Low-field NMR T ₂ Relaxation

In NMR relaxation experiments, the magnetization decay characterized by exponential decay curves is measured, resulting essentially from liquid–solid interactions of the spins carried by water molecules exploring the pore space by diffusion (Godefroy et al., Reference Godefroy, Korb, Fleury and Bryant2001). The solid–liquid interactions are effective only close to the surface in a layer of thickness, ε_S (<1 nm). In a single pore, the volume fraction of bulk water (unaffected by surface interactions) is f _b, and f _s is the volume fraction of the surface layer (f _b + f _s = 1). As a result of molecular diffusion, an exchange occurs between the surface and bulk volumes with an exchange time given by τ_ex. In the so-called fast exchange (or fast diffusion) regime (τ_ex<< T ₂, the latter being the relaxation time), the measured relaxation rate 1/T ₂ is an average of the bulk and surface-relaxation rates weighted by the volume fractions:

(1) $\frac{1}{T_2}=\frac{f_s}{T_{2S}}+\frac{f_b}{T_{2B}}\approx \frac{S_p}{V_p}\frac{{\epsilon }_S}{T_{2S}}+\frac{1}{T_{2B}}$

An additional term involving internal gradients is ignored because low magnetic fields typically of the order of <0.5 T are considered; T _2S is the relaxation time characteristic of the surface layer, T _2B is the relaxation time of the bulk liquid (T _2S<<T _2B), and V _p and S _p are the volume and surface area of a pore, respectively. The intuitive explanation of the equation above that, as the pore size decreases, the number of collisions with the surface increases and, hence, the relaxation time decreases, is incorrect because the model assumes a fast diffusion regime, meaning that numerous collisions occur during the magnetization lifetime. An important parameter describing the strength of solid–liquid interactions is the surface relaxivity, ρ₂, or relaxation velocity at the pore surface defined as ρ₂ = ε_S /T _2S. The above equation is the basis for the interpretation of relaxation time as an indicator of pore size expressed as the ratio V _p /S _p. From this starting point, important amendments should be made:

• • The ratio V _p /S _p can be quite confusing when compared to imaging techniques that aim at pore body sizes or mercury intrusion experiments (yielding pore entry sizes); e.g. for a rhombohedric packing of spherical grains of diameter d yielding the lowest possible porosity (0.259), the largest sphere in the pore body, the pore-entry size, and the ratio V _p /S _p, will be 0.224 d, 0.154 d, and 0.054 d, respectively. Hence, the scaled NMR pore size will always be smaller compared to these techniques; if considering rugosity at a small scale, typically below the resolution of imaging techniques, the difference will be even larger.

• • The solid–liquid interactions are dominated by paramagnetic impurities (Fe or Mn) at the solid surfaces and the water molecules can be viewed as a probe exploring the surface by diffusion; hence, the surface S _p in Eq. 1 should rather be compared to values obtained by techniques describing the surface at the same molecular scale, e.g. nitrogen adsorption. Surface relaxivity values are often calculated by comparison with the mercury intrusion method but they are overestimated by at least the ratio of pore body to pore throat (a factor of ~3). The current authors consider that the range of surface relaxivities for most natural minerals is between 1 and 10 μm/s, much larger values being non-physical (Washburn, Reference Washburn2014); hence, a large range of sizes can be observed, from nanometer up to 100 μm (Fig. 1), with an instrument able to detect T ₂ relaxation times starting at 0.1 ms.

• • In the interlayer space of smectites, the V/S model above has been shown to fail (Fleury et al., Reference Fleury, Kohler, Norrant, Gautier, M'Hamdi and Barré2013), presumably due to the fact that the notion of surface and volume becomes ambiguous at <2 nm; another potential reason is the strong interaction of water with the compensating ions (“oriented” water (Fleury & Canet, Reference Fleury and Canet2014)); in calibrated porous silica, the pore-size dependence of the relaxation times has been shown to be valid in the range 2 to 14 nm (Liu et al., Reference Liu, Li and Jonas1991) and above (Godefroy et al., Reference Godefroy, Korb, Fleury and Bryant2001).

