Pressure-dependent joint elastic–electrical properties in brine-saturated artificial sandstones with aligned penny-shaped cracks—Part I: Experimental results

SUMMARY

Elastic and electrical properties can be jointly interpreted for better characterizations of rocks with cracks that are common in geological rocks. However, the cross-property relationship between the elastic and electrical properties of cracked rocks, which forms the key to the successful joint elastic–electrical interpretation, remains poorly understood. We investigate the pressure effects on the joint elastic–electrical properties in brine-saturated artificial sandstones with aligned non-interacting penny-shaped cracks that are far from percolation. We measured and compared the anisotropic electrical conductivity and ultrasonic velocity in the artificial sandstones with and without aligned cracks under applied effective stress from 5 to 50 MPa. We showed that the existence of aligned cracks significantly enhanced the elastic and electrical anisotropies of the rocks, and the difference in the elastic and electrical anisotropies between the cracked and intact samples reduced as the effective stress increased. We also showed that the pressure-dependent electrical conductivity and ultrasonic velocity exhibited strong linear correlations in both the intact and cracked samples cored in different directions, and a difference existed in the slopes between the samples with and without aligned cracks. The distinct contributions of the pressure-induced deformation of cracks to the anisotropic elastic and electrical properties, as well as their different sensitivity to the cracks, were found to plausibly explain the observed experimental results. Theoretical modelling for quantitative interpretation of the experimental data is presented in a companion paper.

1 INTRODUCTION

Cracks are common in many types of sedimentary and crystalline rocks (Nelson 2001), and the importance of cracks has been recognized for a long time in the applications of hydrocarbon exploration and production (Pérez et al. 1999; Barbati et al. 2016), as well as in carbon dioxide geological storage (Friedmann 2007; Barnes et al. 2009), natural gas hydrate quantification and assessment (Lee & Collett 2009; Ghosh et al. 2010), groundwater and contaminant hydrology (Sade et al. 2010; Lu 2013), and civil engineering (Sade et al. 2010; Zhou et al. 2018), among others. Cracks, which can be regarded as small and not necessarily connected sets of fractures, having no shear displacement and small apertures, contribute greatly to the flow and transport properties of rocks and the contribution can be critical in rocks with low matrix porosity and permeability. The enhancement in the flow and transport properties improves the flow ability of pore fluid and electrical current, which in turn affects significantly the elastic and electrical properties of the cracked rock. Therefore, understanding the effects of cracks on the elastic and electrical rock properties plays a key role in the most commonly conducted seismic and electrical surveys for the detection and characterization of cracks.

Encouraging progress has been made to obtain the knowledge of cracks on the elastic and electrical properties of cracked rocks through dedicated experimental and theoretical studies (e.g. Hudson 1980; Sevostianov & Kachanov 1999; Sayers 2002; Sevostianov et al. 2005; Giraud et al. 2007; Guéguen & Sarout 2009; Tillotson et al. 2012; Rubino et al. 2013; Ding et al. 2014; Amalokwu et al. 2015; Guo et al. 2018a,b; Han et al. 2019, 2020a; Fu et al. 2020; Xu et al. 2020; Yan et al. 2020). Most of the studies focus on reservoir rocks with relatively high, uniform and connected pores, and the cracks are small, not interconnected and not close to percolation with a specific penny shape. Although the penny-shaped geometry is not readily available in natural rocks, it is recognized as a good assumption, because it can provide intuitively simple parametrization of enormous complexity of real crack space, and is relatively easily amenable to theoretical analysis (Gurevich et al. 2009). The results of the comprehensive research works have demonstrated that crack density, crack aspect ratio and orientation of the cracks can dramatically affect the elastic rock properties (e.g. Clark et al. 2009; Ding et al. 2017), whereas the electrical properties are more sensitive to the changes in the types of fluids and their saturations in the cracks for clean rocks, where surface conductivity is playing a minor role (e.g. Li et al. 2015; Huang et al. 2017).

