TY - JOUR
AU - Amann,, Florian
AB - SUMMARY A comprehensive characterization of clay shale behavior requires quantifying both geomechanical and hydromechanical characteristics. This paper presents a comparative laboratory study of different methods to determine the water permeability of saturated Opalinus Clay: (i) pore pressure oscillation, (ii) pressure pulse decay and (iii) pore pressure equilibration. Based on a comprehensive data set obtained on one sample under well-defined temperature and isostatic effective stress conditions, we discuss the sensitivity of permeability and storativity on the experimental boundary conditions (oscillation frequency, pore pressure amplitudes and effective stress). The results show that permeability coefficients obtained by all three methods differ less than 15 per cent at a constant effective stress of 24 MPa (kmean = 6.6E-21 to 7.5E-21 m2). The pore pressure transmission technique tends towards lower permeability coefficients, whereas the pulse decay and pressure oscillation techniques result in slightly higher values. The discrepancies are considered minor and experimental times of the techniques are similar in the range of 1–2 d for this sample. We found that permeability coefficients determined by the pore pressure oscillation technique increase with higher frequencies, that is oscillation periods shorter than 2 hr. No dependence is found for the applied pressure amplitudes (5, 10 and 25 per cent of the mean pore pressure). By means of experimental handling and data density, the pore pressure oscillation technique appears to be the most efficient. Data can be recorded continuously over a user-defined period of time and yield information on both, permeability and storativity. Furthermore, effective stress conditions can be held constant during the test and pressure equilibration prior to testing is not necessary. Electron microscopic imaging of ion-beam polished surfaces before and after testing suggests that testing at effective stresses higher than in situ did not lead to pore significant collapse or other irreversible damage in the samples. The study also shows that unloading during the experiment did not result in a permeability increase, which is associated to the persistent closure of microcracks at effective stresses between 24 and 6 MPa. Microstructure, Permeability and porosity, Hydrogeophysics 1 INTRODUCTION Clay formations are considered suitable natural geological barriers for nuclear waste underground storage. In Switzerland, the Opalinus Clay (OPA) has been selected as the host rock formation for nuclear waste disposal, because of its favorable properties such as high sorption capacity, high self-sealing potential and very low permeability (e.g. Bossart et al. 2018). As the transport of radionuclides is controlled by diffusion and hydraulic conductivity, the assessment of the long-term storage capability must include the investigation of permeability and storativity, as well as its changes upon stress-variations over long timescales (e.g. Gautschi 2001, 2017; Marschall et al. 2005; Nussbaum et al. 2011; Yu et al. 2017; Laurich et al. 2018). However, the accurate measurement of these parameters is difficult, both in situ and in the laboratory. For very low permeable rocks, steady-state flow-through experiments are challenging as this requires the precise detection of very small outflow rates over a long time. Therefore, low-permeable media are often investigated using transient (non-steady-state) methods. In this study, we compared three different non-steady-state laboratory methods for hydraulic testing of Opalinus Clay: (i) The pore pressure oscillation method (PPO), (ii) the pressure pulse decay method (PPD) and (iii) the pore pressure transmission technique (PPT). The main objective of this study is to compare these techniques in terms of applicability, time-efficiency and data consistency. In a first step, we focus on the PPO technique by conducting a series of tests with different oscillation periods and amplitudes to understand their influence on permeability. Based on these results, we applied PPD and PPT under the same boundary conditions. Then, we investigated the dependence of permeability on effective confining pressure by systematically isostatic unloading. All experiments were conducted on the same sample over a period of six months at constant temperatures of 30 °C at isotropic total stress between 30 and 6 MPa and pore pressure between 6 and 2 MPa. 2 MATERIAL AND METHODS 2.1 Sample description The Opalinus Clay formation (Aalenian, Lower Jurassic) consists of over-consolidated shales that are subdivided into three different facies: sandy facies, carbonate-rich facies and shaly facies. Approximately 25 core meter (BHM-C1) were taken from the shaly facies, a dark-grey, mica-bearing, partly silty claystone (Bossart et al. 2018). The required test samples for this study were drilled from a core extracted approximately 8 m from the tunnel side wall in the Mont Terri underground laboratory (MT URL), Switzerland. The EDZ (excavation damage zone) extends to 2.2 times the radius of the tunnel from the tunnel axis, that is 2.7 m from the tunnel wall, (Lanyon et al. 2014) and, therefore, the core material is considered undisturbed. The shaly facies consists of 50–80 wt per cent clay minerals (15–25 wt per cent illite, 5–15 wt per cent illite-smectite mixed layers, 5–15 wt per cent chlorite and 20–30 wt per cent kaolinite), 10–20 wt per cent quartz, 5–20 wt per cent calcite and minor amounts of dolomite, siderite, pyrite, feldspars and organic carbon (Thury & Bossart 1999; Nagra 2002; Klinkenberg et al. 2009). The shale is transversely isotropic and has an in situ hydraulic conductivity between 1E-12 m s–1 and 1E-14 m s–1, that is 1E-19 and 1E-21 m2 (Marschall et al. 2004). 2.2 Theoretical background of permeability testing methods We used three different non-steady-state methods to determine the hydraulic properties of Opalinus Clay which are commonly used for the measurement of the water and gas permeability for low permeable media, i.e. permeability coefficients less than 1E-19 m² (1E-12 m s–1). All different non-steady-state evaluation procedures are based on the 1-D pressure diffusion equation (Brace et al. 1968; Davy et al. 2007; Song & Renner 2007; Liu et al. 2015; Yang et al. 2019). Details are presented in the Appendix, where associated different terms and definitions are outlined. 2.2.1 Pore pressure oscillation method The oscillation pore pressure method (PPO) was initially used for high-permeable reservoir rocks such as sandstones (Kranz et al. 1990). Later, this technique has been increasingly used for low-permeable rocks such as mudstones (McKernan et al. 2014), clay-bearing fault gouges (Faulkner & Rutter 2000), argillaceous rocks (Boulin et al. 2012) and crystalline rocks (David et al. 2018). In this technique, sinusoidal fluid pressure pulses are applied at the upstream end of the sample and the fluid pressure response is recorded on the opposite side in a closed reservoir of known volume (downstream, Fig. 1). The resulting phase shift δ and amplitude ratio R between the downstream and upstream (Adn/Aup) signals are used to calculate hydraulic properties of the sample, that is hydraulic diffusivity (permeability and storativity). The downstream pressure signal initially shows a transient response (Fig. 1). Therefore, multiple cycles are required to reach stable oscillation cycles. Various analytical solutions have been proposed to estimate the hydraulic properties knowing the phase shift and amplitude ratio (Turner 1958; Stewart et al. 1961; Kranz et al. 1990; Fischer 1992; Bernabé et al. 2004). Kranz et al. (1990) correlates the amplitude ratio R, that is the ratio between downstream and upstream amplitude, and phase shift δ with two dimensionless parameters (α and γ) through a set of non-linear equations: $$\begin{eqnarray*} R = \frac{{4{\alpha ^2}}}{{\left( {2{\alpha ^2} + 1} \right)\cosh \left( {2\gamma } \right) + \left( {2{\alpha ^2} - 1} \right)\cos \left( {2\gamma } \right) + 2\alpha \ \left( {\sinh \left( {2\gamma } \right) - \sin \left( {2\gamma } \right)} \right)}} \end{eqnarray*}$$(1) $$\begin{eqnarray*} \delta = \arctan \left\{ {\frac{{\tanh \left( {2\alpha \tan \left( \gamma \right) + 1} \right) + \tan \left( \gamma \right)}}{{\tan \left( \gamma \right) - \tanh \left( \gamma \right) + 2\alpha }}} \right\}\ \end{eqnarray*}$$(2) These parameters are used to calculate