• • In the presence of a distribution of pore sizes, the magnetization decay, M(t), is not a single exponential but the sum of the contribution from all pores. M(t) is then usually analyzed in terms of a sum of exponential decays. This does not mean, however, that the resulting distribution of relaxation times will represent a pore-size distribution; molecules may diffuse into several pores during the magnetization decay yielding the so-called diffusion coupling effect (Fleury & Soualem, Reference Fleury and Soualem2009; Monteilhet et al., Reference Monteilhet, Korb, Mitchell and McDonald2006; Washburn & Callaghan, Reference Washburn and Callaghan2006). It leads to a narrower distribution or, in extreme cases, a unique exponential decay even in the presence of pores of different sizes. This effect is a combination of diffusion length, pore sizes, and spatial distribution of these pores. For aquitards or caprocks and shales, diffusive pore coupling is thought to be predominant (Washburn, Reference Washburn2014) and, therefore, relaxation-time distribution must be interpreted carefully. An important consequence of the diffusive coupling for clay systems is that the smallest pores (typically interlayer) are accessible by most NMR instruments and not only by those with the highest T ₂ resolution; indeed, the average relaxation time becomes larger and can be reached more easily, yielding realistic porosity values including interlayer water (often called total porosity). On the other hand, the effect of diffusive coupling also means that while the binding environments of water in the interlayer and in the bulk pore space are different, they cannot be resolved because diffusive exchange is fast in relation to the timescales accessible by NMR. What can be measured is a weighted average of the relaxation times in these environments.

Fig. 1. Graphical representation of Eq. 1 with two extreme values of surface relaxivities. For completeness, the fast diffusion limit is also indicated

The water content or porosity can be obtained from the magnetization curve in the native state. It is the very first and important parameter characterizing porous media. In clay-rich samples, determination of porosity is not a trivial operation when using simple drying techniques. At the standard drying temperature of 105°C, some of the more strongly bound water may stay in the sample, and higher drying temperatures may result in the volatilization of organics. The NMR techniques have a great advantage because the sample can stay in a fully saturated state, even though some difficulties remain.

Here, some details are given on how to determine the water content from the magnetization measurements (Fig. 2). The M(t) curve is a collection of echoes collected at regular time intervals, and for the instrument used here, the first one is at 0.08 ms. As a practical rule of thumb, the first echo time also determines the T ₂ resolution in the distributions shown later (e.g. for a component at T ₂=0.08 ms, the first echo at M(t=0.08 ms) will already be attenuated by exp(–t=0.08/T ₂=0.08)=exp(–1)=0.37). When short components are present below the limit of resolution, the calculated distribution will contain components around the resolution limit; hence, one can detect such components but not quantify their fractions. The water content is given by M(t=0) and the inverse Laplace transform yielding the relaxation time distributions was used to extrapolate the signal (full line in Fig. 2); if short T ₂ components exist, the extrapolated value M(t=0) is much larger than the first echo and may be uncertain; e.g. in Fig. 2 in which two components are present mainly at 0.07 and 0.6 ms (see inset in Fig. 2), the extrapolated value taking all components is ~50% larger than the first echo amplitude. Using T ₁-T ₂ maps, the short components clearly correspond to protons being part of the solid structure and not belonging to water molecules. For these protons, the exponential model used to generate the T ₂ distributions is probably not valid and should be replaced by a Gaussian model (Washburn et al., Reference Washburn, Anderssen, Vogt, Seymour, Birdwell, Kirkland and Codd2015). The present authors thus removed systematically all T ₂ components of <0.15 ms and the corresponding extrapolated value M(t=0) is then much closer to the first echo amplitude, yielding minor uncertainties. Note that the signal to noise ratio is high (in this case S/N=504) and the relative error in water content is, at most, 1%.

Fig. 2. Determination of the water content from NMR magnetization measurements (sample CW6, Opalinus Clay from Schlattingen). The solid line represents the inverse Laplace transform in the time domain and the circles represent the acquired data. The time axis is plotted using logarithmic scales to highlight the short time decay. The inset indicates the calculated T ₂ distribution using the recorded magnetization curve M(t)

After calibrating the echo amplitudes with a known volume or mass of pure water measured under the same conditions, the water content is obtained. The result may still depend on the salinity of the saturating brine in the sample, however, because the hydrogen index of brine decreases gradually as the salinity increases (Dunn et al., Reference Dunn, Bergman and Latorraca2002). This is very significant for the Canadian samples for which total dissolved salts can reach up to 300 g/L. For these samples, the native porewater was exchanged by simple immersion with a 20 g/L KCl solution; this solution was chosen in order to minimize any potential clay swelling.