Since the elastic and electrical properties of cracked rocks are complementarily impacted by cracks, recent efforts are devoted to exploring the cross-property relationships between the elastic and electrical properties, with the hope to reveal how naturally the elastic and electrical properties are correlated in cracked rocks and to aid the interpretation of joint seismic and electrical survey data for the better characterization of cracked rocks (Dashevskii et al. 2006; Han 2018). Systematic progress has been made for the joint elastic–electrical properties of isotropic rocks without cracks (e.g. Carcione et al. 2007; Han et al. 2011; Cilli & Chapman 2021), and a detailed review of the systematic progress in the connections between the elastic and conductive properties of heterogeneous materials can be found in Sevostianov & Kachanov (2009). A more focused review and summary of the most recent advances in the theoretical correlations between the elastic and electrical properties of layered porous rocks with cracks of varying orientation is available from Han et al. (2020c). Despite the achievements made over the years, however, the knowledge about the joint elastic–electrical properties of cracked rocks under loading is still poorly understood. Such knowledge is important because all rocks are experiencing geological pressures, which will vary the geometry and amounts of the cracks and hence the joint properties, and therefore understanding the pressure effects on the joint elastic–electrical properties of cracked rocks will help to better characterize the cracks under pressure, which is one of the key goals of joint elastic–electrical surveys.

This work aims to study the pressure-dependent joint elastic–electrical properties in brine-saturated artificial sandstones with aligned penny-shaped cracks. We first offer a method to manufacture the required layered porous rocks with and without penny-shaped cracks parallel to the layers and describe the experimental procedure employed to measure the anisotropic elastic and electrical properties of the artificial samples with full brine saturation as a function of effective stress. The experimental results are then analysed and interpreted in terms of the effects of effective stress on the anisotropic joint elastic–electrical properties and the distinction that the cracks have made on the joint properties between the samples with and without cracks. In a companion paper (i.e. paper 2), theoretical models are developed to understand the deformation of cracks with pressure in rocks with transversely isotropic (TI) matrix and its effects on the anisotropic elastic, electrical and joint elastic–electrical properties. The impact of cracks with different aspect ratios and crack porosities on the pressure-dependent joint properties is also investigated.

2 LABORATORY EXPERIMENTS

2.1 Synthetic sandstone samples

Several methods have been proposed to make synthetic silica-cemented sandstone samples with similar mineral composition, pore structure and cementation to natural sandstones (Tillotson et al. 2012; Ding et al. 2014, 2017). Although different proportions of the solid components are employed, the methods all use aqueous sodium silicate as the ‘glue’ that reacts with kaolinite at high temperature to form silica cementation. A similar recipe was used in this work to make the required sandstone samples for the experiments.

Two sample blocks consisting of an intact block (without cracks) and a cracked block (with cracks) were made. We mixed evenly different sized sand (700 g of 0.15 mm and 300 g of 0.038 mm), Na-feldspar (200 g) and kaolinite (150 g) with aqueous sodium silicate gel (270 g), and packed the mixture in successive layers of about 3 mm thickness into a mould made of stainless steel. The sand with different sizes was employed to reduce the porosity of the samples. We applied an axial stress of about 20 MPa to compact the mixture after each layer was packed, so as to form a clear boundary between layers. We distributed a pre-determined number of nitrate cellulose discs with diameter of 3 mm and thickness of 0.063 mm (giving rise to crack aspect ratio of about 0.021) on top of each layer of the mixture for the creation of penny-shaped cracks. The blocks were compacted axially within the indeformable mould to the stress of 100 MPa for 24 h to reduce the porosity and to consolidate, and were then heated at the temperature of 60 °C for 48 h for further consolidation and for release of the applied stress. The consolidated blocks were placed into a muffle oven and sintered at the temperature of 1200 °C for 8 h, for the sodium silicate and kaolinite to transform to silica, and for the polymeric material discs to be decomposed to leave penny-shaped empty cracks. The intact and cracked sample blocks were treated in exactly the same way to make them undergo the same process so that the difference in the physical properties can be regarded to be caused solely by the cracks. The crack density (ε) of the cracked block was determined to be approximately 6.2 per cent based on the number of crack layers and the number of cracks laid on each layer, according to the equation |${\rm{\varepsilon \ }} = ({N}/{V})\ {a^3}$|⁠, where N/V is the number of penny-shaped cracks of radius a per unit volume (Mavko et al. 2009).