permeability (k) and sample storativity (⁠|${\rm{\beta_{st}}}$|⁠): $$\begin{eqnarray*} k = \frac{{\mu \ {\beta _{fl}}\ {V_{dn}}\ L}}{A}\ \ \frac{{\alpha \ \omega \ }}{\gamma } \end{eqnarray*}$$(3) $$\begin{eqnarray*} {\rm{\beta_{st}}} = \frac{{2\ {\beta _{fl\ }}{V_{dn}}\ \alpha \ \gamma }}{{A\ L}}\ , \end{eqnarray*}$$(4) where k is the permeability in m², µ the fluid viscosity in Pa·s, |${\beta _{fl}}$| the fluid compressibility in Pa−1, Vdn the downstream reservoir in m³, |$\ \omega $| the angular frequency in s−1, L the sample length in m and A is the sample cross-sectional area in m², |${\beta _{st}}$| the storage capacity of the sample in Pa−1. Figure 1. Open in new tabDownload slide Principle of the pore pressure oscillation technique. A sinusoidal upstream pressure is applied at one side of the sample and the attenuated and phase shifted pressure signal is recorded at the other side of the sample simultaneously. Aup and Adn indicate the upstream and downstream amplitude and δ denotes the phase shift between the two pressure signals. Figure 1. Open in new tabDownload slide Principle of the pore pressure oscillation technique. A sinusoidal upstream pressure is applied at one side of the sample and the attenuated and phase shifted pressure signal is recorded at the other side of the sample simultaneously. Aup and Adn indicate the upstream and downstream amplitude and δ denotes the phase shift between the two pressure signals. Bernabé et al. (2004, 2006) re-evaluated the solution of the sinusoidal pressure response at the downstream side, and rearranged the formulation by introducing new dimensionless parameters (⁠|$\eta $| and |$\xi $|⁠) for permeability and storage capacity: $$\begin{eqnarray*} R\ \ {e^{ - {\rm{i}}\delta }} = {\left( {\frac{{\left( {1 + {\rm{i}}} \right)}}{{\sqrt {\xi \ \eta } }}\ \sinh \left[ {\left( {1 + {\rm{i}}} \right)\sqrt {\frac{\xi }{\eta }} } \right] + \cosh \left[ {\left( {1 + {\rm{i}}} \right)\sqrt {\frac{\xi }{\eta }} } \right]} \right)^{ - 1}}\ . \end{eqnarray*}$$(5) Both solutions can be solved using numerical iterative solvers. In the latter solution, the dimensionless parameters are explicit since the calculation of permeability and storage capacity only depends on one parameter, that is |$\eta $| and |$\xi $|⁠, respectively, $$\begin{eqnarray*} k = \frac{{\eta \ \omega \ L\ \mu \ {\beta _{dn}}}}{{2\ A}} \end{eqnarray*}$$(6) $$\begin{eqnarray*} {\beta _{st}} = \ \frac{{\xi \ {\beta _{dn}}}}{{A\ L}}, \end{eqnarray*}$$(7) where |${\beta _{dn}}$| is the storage of the downstream reservoir in m³ Pa–1. Here, Bernabé et al. (2006) account for the influence of downstream reservoir size which can lead to very large uncertainties in the storativity measurements. In addition, the solutions for the non-linear equations can also be graphically evaluated using nomographs (Fig. 2). Note here that values for |$\eta $| and |$\xi $| smaller than 0.25 and larger than 1, respectively, are subjected to high uncertainties as curves isolines are close. Instead, a numerical non-linear solver can be used to obtain the dimensionless parameters with 0 ≤ |$\xi $| +|$\infty $|⁠. Figure 2. Open in new tabDownload slide Nomographes illustrating graphical solution for non-linear equations after Kranz et al. (1990) and Bernabé et al. (2006). R and δ represent amplitude ratio and phase shift between up- and downstream pressure signals whereas α, γ, ζ and η are dimensionless parameters used to calculate permeability and storativity. Figure 2. Open in new tabDownload slide Nomographes illustrating graphical solution for non-linear equations after Kranz et al. (1990) and Bernabé et al. (2006). R and δ represent amplitude ratio and phase shift between up- and downstream pressure signals whereas α, γ, ζ and η are dimensionless parameters used to calculate permeability and storativity. 2.2.2 Pulse decay technique For the pressure pulse decay approach (PPD), introduced by Brace et al. (1968), a pressure pulse is applied at one end of the sample, leading to a pressure propagation through the sample to the downstream reservoir. Considering Darcy's law and conservation of mass, the pressure-time response in the upstream and downstream volumes is a function of the sample's permeability and expressed by the following equation (Ghanizadeh et al. 2014): $$\begin{eqnarray*} {P_{up}}\left( t \right) - {P_{dn}}\ \left( t \right) = \left( {{P_{up}}\left( {{t_0}} \right) - {P_{dn}}\left( {{t_0}} \right)} \right)\ {e^{ - \epsilon t}}, \end{eqnarray*}$$(8) where |${P_{up}}( t )$| and |${P_{dn}}( t )$| are the pressures in upstream and downstream reservoirs, respectively. |${P_{up}}( {{t_0}} ) - {P_{dn}}( {{t_0}} )$| is defined as the initial pressure difference ΔP0, that is the pressure pulse applied at the beginning of the experiment, and Vup and Vdn the volumes of up- and downstream reservoir in m3. The pressure decay parameter |$\epsilon $| is the slope of the term ln(Pup–Pdn) as a function of time that can be solved graphically (Fig. 3) and is related to permeability with: $$\begin{eqnarray*} \epsilon = \frac{{ - k\ A}}{{\mu \ {\beta _{fl\ }}L}} \left( {\frac{1}{{{V_{\rm up}}}} + \frac{1}{{{V_{\rm dn}}}}} \right). \end{eqnarray*}$$(9) Figure 3. Open in new tabDownload slide Principle of the pulse decay technique in which a sudden increase in pressure is applied at the upstream side of the sample. The pressure decay curves are fitted and the slope of Δln(Pup_fit–Pdn_fit) over time is used for the calculation of permeability. Figure 3. Open in new tabDownload slide Principle of the pulse decay technique in which a sudden increase in pressure is applied at the upstream side of the sample. The pressure decay curves are fitted and the slope of Δln(Pup_fit–Pdn_fit) over time is used for the calculation of permeability. The solution given above is essentially based on Brace et al. (1968) developed for a test on low porosity rocks and assuming zero sample storage capacity. This assumption may be suitable for crystalline, low-porous rocks, but not for shales such as Opalinus Clay with considerable porosity. Several authors (e.g. Hsieh et al. 1981, Neuzil et al. 1981; Trimmer et al. 1980; Dickers & Smits 1988) presented analytical solutions to account for the effect of porosity and associated sample storage. By including the parameters a and b as ratios between effective pore volume and up- and downstream reservoirs size, the transcendental equation is solved (Dicker & Smits 1988): $$\begin{eqnarray*} \tan \left( \theta \right) = \ \frac{{\left( {a + b} \right)\ \theta }}{{{\theta ^2} - a\ b}}. \end{eqnarray*}$$(10) Eq. (9) is expanded by a denominator f1 being solved from eq. (11): $$\begin{eqnarray*} {f_1} = \ \frac{{{\theta _1}}}{{a + b}}, \end{eqnarray*}$$(11) where |${\theta _1}$| is the first root of eq. (10). Hsieh et al. (1981) and Neuzil et al. (1981) showed that if the ratio between compressive storage in the sample to compressive storage in the upstream reservoir lies between 0.01 and 10, permeability can be correctly determined. An alternative way of evaluating the PPD technique is the semi-steady-state interpretation. Under the assumption that the pressure gradient is linear through the sample, the fluid mass inside the sample is quite constant and, hence, the sample has zero storage capacity. Within individual time-intervals (⁠|$\partial t$|⁠), the pressure transients in up- and downstream reservoirs are treated as steady-state flow increments based on the Darcy equation: $$\begin{eqnarray*} k = \frac{Q}{A}\ \frac{{\mu \ L}}{{\Delta P}} \end{eqnarray*}$$(12) Where Q is the fluid flow in m3/s being solved by: $$\begin{eqnarray*} Q = \frac{{{\beta _{fl}}\ V}}{A}\ \frac{{\partial P}}{{\partial t}} \end{eqnarray*}$$(13) These equations are solved incrementally for time steps of approximately 2 min over the entire experiment and an average permeability value is calculated from up- and downstream compartment. By using this solution, the effective pore volume is not needed for the determination of permeability. Using this approach, we do not determine the sample storativity. 