Finally, to obtain porosities, two possibilities exist: first, a direct calculation of volume ratio according to:

(2) ${\Phi }_{\mathrm{NMR}}=\frac{\text{Volume of water}}{\text{Total volume}}$

where the volume of water is measured by NMR as explained above, and the total volume is obtained by the dimension of the sample when its geometry is well defined (e.g. a cylinder). In this case, the result characterizes the water-filled pore space, which may be less than total porosity in the case of partially saturated conditions. The second possibility is to use the grain density, ρ_G, measured after drying the sample at 105°C; from the total mass, M _t , of the sample and the measured mass of water, M _w , by NMR, the porosity can be estimated according to:

(3) ${\Phi }_e=1-\frac{\text{Solid volume}}{\text{Total volume}}=1-\frac{\left(M_t-M_w\right)/{\rho }_G}{\text{Total volume}}$

This equation does not depend on the state of saturation and so represents the entire pore space.

T ₁-T ₂ and T ₂-T ₂ Maps

The T ₁-T ₂ maps are classically used for identifying different proton species essentially by their T ₁/T ₂ ratio; e.g. water, oil, gas, and organic matter in shales have distinct positions in such maps (Fleury & Romero-Sarmiento, Reference Fleury and Romero-Sarmiento2016; Khatibi et al., Reference Khatibi, Ostadhassan, Xie, Gentzis, Bubach, Gan and Carvajal-Ortiz2019), providing a considerable improvement in the understanding compared to T ₂ relaxation distributions alone. When saturated with a single fluid as considered in the present study, the value of the T ₁/T ₂ ratio is also of interest as an indication of the strength of the confined water interactions with the solid surface. This ratio depends on the magnetic field of the instrument (i.e. the Larmor frequency), however, and the basic principles of the analysis need to be explained. As mentioned above, solid–liquid interactions are characterized macroscopically by a global surface relaxivity parameter but a more detailed description of these interactions involves essentially a surface diffusion mechanism: water molecules are adsorbed onto the surface and may diffuse in a thin water layer, ε_S, such that short-distance spin interactions can occur. In the present situation, only the dominant interactions between the nuclear spins and the electronic spins of paramagnetic impurities distributed at the solid surface are considered. The motions are then described by two timescales (Fig. 3): τ_m is the correlation time of the dipole–dipole interactions at the surface, and τ_S is the surface residence time before desorption (Godefroy et al., Reference Godefroy, Korb, Fleury and Bryant2001). The relaxation times T ₁ and T ₂ can then be calculated and the ratio is given by (Godefroy et al., Reference Godefroy, Korb, Fleury and Bryant2001; Korb, Reference Korb2018; Tian et al., Reference Tian, Wei and Yan2019):

Fig. 3. Model of the two-dimensional translational diffusion of the proton species at the pore surface. The spin-bearing molecules (e.g. water) diffuse at the surface, sometimes reaching fixed surface paramagnetic impurities where the spins relax. The translational surface correlation time is defined as τ_m. This surface motion is interrupted by the surface desorption, characterized by a surface residence time, τ_S (adapted from Godefroy et al. (Reference Godefroy, Korb, Fleury and Bryant2001)

(4) $\frac{T_1}{T_2}=2\frac{\left(ln\left(\frac{{\tau }_S^2}{{\tau }_m^2}\right)+\frac{3}{4}ln\left(\frac{1+{\omega }_I^2{\tau }_m^2}{{\left({\tau }_m/{\tau }_S\right)}^2+{\omega }_I^2{\tau }_m^2}\right)+\frac{13}{4}ln\left(\frac{1+{\omega }_S^2{\tau }_m^2}{{\left({\tau }_m/{\tau }_S\right)}^2+{\omega }_S^2{\tau }_m^2}\right)\right)}{3ln\left(\frac{1+{\omega }_I^2{\tau }_m^2}{{\left({\tau }_m/{\tau }_S\right)}^2+{\omega }_I^2{\tau }_m^2}\right)+7ln\left(\frac{1+{\omega }_S^2{\tau }_m^2}{{\left({\tau }_m/{\tau }_S\right)}^2+{\omega }_S^2{\tau }_m^2}\right)}$