2.2 Experimental procedure

Both the manufactured sandstone blocks are TI, and we will need to measure five independent velocities (i.e. V_p(0°), V_p(45°) and V_p(90°), corresponding to compressional waves propagating normal, at 45° and parallel to the bedding, respectively, and V_sh(0°) and V_sh(90°), representing shear waves traveling vertical and parallel to the bedding respectively but both with polarization both parallel to the bedding) to characterize the elastic anisotropy, and two orthogonal conductivities [i.e. σ(0°) and σ(90°) representing for the conductivities across and parallel to the bedding, respectively] to study their electrical anisotropy. However, while there have been experimental set-ups to determine all the required velocities from a single cylindrical core sample (Wang 2002; Dewhurst & Siggins 2006; Sarout et al. 2015; Han et al. 2020a), the simultaneous collection of two orthogonal conductivities from a single cylindrical sample can be challenging (North & Best 2014). Therefore, we employed the conventional multicore method for the measurements of the anisotropic elastic and electrical properties.

Three core plugs were extracted from each synthetic block at 0°, 45° and 90°, respectively to the lamination and crack plane (as schematically shown in Fig. 1a). We denoted the samples as I-0, I-45 and I-90 for the intact samples, and as F-0, F-45 and F-90 for the cracked samples (see Fig. 2 for the X-ray CT images of the cracked samples with varying crack orientations) parallel, oblique, and vertical coring with respect to the vertical axis to lamination. The samples were about 2.54 cm in diameter with length varying between approximately 3 and 5 cm. The two ends of each sample were carefully polished to reduce errors in the length measurements and to enhance the contact between the samples and the ultrasonic transducers and electrodes.

The six cylindrical samples were dried in an oven at 60 °C for 48 h and vacuumed to the pressure of −0.1 MPa for more than12 h before they were saturated with 35 g L⁻¹ brine (made from sodium chloride and distilled and deaired water) under a pressure of 16 MPa for a successive 12 h to ensure full brine saturation. The fully saturated samples were then quickly loaded into an electrical rig used by Han et al. (2020b), where the electrical resistance was measured using a standard two-electrode method at hydrostatic confining stresses between 6 and 51 MPa at an interval of 5 MPa with the pore pressure maintained at 1 MPa. The samples were allowed to equilibrate at each confining stress for a minimum of 15 min before the next electrical measurement commenced. The samples were washed to leach the salt out after the electrical measurements, and the drying and saturating procedures were repeated before the ultrasonic P- and S-wave velocities (Fig. 1b) were measured using an ultrasonic transmission technique (AutoLab-1500 system) at exactly the same pressure conditions and time intervals as in the electrical measurements. The size of the ultrasonic transducers and the electrodes that directly contacted the sample was all 2.54 cm in diameter. Fig. 3 shows the acquired ultrasonic waveforms from the cracked sample F-90 as the effective stress varies between 5 and 50 MPa. When both the electrical and elastic measurements were finished, the samples were washed and dried, and their pressure-dependent (in the range between 5 and 50 MPa at an interval of 5 MPa) porosity and permeability were measured using Core Laboratories' CMS-300 Core Measurement System with absolute accuracy of ±0.0001 and relative accuracy of ±0.1 per cent, respectively.

The electrical and elastic measurements were carried out in a laboratory with controlled temperature (22 ± 1 °C) to minimize the effects of varying temperature on the experimental results. The central frequency of the ultrasonic waves was about 500 kHz, and the frequency of the alternating current employed for the electrical tests was 1 kHz. According to the accuracy-estimation method described by Hornby (1998), we estimated the measurement errors to be approximately ±0.8 and ±1.2 per cent for the P- and S-wave velocities, respectively, and about ±2 per cent for the electrical conductivity, assuming that the electrode polarization effect associated with the two-electrode (made of stainless steel) system was negligible for the high-porosity samples and for the high brine salinity employed.

2.3 Calculation of anisotropic parameters

The measured ultrasonic velocities and electrical conductivities were employed to determine the elastic and electrical anisotropic parameters to characterize the anisotropy of the elastic and electrical properties, respectively.

3 EXPERIMENTAL RESULTS AND INTERPRETATION

The experimentally measured porosity (φ), permeability (K), electrical conductivity (σ), P-wave velocity (V_p) and S-wave velocity with SH and SV modes of propagation (V_sh and V_sv, respectively) as functions of effective stress (the difference between the hydrostatic confining stress and pore fluid pressure) are tabulated in Table 1.

3.1 Pressure-dependent anisotropic electrical properties

Fig. 4 shows the variations of the measured anisotropic electrical conductivity of the intact and cracked samples with effective stress. As a whole, all the electrical conductivity decreases with increasing effective stress, in an exponential manner. This is believed to be caused by the closure of compliant pores at the initial increase in the effective stress that will significantly reduce the connectivity between more rounded stiff pores, and hence dramatically reduces the electrical conductivity; and as most compliant pores are already closed at higher effective stresses, their impact on reducing electrical conductivity will become gentler (Han et al. 2011; Falcon-Suarez et al. 2020).