2.2.3 Pore pressure transmission technique Similar to the PPD approach, the pore pressure transmission technique (PPT) is based on the pressure propagation through the sample after applying an initial pressure difference (⁠|${\rm{\Delta }}{P_0}$|⁠, Fig. 4). In contrast to the PPD, the upstream is held constant (van Oort 1994; Metwally & Sondergeld 2011). In this technique, the storage capacity of the sample is integrated into the calculation of permeability similar as described by Hsieh et al. (1981). Hence, the pressure response depends on the effective porosity of the sample and the size of the downstream reservoir. The evaluation procedure is similar to the one described before: $$\begin{eqnarray*} {P_{\rm up}}\left( t \right) - {P_{\rm dn}}\ \left( t \right) = \left( {{P_{\rm up}}\left( {{t_0}} \right) - {P_{\rm dn}}\left( {{t_0}} \right)} \right)\ {e^{ - \epsilon t}}, \end{eqnarray*}$$(14) $$\begin{eqnarray*} \epsilon = \frac{{ - k\ {\theta ^2}}}{{\mu \ {\beta _{fl}}\ L\ {V_p}}}\ \end{eqnarray*}$$(15) Where |${V_p}$| is the effective pore volume. For samples with considerable porosity (>10 per cent), the effective pore volume and the downstream volume are expressed as ratio b which is used for the calculation of θ in eq. (16). It is defined as the first root of: $$\begin{eqnarray*} {\rm{tan\ }}\left( \theta \right) = \frac{b}{\theta }\ , \end{eqnarray*}$$(16) Equally to the PPD technique, we do not measure the sample storativity with this technique. Figure 4. Open in new tabDownload slide Principle of the pore pressure transmission technique in the upstream pressure is decreased and kept constant for the equilibration of the downstream pressure. Both curves are fitted and Δln(Pup_fit–Pdn_fit) over time is used for the permeability calculation. Figure 4. Open in new tabDownload slide Principle of the pore pressure transmission technique in the upstream pressure is decreased and kept constant for the equilibration of the downstream pressure. Both curves are fitted and Δln(Pup_fit–Pdn_fit) over time is used for the permeability calculation. 2.3 Sample preparation Cores in Mont Terri were obtained by triple-tube core barrel drilling with compressed air-cooling, followed by vacuum sealing in aluminium foil. Disk-shaped subsamples with 36–37 mm in diameter and 22–25 mm length were drilled and cut with bedding parallel to the sample axis. After drilling, the samples were stored at constant humidity in desiccators at approximately 90 per cent relative humidity (RH) to prevent desaturation. From these samples, we selected the macroscopically most homogeneous sample further used for all hydraulic tests. 2.4 Water content and porosity During drilling in the MT-URL, multiple core pieces were collected outside the excavation damage zone at intervals of approximately 1.5 m to determine the in situ gravimetric water content (Fig. 5). Additionally, three cylindrical subsamples were selected in close vicinity to the hydraulically tested sample for the determination of the porosity, water content, and degree of saturation. These have been stored in desiccators at high relative humidity to approximate the petrophysical properties of the tested sample stored equally prior to testing. Grain densities were derived from these samples by He-pycnometry after oven-drying at 105 °C and total porosities were then calculated based on caliper bulk volume measurements. The reference dry weight was obtained after oven drying at 105 °C until weight constancy. A summary of the results is given in Table 1, and are found to be in the range of the in-situ water content and published porosity values (Pearson et al. 2003; Busch et al. 2017). Figure 5. Open in new tabDownload slide Gravimetric water content measured with distance from tunnel side wall. Dashed line indicates the mean value of 7.27 per cent. Figure 5. Open in new tabDownload slide Gravimetric water content measured with distance from tunnel side wall. Dashed line indicates the mean value of 7.27 per cent. Table 1. Water content, porosity, and degree of saturation of selected subsamples retrieved adjacent to the sample tested for permeability measurements. Uncertainties are associated to uncertainties of caliper measurements of total sample volume. Subsample # . Water content (per cent) . Total porosity (per cent) . Water-loss porosity (per cent) . Degree of saturation (per cent) . 1 7.9 20.6 ± 0.8 19.2 84 ± 4 2 7.7 22.2 ± 0.7 19.2 77 ± 3 3 7.5 19.4 ± 0.6 18.1 85 ± 3 Subsample # . Water content (per cent) . Total porosity (per cent) . Water-loss porosity (per cent) . Degree of saturation (per cent) . 1 7.9 20.6 ± 0.8 19.2 84 ± 4 2 7.7 22.2 ± 0.7 19.2 77 ± 3 3 7.5 19.4 ± 0.6 18.1 85 ± 3 Open in new tab Table 1. Water content, porosity, and degree of saturation of selected subsamples retrieved adjacent to the sample tested for permeability measurements. Uncertainties are associated to uncertainties of caliper measurements of total sample volume. Subsample # . Water content (per cent) . Total porosity (per cent) . Water-loss porosity (per cent) . Degree of saturation (per cent) . 1 7.9 20.6 ± 0.8 19.2 84 ± 4 2 7.7 22.2 ± 0.7 19.2 77 ± 3 3 7.5 19.4 ± 0.6 18.1 85 ± 3 Subsample # . Water content (per cent) . Total porosity (per cent) . Water-loss porosity (per cent) . Degree of saturation (per cent) . 1 7.9 20.6 ± 0.8 19.2 84 ± 4 2 7.7 22.2 ± 0.7 19.2 77 ± 3 3 7.5 19.4 ± 0.6 18.1 85 ± 3 Open in new tab 2.5 Experimental setup and testing procedure The experimental setup consists of a triaxial flow cell containing the sample disk with dimensions of 24 mm in length and 36.5 mm in diameter. A jacket, consisting of an inner layer of lead and an outer layer of copper, covers and seals the sample from the surrounding confining pressure fluid (Fig. 6). Axial load is applied by a piston corresponding to the lateral confining pressure to establish an isostatic stress regime. The size of upstream and downstream reservoirs (2.7E-6 m³ and 3.3E-6 m³) have been determined by He-expansion prior to hydraulic testing. Two syringe pumps control the pore pressure and confining pressure. The pumps and valves are set up in such a way that all permeability measurement techniques can be applied without any changes in the system. A sinusoidal stepwise increase and decrease of pressure every 36–432 s, depending on the oscillation frequency, generates the oscillating upstream signal. To prevent chemical alterations a synthetic in situ formation water pore fluid was used throughout the experiments, following Mäder (2011). The experiments were conducted at constant temperatures of 30 ± 1 °C. Figure 6. Open in new tabDownload slide (a) Experimental setup used in this study. Upstream and downstream compartment can be connected to a vacuum pump to evacuate the system subsequently to the pore pressure pump. A reference volume is used for calibration of the reservoir volumes using Helium expansion (b) Close-up view on the sample jacketing system and pore pressure tubing. Bedding is oriented vertically and hydraulic properties are measured along the bedding. Figure 6. Open in new tabDownload slide (a) Experimental setup used in this study. Upstream and downstream compartment can be connected to a vacuum pump to evacuate the system subsequently to the pore pressure pump. A reference volume is used for calibration of the reservoir volumes using Helium expansion (b) Close-up view on the sample jacketing system and pore pressure tubing. Bedding is oriented vertically and hydraulic properties are measured along the bedding. The confining pressure was increased to 30 MPa to assure proper sealing of the jacketing system. Before full re-saturation of the sample, a vacuum pump was connected to the top and bottom compartment for one hour to de-air the pore pressure lines. Subsequently, the pore pressure was increased to 1 MPa for two days from both sides. After 10 d, the pore pressure was increased at one side of the sample to 6 MPa and the pressure was allowed to equilibrate within the sample reaching 6 MPa at the opposite side within a period of 24 hr. The oscillating pore pressure technique was applied prior to the other techniques to define suitable testing conditions practicable for this low permeable rock. A sinusoidal upstream pressure was generated, oscillating around a mean pore pressure of 6 MPa. We used oscillation frequencies of 0.26–0.023 mHz, corresponding to oscillation periods of approximately 1.1–12.1 hr. Depending on the applied frequency, the duration of a single test ranged from 1 to 7 d to obtain at least 6–7 steady oscillations for the permeability analysis. Applied amplitudes corresponded to 5, 10 and 25 per cent of the mean pressure. In this test series, the confining pressure was kept constant at 30 MPa. The second part of the experimental program consisted of the comparison to the other non-steady state techniques. Based on the results of the first PPO test series, we performed oscillation experiments with a frequency of 0.068 mHz, that is an oscillation period of 4.1 hr. For all methods, we applied a pressure amplitude of 10 per cent of the mean pressure (0.6 MPa). Furthermore, the influence of effective mean stress was investigated by lowering the confining pressure by steps of 5 MPa to a final effective stress of 4 MPa (Table 2). During the drained unloading, the pore pressure is kept constant at 6 MPa and the backflow of expelled pore water due to the poroelastic response is recorded. When the change in backflow is zero, the sample is considered consolidated and hydraulic testing using the PPO, PPD and PPT method were applied successively. Table 2. Overview of all permeability tests performed. The first part of this study is covered by tests 1 -36. The second part consists of tests 37–81. Note that tests 53–81 are summarized for simplification and not in chronological order since each method was applied at each unloading step and some testes were repeated. No. . Test type . σconf [Pmean] (MPa) . σeff (MPa) . Tosc (hr) . Aup/ΔP0 (percentage of Pmean in MPa) . 