Whereas T ₁ or T ₂ contain pre-factors that are difficult to determine, the ratio T ₁/T ₂ depends solely on the two timescales and the Larmor frequency, ω _I , of the instrument (ω _S = 658.21 ω _I in Eq. 4 is the electronic spin frequency related to the nuclear spin frequency). Taking typical ranges of values for τ_m and τ_S and the frequency of the instrument used (20.9 MHz), the T ₁/T ₂ ratio is sensitive to both τ_m and τ_S for moderate values (e.g. T ₁/T ₂ = 1.8) and mostly sensitive to τ_m at high values (e.g. T ₁/T ₂ = 4, Fig. 4). The meaning of τ_m can be understood better if τ_m is converted into a surface-diffusion coefficient, D _S = ε _S ²/4τ_m. Note that the T ₁/T ₂ ratio is equal to 1 when τ_S = τ_m as for bulk water (τ_m ≅10 ps). Some authors also interpret the T ₁/T ₂ ratio as being linked to a surface energy (D'Agostino et al., Reference D'Agostino, Mitchell, Mantle and Gladden2014). Using measurements performed at variable frequencies ω _I (with field cycling instruments (Korb, Reference Korb2018)), the time scales τ_m and τ_S could be retrieved using various procedures (Faux et al., Reference Faux, Kogon, Bortolotti and McDonald2019). As will be seen in the results, however, relaxation times are too short for such instruments due to dead-time issues and one is limited by measurements at a spot frequency with reduced capability of more detailed analysis. The T ₁/T ₂ ratio will be used as a relative comparison between samples with the point above in mind.

Fig. 4. Solutions of Eq. 2 for two values of the T ₁/T ₂ ratio at 20.9 MHz; τ_m is the correlation time of the dipole–dipole interactions at the surface governed by paramagnetic impurities and τ_S is the surface residence time before desorption (see Fig. 3). A variation of the T ₁/T ₂ ratio from 1.8 to 4 implies large variations of τ_m and τ_S

T ₂–T ₂ maps are very useful for demonstrating diffusive pore coupling as mentioned above (Bernin & Topgaard, Reference Bernin and Topgaard2013; Fleury & Soualem, Reference Fleury and Soualem2009; Monteilhet et al., Reference Monteilhet, Korb, Mitchell and McDonald2006; Washburn & Callaghan, Reference Washburn and Callaghan2006). This technique, also called relaxation exchange spectroscopy (REXSY), is a combination of two 1D T ₂ relaxation experiments separated by an exchange time t _E that can be varied experimentally. When spin-bearing molecules move by diffusion from one relaxation environment to another during the time t _E, off-diagonal peaks are present in the map at well defined locations (Fig. 5). The exchange times that can be explored are limited by the lifetime of magnetization (about the largest T ₂ relaxation time of the system) and molecular exchange will finally occur at long time. To test if an exchange is occurring in a given system characterized by at least two distinct relaxation times, the exchange time, t _E, should be set close to the largest T ₂ (population 1 in Fig. 5 (Fleury & Soualem, Reference Fleury and Soualem2009)). If exchange is present during that time interval, it means first that the 1D T ₂ relaxation time distribution does not represent the true fraction of population 1 or 2. Second, it also means that the porous system is well connected at the time scale explored; when analyzing the different collected maps at different times, t _E, a coupling coefficient expressing the degree of connectivity of the system can be calculated (Fleury & Soualem, Reference Fleury and Soualem2009). If the system is completely coupled (i.e. a single peak is observed either in 1D or 2D because diffusive exchange is fast), nothing can be observed and another fluid with a smaller diffusion coefficient must be used. The measured T ₂ time will then represent the ratio of total volume to the total surface (as in Eq. 1) and may be an alternative way for estimating a specific surface in the wet state. The pore-coupling effect should not be viewed as a pore-to-pore exchange but rather as a pore-cluster exchange as small pores are never isolated in practice in natural samples. Hence, the distance between these clusters of pores with different sizes may also play a role and the availability of pore-network images is very useful for further interpreting the data.