In addition to showing the overall conductivity reduction with effective stress, Fig. 4 also illustrates the conductivity difference between samples, especially for the cracked rocks. However, this difference cannot be regarded as a full indication of the electrical anisotropy, because of the porosity difference between the samples, as shown in Fig. 5. Although we have made efforts to keep exactly the same ingredients and manufacturing procedures when making the intact and cracked sandstone blocks to reduce the potential porosity discrepancy between the blocks, inevitable heterogeneity (Tillotson et al. 2012) still exists that leads to the porosity difference between the three samples cored from each artificial block and between the intact and cracked sample groups. It can be seen from Fig. 5 that the porosity difference between the three samples from each block is about 0.01, and the porosity of the cracked samples can be higher than that of the intact samples by 0.02, which is significantly greater than the porosity of the cracks (which is calculated to be 0.0055, determined as the ratio between the crack volume and the volume of the rock sample). Since electrical conductivity is very sensitive to the changes in the sample porosity, such porosity difference in each group may cover the effects of electrical anisotropy and the porosity discrepancy between the cracked and intact samples might mask the effects caused by the cracks.

To exclude the effects of varying porosity on the electrical properties, we calculate the cementation exponent in Archie's equation (Archie 1942) as a function of effective stress. Even though it is still not clear about the exact physical meaning of cementation exponent, it is generally accepted that cementation exponent represents implicitly the ‘connectedness’ of the pore and fracture network for the availability of pathways for hydraulic and electrical flow (Glover 2009). A lower cementation exponent indicates the pores in a sample show better ‘connectedness’ and therefore the electrical conductivity will be higher compared with a sample with a higher cementation exponent but the same porosity. As shown in Fig. 6, the cementation exponent for the samples in the 90° direction (i.e. in the direction parallel to the layers and cracks) is lower than that in the 45° direction, which in turn is smaller than that in the 0° direction (corresponding to the direction perpendicular to the layers and cracks). This implies that the samples cored parallel to the layers and cracks exhibit greater flow ability for the electrical current (i.e. higher electrical conductivity) than those drilled in the direction vertical to the layers and cracks. The greater electrical conductivity in the direction parallel to the layer and cracks is understandable because the alignment of the grains and cracks in the 90° cores provide more conductive paths for the charge carriers, and exhibit less tortuosity making the movement of electrical charges enhanced (Ellis et al. 2010; North & Best 2014; Han et al. 2019).

Comparison of the cementation exponent in the samples between the intact and the cracked groups (i.e. Figs 6a and b) demonstrates that the cracked samples show larger separation in the cementation exponent, especially in the low effective stress range. This suggests that the cracked samples are more anisotropic in the electrical properties, and the difference in the electrical anisotropy between the intact and cracked rocks reduces with increasing effective stress. This is also explainable because the cracks are less deformed in the low pressure range and therefore contribute more to the electrical anisotropy. As effective stress gradually elevates, the cracks will be compressed (see the modelling results in paper 2), which can be regarded as the number of cracks are reducing, and as a result the effect of the cracks on the anisotropic electrical properties is weakening. In the limiting case of high enough effective stresses, the cracks will completely close (if the rocks are elastic and do not fail) and the anisotropic electrical conductivity of the cracked rocks will then be expected to be the same as that of the intact samples.

We have implicitly demonstrated that the electrical anisotropy of the cracked rocks is greater than that of the intact samples, and the difference reduces with increasing effective stress. This can be more directly and explicitly seen from the variation of the electrical anisotropic parameter λ with effective stress in Fig. 7. In addition, Fig. 7 shows that the electrical anisotropy of the intact rocks increases with effective stress, which is consistent with the observations of North et al. (2013) and Falcon-Suarez et al. (2020). The electrical anisotropy of the intact samples is generally considered to be caused by aligned microcracks, thin layers and the preferential alignment of mineral grains (Deng et al. 2014). Considering the latter two factors change negligibly under the relatively small pressure range, the pressure dependence of electrical anisotropy may be considered as a result of the closure of aligned microcracks. The diminishing crack effects on the electrical anisotropy with pressure are due to the fact that the reduction in the electrical conductivity with increasing pressure is more significant in the direction along the cracks than in the direction across the cracks (see the modelling results in paper 2), and therefore the electrical anisotropy caused by the cracks reduces as the effective stress increases.