1–36 PPO 30 [6] 24 1.1–12.1 5, 10, 25 37–48 PPD 30 [6] 24 - 5, 10, 25 49–52 PPT 30 [6] 30 - ∼ 5–15 53–60 PPO 30 [6] 24 4.1 10 25 [6] 19 20 [6] 14 15 [6] 9 10 [6] 4 10 [4] 6 8 [2] 6 6 [2] 4 61–66 PPD 30 [6] 24 - 10 25 [6] 19 20 [6] 14 15 [6] 9 10 [6] 4 10 [4] 6 8 [2] 6 67–81 PPT 30 [6] 24 - ∼ 3–25 25 [6] 19 20 [6] 14 15 [6] 9 10 [6] 4 10 [4] 6 8 [2] 6 6 [2] 4 No. . Test type . σconf [Pmean] (MPa) . σeff (MPa) . Tosc (hr) . Aup/ΔP0 (percentage of Pmean in MPa) . 1–36 PPO 30 [6] 24 1.1–12.1 5, 10, 25 37–48 PPD 30 [6] 24 - 5, 10, 25 49–52 PPT 30 [6] 30 - ∼ 5–15 53–60 PPO 30 [6] 24 4.1 10 25 [6] 19 20 [6] 14 15 [6] 9 10 [6] 4 10 [4] 6 8 [2] 6 6 [2] 4 61–66 PPD 30 [6] 24 - 10 25 [6] 19 20 [6] 14 15 [6] 9 10 [6] 4 10 [4] 6 8 [2] 6 67–81 PPT 30 [6] 24 - ∼ 3–25 25 [6] 19 20 [6] 14 15 [6] 9 10 [6] 4 10 [4] 6 8 [2] 6 6 [2] 4 Open in new tab Table 2. Overview of all permeability tests performed. The first part of this study is covered by tests 1 -36. The second part consists of tests 37–81. Note that tests 53–81 are summarized for simplification and not in chronological order since each method was applied at each unloading step and some testes were repeated. No. . Test type . σconf [Pmean] (MPa) . σeff (MPa) . Tosc (hr) . Aup/ΔP0 (percentage of Pmean in MPa) . 1–36 PPO 30 [6] 24 1.1–12.1 5, 10, 25 37–48 PPD 30 [6] 24 - 5, 10, 25 49–52 PPT 30 [6] 30 - ∼ 5–15 53–60 PPO 30 [6] 24 4.1 10 25 [6] 19 20 [6] 14 15 [6] 9 10 [6] 4 10 [4] 6 8 [2] 6 6 [2] 4 61–66 PPD 30 [6] 24 - 10 25 [6] 19 20 [6] 14 15 [6] 9 10 [6] 4 10 [4] 6 8 [2] 6 67–81 PPT 30 [6] 24 - ∼ 3–25 25 [6] 19 20 [6] 14 15 [6] 9 10 [6] 4 10 [4] 6 8 [2] 6 6 [2] 4 No. . Test type . σconf [Pmean] (MPa) . σeff (MPa) . Tosc (hr) . Aup/ΔP0 (percentage of Pmean in MPa) . 1–36 PPO 30 [6] 24 1.1–12.1 5, 10, 25 37–48 PPD 30 [6] 24 - 5, 10, 25 49–52 PPT 30 [6] 30 - ∼ 5–15 53–60 PPO 30 [6] 24 4.1 10 25 [6] 19 20 [6] 14 15 [6] 9 10 [6] 4 10 [4] 6 8 [2] 6 6 [2] 4 61–66 PPD 30 [6] 24 - 10 25 [6] 19 20 [6] 14 15 [6] 9 10 [6] 4 10 [4] 6 8 [2] 6 67–81 PPT 30 [6] 24 - ∼ 3–25 25 [6] 19 20 [6] 14 15 [6] 9 10 [6] 4 10 [4] 6 8 [2] 6 6 [2] 4 Open in new tab 2.6 Microstructural analysis To compare the loaded and hydraulically tested to a non-tested, non-loaded sample, microstructural investigations were carried out. Therefore, the sample was removed from the setup after hydraulic testing. This sample and a twin sample, taken from close vicinity and stored at constant humidity during lab testing, were dried at constant temperatures of approximately 8 °C for several weeks. From each sample, a mm-sized subsample was dry cut and polished by broad ion beam milling using a JEOL SM 0 9010 producing a planar surface of approximately 2 mm² perpendicular to bedding. After tungsten coating, these subsamples were imaged in a Zeiss SUPRA 55 scanning electron microscope (SEM). For pore identification, secondary electron (SE2) images were used to distinguish pore space from solid material at different magnifications. Additionally, the combination of back-scattered electron (BSE) images and energy-dispersive X-ray spectroscopy (EDX) was used for the analysis of mineral phases. 3 RESULTS AND DISCUSSION For the analysis of pore pressure data, we fitted the recorded data to the governing equations of the pressure propagation. These are, for the PPO method, the sinusoidal pressure function and, for the PPD and PPT techniques, the pressure equations 8 and 14, respectively. For the fitting, the least-squared-difference method is used and plotted as fitting curves shown in Figs 1, 3 and 4. 3.1 Comparison of analytical solutions for oscillation tests The two different analytical solutions used to evaluate the permeability and storativity coefficients in the pore pressure oscillation tests are consistent for all tests, with permeability coefficients ranging from 6.1E-21 to 9.4E-21 m2 and sample storativities ranging from 8.0E-11 to 1.7E-10 (Fig. 7). The deviation between the two approaches for all tests is on average 0.5 per cent for permeability and 1.1 per cent for storativity. The advantage of eq. (5) (solution of Bernabé et al. 2006) over eqs (1) and (2) (solution of Kranz et al. 1990) is that the dimensionless parameters can be treated as independent material properties. Since the deviations between the solutions are minor, only the solution of Bernabé et al. (2006) is used in the following discussion. Figure 7. Open in new tabDownload slide Comparison of permeability and storativity values obtained by oscillation method for solutions after Kranz et al. (1990) and Bernabé et al. (2006). Identical values of both methods would plot on the grey 1:1 line. Figure 7. Open in new tabDownload slide Comparison of permeability and storativity values obtained by oscillation method for solutions after Kranz et al. (1990) and Bernabé et al. (2006). Identical values of both methods would plot on the grey 1:1 line. 3.2 Comparison of permeability obtained by different methods In general, permeability values obtained from the PPO technique are slightly lower (kmean = 7.2 ± 0.67E-21 m2) than those from PPD technique (kmean = 7.5 ± 0.77E-21 m2) and higher than those from the PPT technique (kmean = 6.6 ± 0.46E-21 m2) at constant effective stresses of 24 MPa and assuming an effective porosity of 20 per cent (Fig. 8). By decreasing the effective porosity from 20 to 18 per cent, for instance, the permeability values reduce by 2.4 and 3.7 per cent for the PPD and PPT technique, respectively. Without consideration of sample porosity, the permeability coefficients are generally smaller with 5.8 ± 0.56E-21 m2 for the PPD and 5.5 ± 0.71E-22 m2 for semi-steady-state evaluation of the PPD. Figure 8. Open in new tabDownload slide Overview of mean permeabilities obtained by different methods at constant effective stresses of 24 MPa. For the PPD and PPT different effective porosities have been considered for the calculation of permeability. Error bar indicate standard deviation based on results of different tests performed by each measurement technique. Figure 8. Open in new tabDownload slide Overview of mean permeabilities obtained by different methods at constant effective stresses of 24 MPa. For the PPD and PPT different effective porosities have been considered for the calculation of permeability. Error bar indicate standard deviation based on results of different tests performed by each measurement technique. The discrepancies between the permeability values obtained by different techniques cannot be explained by sample heterogeneity or changing boundary conditions since only one sample was used for all tests and the measurement accuracy of sensors and reservoir sizes remained constant. We can also exclude alterations of the sample due to water-clay interactions since there is no trend of permeability changes over time. Therefore, differences are mainly associated with the data analysis and interpretation. These are related to uncertainties in the curve-fitting procedure and the numerical solution of eqs (1), (2) and (5). For the latter, the uncertainties are associated with the sensitivity of R and δ for the solution of the dimensionless parameters. The curve fitting approach based on least-squared differences can be optimized by increasing the test duration and running multiple oscillation cycles. Hence, the variance of squared differences becomes stable over