Fig. 5. T ₂–T ₂ maps showing off-diagonal peaks at an exchange time, t _E, indicating diffusive exchange between the two populations

NMR Cryoporometry Technique (NMRC)

The principle of cryoporometry is based on the shift of the melting temperature of a fluid when located in a pore (Mitchell et al., Reference Mitchell, Webber and Strange2008; Petrov & Furó, Reference Petrov and Furó2009). A simplified form of the Gibbs-Thomson equation describing this behavior may be written as:

(5) $△T_m\left(x\right)=T_m^{\text{bulk}}-T_m\left(x\right)=\frac{k_{GT}}{x}$

where T _m ^bulk is the bulk melting temperature, x is a dimension related to the pore size, and k_GT is the so-called Gibbs-Thomson constant. In the melting cycle, x corresponds to a radius of curvature dV/dS (Petrov & Furó, Reference Petrov and Furó2009). In this way the melting temperature depends on the nature of the liquid and on pore size. For water at a given temperature below zero, smaller pores will contain liquid instead of ice. For water, the value k_GT = 58.2 K nm (Webber, Reference Webber2010; Webber et al., Reference Webber, Corbett, Semple, Ogbonnaya, Teel, Masiello, Fisher, Valenza, Song and Hu2013) determined using a set of well characterized systems has been chosen; hence at x = 2 and 10 nm, water will melt, respectively, at –29.1 and –5.8°C. As expressed in Eq. 5, the constant k_GT contains a shape factor of 2 corresponding to a cylinder. Hence, if the porous system considered contains cylindrical pores, the measured pore size corresponds to a diameter d. In the following the notation, P(d) will be used for clarity.

In practice, if one detects the amount of liquid volume, V(T), present in the sample as a function of temperature, T, one can obtain the pore-size distribution, P(d), from the derivative of the V(T) curve using the following equation:

(6) $P\left(d\right)=-\frac{k_{\mathrm{GT}}}{d^2}·\frac{\mathrm{dV}}{\mathrm{dT}}$

In equation 6, P(d) has units of μL/nm. Because the distributions are plotted using log scales, however, an appropriate representation is P(d).d vs. ln(d), yielding units of μL. The distribution is then further normalized by the initial (wet) mass of the sample, yielding units of μL/g in the graphs. The integration of the distribution P represents the amount of melted volume V _m during the heating of the sample. The cryoporometry system used here is essentially a special probe part of the low-field spectrometer. Small cylinders, 4 mm in diameter, and of maximum length 20 mm, are needed to perform the measurements. After inserting the sample into the spectrometer, the temperature is first reduced to –29°C as rapidly as possible (<1 min). Then, a temperature cycle –29 ➔ –0.5 ➔ –29°C during ~30 min is performed to avoid residual hysteresis issues in the melting cycle. Finally, a temperature ramp starting at –29°C gradually reaching 0°C and above over a ~10 h period was performed and the amount of liquid was measured at regular intervals by NMR (Fig. 6). More details about the system used to vary the temperature and measure the liquid volume can be found elsewhere (Fleury et al., Reference Fleury, Chevalier, Jorand, Jolivet and Nicot2021). The experimental set-up allows the pore sizes from 2 nm up to ~1 μm to be resolved. The system is also checked regularly using a mixture of calibrated porous glass containing two narrow pore sizes (15 and 139 nm) (Fleury et al., Reference Fleury, Chevalier, Jorand, Jolivet and Nicot2021). A typical signal recorded during NMRC experiments is shown in Fig. 6; the NMR amplitude is the maximum of the recorded Hahn echo at the echo time TE = 0.3 ms. The curve is then fitted with a MATLAB least squares spline approximation function in order to obtain a smooth derivative of V(T) (Eq. 6). The duration of the experiment was 15 h. The cryoporometry technique described here has been applied recently to source rocks originating from the Vaca Muerta formation in Argentina (Fleury et al., Reference Fleury, Chevalier, Jorand, Jolivet and Nicot2021), both at 100% water and at partial oil–water saturation to demonstrate the pore occupancy of each fluid within the porous network.

