstd is the X-ray attenuation difference between the SPW and the initial tracer solution (C0).
Porewater diffusion coefficients are obtained by fitting experimental profiles of relative iodide concentrations with theoretical profiles obtained from an analytical solution for Fick's Law (Fig. 3-6):
where C is the concentration of the tracer at position x (m); C0 is the constant concentration of the tracer at the influx boundary; t is the time (s) since the start of diffusion; and Dp is the porewater diffusion coefficient (m2/s). The curve fitting is conducted using a least squares approach, and for datasets with three or more time-series profiles it is possible to calculate a standard deviation for Dp.
A blank sample made from a non-porous Delrin® (acetal homopolymer) (10 mm diameter, 16 mm length) was measured to establish the background noise inherent in values. It was determined that the background noise threshold for values is approximately 0.005 for the experimental operating conditions reported here.
Benchmarking of the radiography method
The radiography method has been benchmarked using samples from Canadian sedimentary formations against through-diffusion measurements conducted at three different labs – Atomic Energy of Canada Limited (AECL), PSI and the University of New Brunswick (UNB). In all cases the measurements were conducted using iodide tracer. The AECL and UNB comparisons were conducted on closely matched samples collected from adjacent material in the parent core.
Samples for the PSI comparison were collected between 2 and 10 m apart from the radiography samples. The comparison with through diffusion measurements at AECL has been published (Cavé et al. 2009), while the comparison with PSI results is presented in a report on the Ontario Power Generation DGR project (Geofirma 2011), and the data for radiography and through diffusion measurements conducted at UNB are presented in a DGR technical report (Al et al.
2009). The AECL and UNB comparisons are presented in Fig. 3-7 but the PSI data are not included in this figure because they do not represent closely matched samples. The PSI data are presented in Tab. 3-10.
Fig. 3-7: Comparison of Dp values determined by radiography versus through diffusion.
Where present, the bars represent the range of values obtained for multiple measurements on closely spaced, but not identical samples, from the same core
Tab. 3-10: Comparison of Dp values determined by radiography vs. through diffusion at PSI.