time and allows a robust data fitting. Additionally, the influence of small temperature fluctuations is reduced. As shown in Fig. 8, the consideration of effective porosity and, hence, the sample storage capacity influences the calculation of permeability. This consideration involves more uncertainties: On the one hand, the pore volume available for fluid flow and storage is essentially not known since only an unknown fraction of the entire pore space is used as an active transport pathway. Additionally, the pore space is reduced due to loading-induced compaction. Ferrari et al. (2016) found from drained Oedometer tests on OPA samples, taken from the shaly facies at the MT URL, a reduction of porosity—calculated from void ratio—of approximately 17 per cent at vertical loads of 30 MPa. In this study, the calculated changes of permeability assuming varying effective pore volumes are very small in the order of 0.08E-21 m² (PPD) and 0.2E-21 m² (PPT) per absolute change of 1 per cent in porosity. On the other hand, the reservoir size can introduce uncertainties in the estimation of permeability and an appropriate choice of reservoir size is crucial. The ratio between compressive storage, derived from sample dimensions and sample storativity obtained from PPO tests, and reservoir storage, approximated by fluid compressibility and reservoir volume, should be between 0.01 and 10 according to Neuzil et al. (1981). In our study, this ratio is approximately 2 and the permeability estimation should be considered correct. In the same way, Escoffier et al. (2005) successfully performed pulse decay permeability tests on a low-permeable mudstone (Callovo-Oxfordian claystone) with similar experimental setup conditions and similar sample characteristics. Also, the calculation of storativity using the pore pressure oscillation technique can produce erroneous results, if the experimental setup has a large downstream volume. In such cases ξ (i.e. the dimensionless storativity) becomes small and the estimation of sample storativity uncertain (Bernabé et al. 2006). However, the values for ξ in our study are between 1 and 2, which suggests negligible uncertainties in our storativity estimations. 3.3 Comparison to previous studies of OPA The water permeability was obtained in this study at relatively high effective stresses compared to the in-situ mean effective stress at the MT URL of 1.5–2.7 MPa (Martin & Lanyon 2003). Marschall et al. (2005) conducted hydraulic lab tests at similar effective confinements of 19 MPa with flow parallel to bedding and obtained permeabilities of 3–8E-21 m². Amann-Hildenbrand et al. (2015) and Philipp et al. (2017) conducted pulse decay experiments at similar effective confinements of 17–21 MPa and 27 MPa on Opalinus Clay samples of the shaly facies perpendicular to bedding and reported coefficients of 1–6E-21 m² and 1.6E-21 m², respectively. Horseman et al. (2005) determined specific storage coefficients for Opalinus Clay samples at effective stress of 24 MPa derived from consolidation measurements and pore water displacement of 8.4E-6 m−1, corresponding to storativity of 8.4E-10 Pa−1. Many researchers have investigated gas transport properties of Opalinus Clay (e.g. Marschall et al. 2005; Zhang & Rothfuchs 2008, Amann-Hildebrand et al. 2015, Al Reda et al. 2020) but hydraulic characterization studies from laboratory measurements are sparse. Nevertheless, our results are in very good agreement with earlier results. 3.4 Frequency dependence of permeability Oscillation tests conducted under varying frequencies ranging from periods of 1–12 hr yield permeability values between 6.0E-21 m2 and 9.4E-21 m2 under constant effective mean stress of 24 MPa (Fig. 9). There is a minor trend of increasing permeability towards oscillation frequencies higher than 0.14 mHz, that is Tosc smaller than 2 hr. Frequency-dependent permeability variations have previously been investigated and proposed explanations are end effects, pressure sensitivity, sample heterogeneity and inertia effect (Fischer & Paterson 1992; Bernabé et al. 2004; Song & Renner 2006). Song & Renner (2006) performed oscillation tests on Fontainebleau sandstone utilizing oscillation periods spanning more than three orders of magnitudes. For some of their samples, they observed increasing permeability coefficients with increasing oscillation periods up to a threshold values varying among the tested samples. For oscillation periods above this threshold, permeability coefficients tend to decrease. Hasanov et al. (2017) argued, based on capillary tube experiments, that frequency-dependent permeability coefficients may be associated with partial saturation or internal resonance of the pressure pump. However, the above-mentioned studies used porous media of very different texture compared to our clay shale and, to our knowledge, oscillation experiments that analyse the frequency dependence of such rocks are missing. In our study, the interpretation of the frequency-dependent permeability coefficient remains unclear as oscillation periods only cover one order of magnitude and partial saturation of the sample or the capillary system can be excluded due to our rigorous saturation procedure. Figure 9. Open in new tabDownload slide Permeability values obtained by the pore pressure oscillation methods as a function of applied oscillation frequency. Data are plotted for different oscillation amplitudes (A): 5, 10 and 25 per cent of the mean pore pressure corresponding to 0.3, 0.6 and 1.5 MPa. Figure 9. Open in new tabDownload slide Permeability values obtained by the pore pressure oscillation methods as a function of applied oscillation frequency. Data are plotted for different oscillation amplitudes (A): 5, 10 and 25 per cent of the mean pore pressure corresponding to 0.3, 0.6 and 1.5 MPa. In our study, the minimum oscillation period was found to be 1 hr. However, this limitation is dependent on various experimental factors such as sample dimension and orientation of bedding, reservoir size as well as sample permeability and storage capacity. In general, lower frequencies, that is higher oscillation periods, are more capable to take into account the storage capacity (Fischer 1992). 3.5 Influence of applied pressure difference Different applied pressure differences along the sample have a minor effect on permeability and storativity at a constant effective stress of 24 MPa (Figs 9 and 10). Mean permeability values are given in Table 3 and indicate no significant differences (i.e. less than 3 per cent) but a minor trend of higher permeabilities with increasing applied amplitudes. This may be explained by texture disturbance or compressibility variations with varying effective stress. Several authors (Brace et al. 1968; Walder & Nur 1986; Kranz et al. 1990; Fischer & Paterson 1992; Metwally & Sondergeld 2011) proposed to use amplitudes/initial pressure differences of maximum 10 per cent of the mean pressure to prevent poroelastic effects. Although this may be true, they presented no effective stress range for this underlying suggestion. In this study, no systematic trends were found, which is likely due to the high effective stresses applied in this study (Fig. 9). Figure 10. Open in new tabDownload slide Comparison of all permeability and storativity values at the full range of effective stress obtained by PPO, PPD and PPT technique. The scatter of storativity value becomes larger with increasing applied amplitude. Figure 10. Open in new tabDownload slide Comparison of all permeability and storativity values at the full range of effective stress obtained by PPO, PPD and PPT technique. The scatter of storativity value becomes larger with increasing applied amplitude. Table 3. Hydraulic parameters (permeability and storativity) obtained from pore pressure oscillation tests at different upstream amplitudes of 5, 10 and 25 per cent (i.e. 0.3, 0.6 and 1.5 MPa) of the mean pore pressure. Given are mean values and the corresponding standard deviation (std). Oscillation amplitude Aup (per cent) . Mean k (m2) . std k (m2) . Mean β (Pa−1) . std β (Pa−1) . 5 7.1E-21 0.43E-21 1.1E-10 0.11E-10 10 7.2E-21 0.61E-21 1.2E-10 0.17E-10 25 7.3E-21 0.95E-21 1.2E-10 0.25E-10 Oscillation amplitude Aup (per cent) . Mean k (m2) . std k (m2) . Mean β (Pa−1) . std β (Pa−1) . 