Fig. 6. Example of raw data recorded during NMRC experiments on the sample CW5 (Opalinus Clay). The line is a least square spline approximation used to calculate a smooth derivative dV/dT of the curve and produce the pore-size distribution according to Eq. 6

An important aspect is the effect of salt on pore-size distribution (PSD) derived from NMRC experiments; an aspect not considered much in the literature and not mentioned in two recent reviews (Mitchell et al., Reference Mitchell, Webber and Strange2008; Petrov & Furó, Reference Petrov and Furó2009). In clay systems, using pure water as the saturating liquid is not always feasible for well known clay stability issues (swelling). The theory described above has been developed in the context of pure fluids with well defined thermodynamic properties. A salt solution might not give any useful results; not only is the bulk freezing point shifted to a lower temperature (and for an extreme example, shifted to –21.1°C at the eutectic concentration for NaCl solutions) but, at the same time, liquid and solid phases co-exist, in principle, at a single temperature. Beside these unfavorable bulk thermodynamic properties, the salt exclusion mechanism might also produce uninterpretable experiments. The latter can be avoided easily by freezing the system rapidly and this is done effectively in the experiments. In the NMRC context, the effect of salt has been examined only a little. In the pharmaceutical field, for the purpose of testing polymeric nanoparticles for drug release, the PSD measured on porous silica either saturated with pure water or a solution representing the cerebrospinal fluid (ionic strength of 0.15 mol/L) indicated small differences (Gopinathan et al., Reference Gopinathan, Yang, Lowe, Edler and Rigby2014). In the field of differential scanning calorimetry in which the same Gibbs-Thomson principle is used, more data can be found (Burba & Janzen, Reference Burba and Janzen2015) but only in one single published paper. The shift of the melting-point temperature was determined for two nano-porous silica samples (MCM41 and SBA15) and various NaCl solutions (up to 0.25 mol/kg). The result was a further reduction of the melting temperature compared to pure water, and different for the two porous media, even if the effect is significant in terms of melting temperature (~1°C). No large shift was induced in the PSD at ~10 nm, however. Later (Jantsch et al., Reference Jantsch, Weinberger, Tiemann and Koop2019), the same effects were still found for nano-porous silica but with CaCl₂ and LiCl solutions. A fundamental explanation was given in terms of effective water activity. In summary, the presence of salt solution does not preclude the use of thermoporometry methods but induces a small additional shift of melting temperature. For the present study, the effect of KCl solutions on a meso-porous zeolite sample compared with pure water was also specifically tested (Fig. 7). In the presence of KCL, a small shift of the PSD curve to smaller values, consistent with the literature, was observed. A KCl solution was chosen because it should generate the least swelling of clay materials in general.

Fig. 7. Comparison of the PSD obtained from a zeolite sample with pure water (dashed line) and a potassium chloride solution of concentration 20 g/L (solid line)

To complement the information given by the pore-size distribution derived between 2 nm and 1 μm, the amount of unfrozen water at –29°C was measured, the lowest attainable temperature in our system, yielding, in principle, the amount of water at <2 nm. This method is very similar to the thermoporometry method proposed to determine the amount of interlayer water typically from smectite (Grekov et al., Reference Grekov, Montavon, Robinet and Grambow2019). For this purpose, all components above 0.15 ms were taken in the T ₂ spectra (Fig. 8). The components below 0.15 ms were associated with structural hydroxyls and to plastic ice (frozen water in larger pores). This is only approximate, however, because the T ₂ relaxation time of water in the interlayer that is not in exchange with the surrounding water might be smaller than 0.15 ms; e.g. in smectite powders at various relative humidities and compensating cations, T ₂ values ranged from 0.03 to 0.5 ms when the basal spacing varied from 1.0 up to 1.6 nm (Fleury et al., Reference Fleury, Kohler, Norrant, Gautier, M'Hamdi and Barré2013). T ₁ measurements of the interlayer water in purified bentonite (Ohkubo et al., Reference Ohkubo, Ibaraki, Tachi and Iwadate2016) indicated similar but slightly larger values (1 to 3.5 ms) considering a T ₁/T ₂ ratio of 2 to 4.