3.2 Pressure-dependent anisotropic elastic properties

The experimentally measured 9 ultrasonic velocities with increasing effective stress for the intact and cracked samples, respectively are plotted in Fig. 8. All the velocities show exponential increase with effective stress, again due to the gradual closure of compliant pores that improves the stiffness of the rocks (Toksӧz et al. 1976; Shapiro 2003; Han et al. 2011). It is interesting that although there exists discrepancy in the porosity of the samples, the measured velocities exhibit clear TI features, i.e. both the P- and SH-wave velocities are the highest in the 90° cores and the slowest in the 0° samples, and the shear wave velocities V_sh(0°), V_sv(0°) and V_sv(90°) are approximately the same (Deng et al. 2014). This may indicate that the porosity variation due to heterogeneity that significantly impacts the electrical properties, shows less influence on the elastic properties. The fastest P- and SH-wave velocities in the direction along the layers and cracks are resulting from the enhanced stiffness of the rocks due to the fact that the cracks are the least compressible in such direction while their compressibility is the greatest across the cracks, corresponding to the 0° cored samples.

Comparing the velocities between the intact and the cracked samples shown in Fig. 8, we can find that the existence of cracks slightly reduces V_p(90°) and V_sh(90°) but dramatically decreases V_p(0°), V_sh(0°), V_sv(0°) and V_sv(90°). This is consistent with previous experimental and theoretical observations (Ding et al. 2017; Han et al. 2020a) and can be explained in terms of the contribution of the anisotropic compressibility of cracks to the rock stiffness. As mentioned above, the cracks are difficult to compress along their strike, and therefore the inclusion of cracks will less reduce the rock stiffness in this direction, leading to gently reduced elastic velocities of the cracked rock. However, because the cracks are highly compressible across their strike, the reduction in the rock stiffness in this direction will be significant, resulting in dramatically decreasing velocities as a result of the significant reduction in the stiffness. It should be noted that the above explanation does not take into account the effects of squirt flow, which can be dependent on the frequency of the employed ultrasonic waves (Murphy et al. 1986; Gurevich et al. 2010). At low frequency limit, there is sufficient time for the pore fluid communications between the cracks and their adjacent pores, so that the fluid does not contribute to the stiffness of the cracks. However, at high frequency limit, the pore fluid is trapped in the cracks, and therefore making the cracks stiffer. The squirt flow effects may not affect much V_p(90°) but will more significantly improve V_p(0°).

Fig. 8 also interestingly shows that while V_p(0°), V_sh(0°), V_sv(0°) and V_sv(90°) are more significantly reduced by the aligned cracks in comparison with V_p(90°) and V_sh(90°), the magnitude of the reduction shows apparent pressure dependence. The reduction is most significant at the lowest effective stress, and tends to be less dramatic as the effective stress increases, leading to diminishing differences between V_p(90°) and V_p(0°), and between V_sh(90°) and V_sh(0°) (as well as V_sv(0°) and V_sv(90°)). Such pressure-dependent effects of cracks on the anisotropic elastic properties are similar to those on the electrical properties, and can also be attributed to the deformation of cracks with pressure. On the one hand, it is already clear that the existence of cracks itself has limited effects on V_p(90°) and V_sh(90°), therefore, it can be reasonable that the influence of the deforming cracks with pressure will be even smaller. On the other hand, we have shown above that the contribution of cracks on V_p(0°) and V_sh(0°) can be significant, and it can be easy to understand that the contribution will be weakened with the compressing of the cracks under pressure.

We can infer from the results and analyses presented above that the cracked samples should be more elastically anisotropic than the intact samples, and the elastic anisotropy of the cracked rocks will reduce with increasing effective stress. This is confirmed by the results in Fig. 9, which not only shows the reducing elastic anisotropic parameters of the cracked samples, but also shows the generally decreasing elastic anisotropy of the intact rocks with increasing effective stress. Although the reducing elastic anisotropic parameters of the intact samples with effective stress is consistent with the results of Deng et al. (2014), Song et al. (2015) and Han et al. (2020a) among others, it is different from the electrical anisotropy of the intact samples that increases with elevating pressure (as shown in Fig. 7). In fact, like electrical anisotropy, the decreasing elastic anisotropy with increasing pressure is also resulting from the different contributions of the closing cracks or microcracks to the anisotropic elastic velocities. Velocities of waves propagating or polarization across the cracks (or microcracks) increase more significantly with the compressing cracks (or microcracks) than those along the cracks (or microcracks) under pressure (see the modelling results in paper 2), and therefore the elastic anisotropy reduces as the difference between the velocities in different directions gradually diminishes with increasing effective stress.