5 7.1E-21 0.43E-21 1.1E-10 0.11E-10 10 7.2E-21 0.61E-21 1.2E-10 0.17E-10 25 7.3E-21 0.95E-21 1.2E-10 0.25E-10 Open in new tab Table 3. Hydraulic parameters (permeability and storativity) obtained from pore pressure oscillation tests at different upstream amplitudes of 5, 10 and 25 per cent (i.e. 0.3, 0.6 and 1.5 MPa) of the mean pore pressure. Given are mean values and the corresponding standard deviation (std). Oscillation amplitude Aup (per cent) . Mean k (m2) . std k (m2) . Mean β (Pa−1) . std β (Pa−1) . 5 7.1E-21 0.43E-21 1.1E-10 0.11E-10 10 7.2E-21 0.61E-21 1.2E-10 0.17E-10 25 7.3E-21 0.95E-21 1.2E-10 0.25E-10 Oscillation amplitude Aup (per cent) . Mean k (m2) . std k (m2) . Mean β (Pa−1) . std β (Pa−1) . 5 7.1E-21 0.43E-21 1.1E-10 0.11E-10 10 7.2E-21 0.61E-21 1.2E-10 0.17E-10 25 7.3E-21 0.95E-21 1.2E-10 0.25E-10 Open in new tab Nevertheless, PPO data scatter is more pronounced with increasing applied amplitude. The standard deviation for permeability and storativity shows a difference by a factor of two for amplitudes between 5 and 25 per cent of the mean fluid pressure (Table 3) whereas the mean values do not change significantly. 3.6 Influence of effective stress Within the effective stress range tested in this study (i.e. 24 to 6 MPa), no obvious change in permeability with decreasing effective stress at constant testing conditions (similar upstream pressure/initial pressure difference and mean pore pressure) was observed (Fig. 11). First, we explain this with the high isotropic effective stresses, which resulted efficiently in the closure of microcracks (Walsh 1965), but was not high enough to cause permanent deformation of the microfabric. Such cracks can have an enormous influence on permeability (Benson et al. 2006; Guéguen et al. 2011). Figs 12(a) and (b) show back-scattered electron images (BSE-SEM) of the tested sample in this study and a non-tested sample with sampling location in close vicinity. The images indicate the presence of bedding-parallel microcracks which are larger and more present in the non-tested sample. Houben et al. (2013) found that these cracks account for 20 per cent of the total porosity in OPA samples from the shaly facies. However, their origin remains unclear since core extraction, sample storage, preparation and drying can induce crack formation. We conclude that these microcracks are closed for effective confining stress states >6 MPa and remain partly closed after removing the sample. This is consistent with observations made by Birchall et al. (2008), in which a significant increase in permeability was observed for effective stresses below 1 MPa during an isotropic unloading test on Opalinus Clay. Secondly, there are no indications for major pore collapse or microstructural damages. Figs 12(c) and (d) show the porous structure a non-tested and the tested OPA sample in which no qualitative differences or structural damages can be observed (cf. Houben et al. 2013; Keller et al. 2013). It is important to realize that the tested sample was loaded to higher effective stresses during the experiment than Opalinus Clay at Mont Terri experienced during its burial history defined by a maximum depth of 1350 m (Mazurek et al. 2006). Generally, compaction of mudstones and, hence, the reduction of porosity results in a collapse of larger pores (Yang & Alpin 2007). In our sample, intragranular large pores in fossils and non-clayey mineral aggregates as well as intergranular pores along boundaries of clay matrix and non-clay particles are intact and likely non-deformed (Fig. 12d). If these larger pores experienced no visible damage, the pores in the clay matrix are also assumed to be intact, and these have a major contribution to the permeability of Opalinus Clay (Keller & Holzer 2018). In conclusion, the relatively high effective stress range used in this study shows no qualitative indication of irreversible damage influencing the hydraulic properties of Opalinus Clay, and changes in the pore structure with different effective stresses are mainly elastic (Olgaard et al. 1996, 1997), causing changes in permeability which can not be resolved based on our data. Figure 11. Open in new tabDownload slide Permeability coefficients as a function of effective confinement during unloading at similar oscillation amplitude/initial pressure differences of 10 per cent of the mean pore pressure. For the PPD and PPT methods, an effective porosity of 20 per cent was used for the calculation of permeability. The values show no significant change of for none of the methods used. Figure 11. Open in new tabDownload slide Permeability coefficients as a function of effective confinement during unloading at similar oscillation amplitude/initial pressure differences of 10 per cent of the mean pore pressure. For the PPD and PPT methods, an effective porosity of 20 per cent was used for the calculation of permeability. The values show no significant change of for none of the methods used. Figure 12. Open in new tabDownload slide (a) & (b) Scanning electron images (back-scattered images) of a non-tested and the tested Opalinus Clay sample at 4000× magnification. Both samples are taken from one drill core from locations in close vicinity. Typical minerals, solid components and pores can be distinguished based on density contrast. Image comparison of tested and non-tested sample shows no indication for damage of larger minerals or fossil fragments. Bedding-parallel micro cracks are larger and more abundant in the non-tested sample. (c) Scanning electron images (secondary electron image) of the tested Opalinus sample at 15 000× magnification. Here, pores can be distinguished from solid phase by black color. Porous fossil fragments are intact and show no indication for pore collapse or compaction damage. Figure 12. Open in new tabDownload slide (a) & (b) Scanning electron images (back-scattered images) of a non-tested and the tested Opalinus Clay sample at 4000× magnification. Both samples are taken from one drill core from locations in close vicinity. Typical minerals, solid components and pores can be distinguished based on density contrast. Image comparison of tested and non-tested sample shows no indication for damage of larger minerals or fossil fragments. Bedding-parallel micro cracks are larger and more abundant in the non-tested sample. (c) Scanning electron images (secondary electron image) of the tested Opalinus sample at 15 000× magnification. Here, pores can be distinguished from solid phase by black color. Porous fossil fragments are intact and show no indication for pore collapse or compaction damage. 3.7 Evaluation of the different methods All methods used are applicable to Opalinus Clay and yield permeability coefficient in the same order of magnitude. The pulse decay and pore pressure transmission technique benefit from their simple testing procedure whereas the pore pressure oscillation technique required technically more advanced equipment, for example a high precision sinusoidal pressure generator. In terms of time efficiency, all methods require one to two days of testing time for the sample size used in this study. The pulse decay and pore pressure equilibration technique ideally require a fully equilibrated pore pressure within the sample prior to the test, which significantly increases the experimental time. This pre-equilibration is not necessary for the pore pressure oscillation technique if there is no strong coupling between the effective stress and storage properties. But here, the experimental time depends on the selection of the oscillation period and sufficient cycles. Since we found no change of permeability values for oscillation periods larger than two hours, the experimental time for this sample can be reduced to one day. In fact, the ability to run continuously multiple cycles is a great benefit of this method as influences such as small temperature fluctuation are diminished. This method is especially useful when determining permeability changes during sample deformations. Additionally, the calculation of hydraulic properties is independent of sample porosity which excludes the uncertainty of effective pore volume determination. Contrarily for the other two methods (PPD and PPT), the effective porosity must be included to account for sample storage capacity. Moreover, the effective mean stress remains constant throughout the entire test, which is especially not the case for the pore pressure transmission technique. Furthermore, the PPO method enables the calculation of storativity independently from permeability under consideration of appropriate reservoir volumes. Attention must be