Fig. 8. Determination of the fluid volume in pores of <2 nm taking all components above 0.15 ms

General Description

A suite of 12 drillcore samples selected for the CLAYWAT project of the Nuclear Energy Agency (Mazurek et al., Reference Mazurek, Gimmi, Dohrmann, Emmerich, Fleury and Balcom2022) was used for the study. The samples originated from diverse geological environments and were obtained from deep boreholes drilled from the surface or from short drillings in underground research facilities over a depth range of ~200–900 m below ground (Table 1). All samples were conditioned in sealed plastic bags immediately after core retrieval in order to minimize porewater evaporation and oxidation. The formations from which the samples originated span a wide range of depositional environments (mostly shallow marine to deltaic) and burial histories (Table 2). The maximum burial depths were, in most cases, larger than the current depth location, resulting in variable degrees of over-consolidation. The extremes were, on the one hand, the Belgian units (Boom Clay and Yper Clay) that experienced only shallow burial and, therefore, have high porosities of 0.37–0.4 and, on the other hand, the Boda Clay Fm. that was buried to ~4000 m in the past, resulting in a porosity of ~0.02. The Japanese units (Wakkanai and Koetoi Fm.) were special in that they are rich in marine diatoms and contain substantial components of volcanic material. While their clay contents are relatively small, they contain opal-CT and amorphous silica and have the greatest porosities of all of the samples. The salinity of the porewaters in the formations studied was below that of seawater, except for the Canadian samples (Queenston, Georgian Bay, and Blue Mountain Fm.) that contain hypersaline Ca-Na-Cl waters.

Table 1 Provenance of sample materials

¹URL = Underground Rock Laboratory, ²b.g. = below ground, a.h. = along hole (the latter stated for inclined boreholes drilled from the surface or short boreholes drilled from underground rock laboratories)

Table 2 Main characteristics of studied samples from the CLAYWAT report (Mazurek et al., Reference Mazurek, Gimmi, Dohrmann, Emmerich, Fleury and Balcom2022). Burial depth and temperature data from Kennell-Morrison et al. (Reference Kennell-Morrison, Yang and Jensen2022)

Sample Preparation

The objective was to prepare sample cylinders of 15 mm diameter and ~20 mm long for NMR studies. The geometry of these cylinders should be as regular as possible. For cryoporometry, smaller cylinders with a diameter of 4 mm were needed. The desired total length was 20 mm. Cryoporometry does not require ideal cylindrical geometry, and fragmented cylinders were acceptable also.

Full-size cores were unpacked from the protective wrapping, and 4–5 cm thick core slices were dry cut on a rotary saw. These slices were then fixed on a molding cutter, and cylinders of the desired size (15 and 4 mm) were milled (Fig. 9a, b). The cylinders were then either dry-cut or broken off the rock sample. The length of the cylinders was between 15 and 20 mm. The planar surfaces of the large cylinders were straightened on abrasive paper, using a plastic ring to maintain orthogonality (Fig. 9c). The 4 mm cylinders were not straightened due to the fragility of the thin materials. Both types of cylinders were then heat-sealed in transparent plastic tubes (Fig. 9d). The total exposure time of the samples to the atmosphere was ~30 min, which means that some degree of evaporation may have occurred. The plastic-packed 4 mm and 15 mm cylinders were subsequently heat-sealed in a second layer consisting of Al-coated plastic.

Fig. 9. Preparation of cylindrical cores for NMR studies. a Milling of cylindrical samples, b cylinder of 4 mm diameter for cryoporometry studies, c plastic rings into which the milled cylinders were inserted in order to straighten the end surfaces on abrasive paper, and d wrapping of sample cylinders prior to shipping

Given the fact that milling does not transmit major forces on the sample cylinders (unlike sawing or machining), it was possible to prepare unbroken and geometrically regular cylinders of 15 mm diameter from all samples. In many cases, the 4 mm cylinders broke into 2–4 pieces during preparation, but this was of no concern for the cryoporometry studies.