3.3 Pressure-dependent joint elastic–electrical properties

Having studied the pressure-dependent anisotropic electrical and elastic properties, respectively, we proceed to explore the correlations between the elastic and electrical properties, which we refer to as the joint elastic–electrical properties. To do so, we first illustrate in Fig. 10 the correlations of the pressure-dependent P- and SH-wave velocities, and electrical conductivity with porosity of the intact and cracked samples. The relationships between the physical (i.e. elastic and electrical) properties and porosity are studied because porosity is usually employed as a connection to link the elastic and electrical rock properties (Carcione et al. 2007; Han et al. 2020b; Cilli & Chapman 2021). We do not show the SV-wave velocities because they are either almost the same as V_sh(0°) (i.e. V_sv(0°) and V_sv(90°)) or not needed to characterize the elastic anisotropy of TI rocks (i.e. V_sv(45°)).

It can be seen from Fig. 10 that P- and SH-wave velocities increase while electrical conductivity decreases with decreasing porosity as an implicit function of increasing effective stress, both in an approximately linear way. Such a linear correlation is found in both the intact and cracked samples, and holds in rocks cored from each direction relative to the layers and cracks. A similar linear relationship between the pressure-dependent elastic and electrical properties and porosity has been obtained for isotropic Berea sandstones, and has been explained in terms of the similar variations of porosity and physical properties with pressure (Han et al. 2020b). Accordingly, the linearly correlated pressure-dependent anisotropic physical properties with porosity would suggest that even though the samples are from different directions of an anisotropic block, their elastic and electrical properties also tend to be determined by the varying porosity with effective stress, not matter the cracks exist or not.

Since both the anisotropic elastic and electrical properties are linearly correlated with the pressure-dependent porosity, it is reasonable to speculate that the anisotropic elastic and electrical properties are correlated in a linear manner with each other. The results presented in Fig. 11 confirm such speculation and show that P- and SH-wave velocities increase linearly with decreasing electrical conductivity as functions of reducing porosity and effective stress. The linear anisotropic joint elastic–electrical correlations are consistent with the experimental observations of the stress sensitivity of combined elastic and electrical anisotropies in shallow reservoir sandstones by Falcon-Suarez et al. (2020), who concluded that the stress orientation similarly affects the elastic and electrical properties of poorly consolidated, high-porosity (shallow) sandstone reservoirs. However, it should be noted that while Falcon-Suarez et al. (2020) demonstrated that the linear correlations exhibited very little slope variations between the samples cored from different directions, the normalized joint relationships (i.e. the measured rock properties divided by their values at the lowest effective stress available) in Fig. 11 seem to support such conclusion but also highlight that there does exist a slope difference between the intact and cracked sample groups. The slopes of the joint correlation do not vary much in the samples from each group, but the intact samples show generally steeper slopes of the joint correlation than those of the cracked samples. This suggests that with the same amount of increasing effective stress (i.e. from 5 to 50 MPa), the intact samples reduce more in electrical conductivity than the cracked rocks, but increase less in elastic velocities than the cracked samples. Considering the porosity of the cracked samples is already greater than that of the intact samples, and the cracks are highly deformable under pressure and hence can be regarded as compliant pores, the greater amounts of reduction in the electrical conductivity of the intact samples and the more significant magnitude of the improvement in the elastic velocities of the cracked samples may imply that the electrical properties are more sensitive to the changes in the stiff pores whereas the elastic rock properties are more subject to the variations in the complaint pores. This is similar with the findings of Shapiro et al. (2015) and Falcon-Suarez et al. (2020).