paid when designing the experimental apparatus since the ratio of reservoir and sample pore volume needs to be adjusted to the sample properties (permeability and storativity). For low-permeable media, the reservoir volume should be minimized as far as possible to obtain high-quality data. 3.8 Uncertainty analysis Proper uncertainty analyses include three different types of uncertainties. Type I is associated with errors and imprecisions of sensors, measurement devices, and/or computational inaccuracies (Mann 1993). In our study, these uncertainties are based on the caliper measurements of sample dimensions, the accuracy of pressure transducers and the numerical solver used for the PPO technique. Including the errors for sample dimensions and the numerical solver, it becomes evident that these have only a very marginal effect on the hydraulic parameters being at least one order of magnitude below the resolution of parameters presented. The uncertainty of pressure sensors becomes insignificant since the static off-set of each sensor is determined before each experiment. We used pressure sensors with assigned full-scale errors (0.03 MPa) and, therefore, the error is constant over the entire pressure range. In addition, the calculation of permeability using an incompressible fluid is based on relative quantities (amplitudes or pressure difference) rather than absolute pressures and, hence, shifts would not influence the outcome. Inaccurate measurement and/or fluctuations of temperature as well as associated changes in fluid viscosity and compressibility are not significant either, because we used a fully temperature-controlled system and the uncertainties would be the same for all experiments. Furthermore, the numerical solver used to obtain the dimensionless parameters for the PPO method implies uncertainties. We run the approximation function in multiple loops to decrease the uncertainty of the curve matching. This produces errors which are several order of magnitudes smaller than the calculated values of permeability and storativity. Type II uncertainties are associated with inherent variations in natural parameters caused by inhomogeneity and rock anisotropy (Mann 1993). We can exclude this type since only one sample was used for all measurements in this study. The last type of uncertainty, Type III, lies in the incomplete knowledge of certain parameters needed for the calculation of the hydraulic parameters (Mann 1993). In our case, these uncertainties are subject to the incorrectness of effective porosity used in the PPD and PPT techniques. We have shown the influence of porosity changes on calculated permeability values earlier. The need for simplification is related to (i) the lack of knowledge which fraction of total porosity accounts for fluid flow or storage and (ii) the lack of knowledge of porosity change under experimental loading conditions. Furthermore, uncertainties, which are especially decisive when testing low-permeable rocks, may arise due to fluid leakages or partial saturation. However, these errors are eliminated by intensive leak tests prior to the experiments and our rigorous saturation procedure. In the light of all possible uncertainties and possible error sources, the discrepancies between permeability values obtained by different methods are minor and due to our setup design, possible error sources of each method have likely no significant consequence and are comparable in this study. 4 CONCLUSIONS In this study, the PPO, PPD and the pore PPT were successfully applied for determining the permeability of Opalinus Clay. They yield mean permeability coefficients between 5.5E-21 and 7.5E-21 m2. Without porosity correction, the PPD method yields permeability coefficients which are 20 per cent lower than those obtained from the PPO but assuming a more realistic effective porosity of 20 per cent, the mean permeability from the PPD method is 4 per cent higher than those from the PPO. The mean values obtained by the pressure transmission technique are around 8 per cent lower than those of the pore pressure oscillation methods. The semi-steady state PPD evaluation, which does not require porosity assumptions, yields values similar to those from the PPD without porosity correction. Considering various uncertainties associated with the permeability measurements of low-permeable rocks, these discrepancies are considered minor. The permeability coefficients obtained by the oscillation method are within the range of the values obtained from all three methods. However, data scatter for the PPO method is less. For the applied range of frequencies, permeability is slightly increasing with higher frequencies. For the applied range of amplitudes, the permeability remained constant within a few per cent. The mean storativity values remain constant with applied amplitudes; scattering is less at smaller amplitudes. Experimental times of all tested methods are similar with one to two days. However, the pore pressure oscillation method benefits from continuous measurements and constant mean effective stress conditions. Furthermore, the determination of the effective porosity is not required and tests can be performed without initial pore pressure equilibration, which is mandatory for the other two methods. To conclude, the pore pressure oscillation technique is the most advantageous method for the measurement of hydraulic properties of a very low permeable clay-rich sample. When testing other low permeability rocks like the Callovo-Oxfordian claystone or the Boom Clay, we recommend other researchers to adopt our experimental protocol, which includes the experimental pre-treatment, that is the careful sample preparation, sample storage under controlled humidity conditions in order to maintain the initial water content, and the saturation procedure. The experimental conditions were shown to be adequate, that is with oscillation periods in the range of hours, sample dimensions in the 10th mm range, and reservoir volumes below 5 ml. ACKNOWLEDGEMENTS The authors gratefully thank the Swiss Federal Nuclear Safety Inspectorate ENSI for financial support. This study was performed in the framework of the HM-C project entitled ‘Material Approach for Opalinus Clay’. Patrick Thelen is thanked for the help provided during the laboratory work. We thank J. Billiotte and C. Davy for their very constructive feedback, which helped to improve the manuscript considerably. In this manuscript, we refer to data shown in tables and figures. Full data sets will be available upon request. REFERENCES Al Reda S.M. , Yu C., Berthe G., Matray J.M., 2020 . Study of the permeability in the Opalinus clay series (Mont Terri-Switzerland) using the steady state method in Hassler cell , J. Petrol. Sci. 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A Sample cross-sectional area m2 a Ratio of effective pore and upstream volume dimensionless Adn Downstream amplitude Pa Aup Upstream amplitude Pa b Ratio of effective pore and downstream volume dimensionless D Diffusivity m2 s–1 g Gravitational acceleration m s–2 k Permeability m2 K Hydraulic conductivity m s–1 L Sample length m P Pore pressure Pa Pdn Pore pressure in upstream reservoir Pa P Pore pressure Pa Pup Pore pressure in upstream reservoir Pa ΔP0 Initial pressure difference Pa Q Flow rate m3 s–1 R Ratio between up- and downstream amplitude dimensionless Tosc Oscillation period s t time s Vdn Downstream reservoir volume m3 Vfl Fluid volume m3 Vp Pore volume m³ Vup Upstream reservoir volume m3 α Parameter in solution of Kranz et al. (1990) dimensionless βB Bulk compressibility Pa−1 βdn Downstream storage m3 Pa–1 βfl Fluid compressibility Pa−1 βG Grain compressibility Pa−1 βst Sample storativity Pa−1 γ Parameter in solution of Kranz et al. (1990) dimensionless δ Phase shift between up-and downstream signal ° or cycles ε Exponential decay parameter s−1 η Parameter in solution of Bernabé et al. (2006) dimensionless θ Root of eq. (10) & (16) dimensionless µ Fluid viscosity Pa·s ξ Parameter in solution of Bernabé et al. (2006) dimensionless ρ Fluid density kg m–3 σconf Confining stress Pa σeff Effective stress Pa ϕ Porosity dimensionless ϕe Effective porosity dimensionless ω Angular frequency s−1 Symbol . Definition . Unit . A Sample cross-sectional area m2 a Ratio of effective pore and upstream volume dimensionless Adn Downstream amplitude Pa Aup Upstream amplitude Pa b Ratio of effective pore and downstream volume dimensionless D Diffusivity m2 s–1 g Gravitational acceleration m s–2 k Permeability m2 K Hydraulic conductivity m s–1 L Sample length m P Pore pressure Pa Pdn Pore pressure in upstream reservoir Pa P Pore pressure Pa Pup Pore pressure in upstream reservoir Pa ΔP0 Initial pressure difference Pa Q Flow rate m3 s–1 R Ratio between up- and downstream amplitude dimensionless Tosc Oscillation period s t time s Vdn Downstream reservoir volume m3 Vfl Fluid volume m3 Vp Pore volume m³ Vup Upstream reservoir volume m3 α Parameter in solution of Kranz et al. (1990) dimensionless βB Bulk compressibility Pa−1 βdn Downstream storage m3 Pa–1 βfl Fluid compressibility Pa−1 βG Grain compressibility Pa−1 βst Sample storativity Pa−1 γ Parameter in solution of Kranz et al. (1990) dimensionless δ Phase shift between up-and downstream signal ° or cycles ε Exponential decay parameter s−1 η Parameter in solution of Bernabé et al. (2006) dimensionless θ Root of eq. (10) & (16) dimensionless µ Fluid viscosity Pa·s ξ Parameter in solution of Bernabé et al. (2006) dimensionless ρ Fluid density kg m–3 σconf Confining stress Pa σeff Effective stress Pa ϕ Porosity dimensionless ϕe Effective porosity dimensionless ω Angular frequency s−1 Open in new tab   Symbol . Definition . Unit . A Sample cross-sectional area m2 a Ratio of effective pore and upstream volume dimensionless Adn Downstream amplitude Pa Aup Upstream amplitude Pa b Ratio of effective pore and downstream volume dimensionless D Diffusivity m2 s–1 g Gravitational acceleration m s–2 k Permeability m2 K Hydraulic conductivity m s–1 L Sample length m P Pore pressure Pa Pdn Pore pressure in upstream reservoir Pa P Pore pressure Pa Pup Pore pressure in upstream reservoir Pa ΔP0 Initial pressure difference Pa Q Flow rate m3 s–1 R Ratio between up- and downstream amplitude dimensionless Tosc Oscillation period s t time s Vdn Downstream reservoir volume m3 Vfl Fluid volume m3 Vp Pore volume m³ Vup Upstream reservoir volume m3 α Parameter in solution of Kranz et al. (1990) dimensionless βB Bulk compressibility Pa−1 βdn Downstream storage m3 Pa–1 βfl Fluid compressibility Pa−1 βG Grain compressibility Pa−1 βst Sample storativity Pa−1 γ Parameter in solution of Kranz et al. (1990) dimensionless δ Phase shift between up-and downstream signal ° or cycles ε Exponential decay parameter s−1 η Parameter in solution of Bernabé et al. (2006) dimensionless θ Root of eq. (10) & (16) dimensionless µ Fluid viscosity Pa·s ξ Parameter in solution of Bernabé et al. (2006) dimensionless ρ Fluid density kg m–3 σconf Confining stress Pa σeff Effective stress Pa ϕ Porosity dimensionless ϕe Effective porosity dimensionless ω Angular frequency s−1 Symbol . Definition . Unit . A Sample cross-sectional area m2 a Ratio of effective pore and upstream volume dimensionless Adn Downstream amplitude Pa Aup Upstream amplitude Pa b Ratio of effective pore and downstream volume dimensionless D Diffusivity m2 s–1 g Gravitational acceleration m s–2 k Permeability m2 K Hydraulic conductivity m s–1 L Sample length m P Pore pressure Pa Pdn Pore pressure in upstream reservoir Pa P Pore pressure Pa Pup Pore pressure in upstream reservoir Pa ΔP0 Initial pressure difference Pa Q Flow rate m3 s–1 R Ratio between up- and downstream amplitude dimensionless Tosc Oscillation period s t time s Vdn Downstream reservoir volume m3 Vfl Fluid volume m3 Vp Pore volume m³ Vup Upstream reservoir volume m3 α Parameter in solution of Kranz et al. (1990) dimensionless βB Bulk compressibility Pa−1 βdn Downstream storage m3 Pa–1 βfl Fluid compressibility Pa−1 βG Grain compressibility Pa−1 βst Sample storativity Pa−1 γ Parameter in solution of Kranz et al. (1990) dimensionless δ Phase shift between up-and downstream signal ° or cycles ε Exponential decay parameter s−1 η Parameter in solution of Bernabé et al. (2006) dimensionless θ Root of eq. (10) & (16) dimensionless µ Fluid viscosity Pa·s ξ Parameter in solution of Bernabé et al. (2006) dimensionless ρ Fluid density kg m–3 σconf Confining stress Pa σeff Effective stress Pa ϕ Porosity dimensionless ϕe Effective porosity dimensionless ω Angular frequency s−1 Open in new tab APPENDIX B: DEFINITION OF HYDRAULIC PARAMETERS Permeability is the ability of fluid to flow through porous media. In fully water-saturated porous media the fluid properties, i.e. viscosity and density, as well as the gravitational acceleration are used to derive the hydraulic conductivity: $$\begin{eqnarray*} K = \frac{{\rho \ g}}{\mu }k, \end{eqnarray*}$$(B1) where K is the hydraulic conductivity in m s–1, ρ the fluid density in kg m–³, µ the dynamic viscosity of water in Pa·s both at ambient pressure and temperature, g the gravitational acceleration in m s–2 and k the permeability in m2. Sometimes, instead of SI units, the units for permeability is denoted as Darcy (D) or, in case for low-permeability media, nDarcy (nD), which equals E-21 m2. Storativity |${\beta _{st}}$| or storage capacity is the volume of fluid stored in porous media due to a change in pore pressure under constant confining pressure (Zimmerman et al. 1986): $$\begin{eqnarray*} {\beta _{st}} = \ \frac{1}{V}\ {\left( {\frac{{\partial {V_{fl}}}}{{\partial P}}} \right)_{\delta \ {\sigma _{conf}} = \ 0}}, \end{eqnarray*}$$(B2) where |$\partial {V_{fl}}$| is the change of fluid volume in m3 as a response to a pore pressure change |$\partial P$| in Pa in the total rock volume V in m3. Furthermore, storativity can be expressed as the sum of the rock components compressibilities (Brace et al. 1968; Zimmerman et al. 1986): $$\begin{eqnarray*} {\beta _{st}} = \ {\beta _B} + \ \phi {\beta _{fl}} - \left( {1 + {\phi _e}} \right){\beta _G}, \end{eqnarray*}$$(B3) where |${\beta _B}$| is the bulk compressibility in Pa−1, |${\phi _e}$| the effective porosity, |${\beta _{fl}}$| the fluid compressibility in Pa−1 and |${\beta _G}$| the grain compressibility in Pa−1. Diffusivity, D, in m²/s is a measure of a hydraulic pressure diffusion in porous media and it relates the permeability to the storativity together with the dynamic viscosity of the fluid (Brace et al. 1968): $$\begin{eqnarray*} D = \frac{k}{{\mu \ {\beta _{st}}}} \end{eqnarray*}$$(B4) APPENDIX C: DERIVATION OF EQUATIONS FOR PORE PRESSURE OSCILLATION TECHNIQUE Kranz et al. (1990) based their equations on diffusivity and permeability as given by eqs (C1), (C2) and (C3). For the derivation of this set of equations, the reader is referred to the original reference source. $$\begin{eqnarray*} {\rm{\alpha = }}\frac{\lambda }{{\sqrt {2\omega \ D} }} \end{eqnarray*}$$(C1) $$\begin{eqnarray*} \lambda = \frac{{k\ A}}{{\mu \ {\beta _{fl}}\ {V_D}}} \end{eqnarray*}$$(C2) $$\begin{eqnarray*} {\rm{\gamma = }}\frac{{\omega \ L}}{{\sqrt {2\omega \ D} }} = \ {\rm{\alpha \ }}\frac{{\omega \ L}}{\lambda } \end{eqnarray*}$$(C3) We rearrange the equations to calculate permeability independently from diffusivity. By substitution of eq. (C2) in (C1) and rearrangement, the equation expands to: $$\begin{eqnarray*} {\rm{k = }}\frac{{\mu \ {\beta _{fl}}\ {V_D}}}{{A\ }}\ \alpha \ \sqrt {2\omega \ D} \end{eqnarray*}$$(C4) By rearranging eq. (C3) and substitution in (C4), we obtain the equation to calculate permeability independently: $$\begin{eqnarray*} k = \frac{{\mu \ {\beta _{fl}}\ {V_D}\ L}}{A}\ \frac{{\alpha \ \omega }}{\gamma } \end{eqnarray*}$$(C5) To derive the storativity, we use eq. (C3) and substitute diffusivity based on the eq. (B4). Additionally, we use (C5) to substitute permeability, so that $$\begin{eqnarray*} \frac{{\mu \ {\beta _{fl}}\ {V_D}\ }}{\alpha }\frac{{\alpha \ \omega \ L}}{\gamma }\ \frac{1}{{\mu \ {\beta _{st}}}} = \ \frac{\omega }{2}{\left( {\frac{L}{\gamma }} \right)^2} \end{eqnarray*}$$(C6) After rearranging, we obtain the storativity independent from permeability: $$\begin{eqnarray*} {\beta _{st}} = \frac{{2\ {\beta _{fl}}\ {V_D}\ \alpha \ \gamma }}{{A\ L}} \end{eqnarray*}$$(C7) Author notes now at: Brenk Systemplanung GmbH, Heider-Hof-Weg 23, 52080 Aachen, Germany © The Author(s) 2020. Published by Oxford University Press on behalf of The Royal Astronomical Society. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model)
TI - A comparative study on methods for determining the hydraulic properties of a clay shale
JF - Geophysical Journal International
DO - 10.1093/gji/ggaa532
DA - 2020-12-09
UR - https://www.deepdyve.com/lp/oxford-university-press/a-comparative-study-on-methods-for-determining-the-hydraulic-B4WAjsGkBs
SP - 1523
EP - 1539
VL - 224
IS - 3
DP - DeepDyve
ER -