4 DISCUSSION

We have designed and implemented dedicated laboratory experiments to study comprehensively the pressure-dependent anisotropic joint elastic–electrical properties in brine-saturated artificial porous sandstones with and without aligned penny-shaped cracks, which are relatively systematic and uniformly distributed, and non-interacting. In our experiments, the anisotropic elastic and electrical behaviours with varying effective stress were measured in separate rigs on independent samples drilled from different directions of the synthetic rock blocks. Although we have made efforts to reduce the heterogeneity in making the artificial rocks, the results still showed systematic differences between the samples. While the heterogeneity-induced difference in porosity did not seem to impact significantly the elastic properties, there was evidence showing that it did affect much the electrical properties. To reduce the influence of multiple cores with different porosity, it is necessary to develop a method to measure simultaneously the required anisotropic electrical conductivity and elastic velocities from a single core plug. Such an experimental advance will also help to minimize the errors and hysteresis associated with the multiple loading–unloading cycles (e.g. Falcon-Suarez et al. 2020) as the elastic and electrical properties were separately measured in this work, although our repeated electrical tests after the porosity measurement provided electrical conductivity that agreed well with the electrical conductivity measured in the first cycle, with relative errors better than ±0.5 per cent, which is much smaller than the uncertainties of the electrical measurement (i.e. ±2 per cent). The integration of the determination method of the full electrical resistivity tensor (North et al. 2013) with the multidirectional single-cylinder-core technique for the anisotropic elastic properties (Han et al. 2020a) may serve as a direction for the development of the mentioned anisotropic joint elastic–electrical cell.

We have presented novel experimental results on the pressure dependence of the anisotropic elastic, electrical and joint elastic–electrical properties of brine-saturated artificial porous sandstones, with the focus on the difference that the aligned cracks have made in the intact and cracked samples. The results can help to discriminate between rocks with and without cracks using elastic and electrical survey methods. With the theoretical models developed in paper 2, we can further obtain quantitatively the crack information (crack porosity and aspect ratio) from the measured joint elastic–electrical properties. Therefore, this work paves the way for the future quantification of cracks in layered porous rocks. In the long run, the results may also be employed in an application for monitoring the production state of a hydrocarbon reservoir or a place where CO₂ is injected, which although requires the knowledge of the effects of multiphase fluids on the pressure-dependent joint elastic–electrical properties. The investigation of the pressure-dependent joint elastic–electrical properties in partially saturated artificial sandstones with aligned penny-shaped cracks will form the topics of our future studies. However, it should be noted that there are systematic differences in the frequency between the laboratory obtained elastic and electrical rock properties and those measured from field surveys. The frequency will affect both the elastic and electrical rock properties of rocks, and in cracked rock the impact may be more significant as the cracks provide additional heterogeneity for the flow of fluids as the elastic and electromagnetic waves propagate through the rock. Therefore, further study towards the frequency effects on the joint elastic–electrical properties of cracked rocks is needed before the obtained results can be applied to practice.

In this work, we have explained and interpreted most of the experimental data in terms of the different contributions of the cracks to the anisotropic physical rock properties as well as the effects of the deforming cracks under pressure on the anisotropic properties. While the explanation and interpretation are reasonable and plausible, they are qualitative and lack theoretical verification. A dedicated theoretical modelling scheme is therefore needed for the better interpretation of the laboratory data. Such a modelling approach should take into account the deformation of aligned penny-shaped cracks within a TI background under loading, and the effects of the deforming cracks on the anisotropic elastic and electrical properties of the TI matrix should then be determined through incorporation with various models for the elastic and electrical properties of TI rocks with cracks (e.g. Han et al. 2020c; Xu et al. 2020; Yan et al. 2020). Once validated, the theoretical models will not only help to better explain the experimental results, but also help to gain new knowledge of the pressure-dependent joint properties of rocks with cracks of different aspect ratios and crack porosities, which can be difficult to obtain in the laboratory. Fortunately, the deliberately designed penny-shaped cracks provide a unique and ideal opportunity for the mathematical parametrization of the cracks, making the theoretical modelling of the crack deformation and its effects on the joint elastic–electrical rock properties possible. The development of the systematic modelling scheme for the interpretation of the experimental results and the study of the impact of cracks with different aspect ratios and crack porosities on the pressure-dependent joint properties based on the developed models will be presented in paper 2.

5 CONCLUSIONS

We have collected novel experimental data to study comprehensively the pressure-dependent joint elastic–electrical properties in layered artificial sandstones with aligned penny-shaped cracks. Comparison of the measured anisotropic electrical conductivity and ultrasonic velocities between the samples with and without aligned cracks showed that the existence of aligned cracks significantly enhanced the elastic and electrical anisotropies of the rocks, and the difference in the elastic and electrical anisotropies between the cracked and intact samples reduced as the aligned cracks were compressed due to increasing effective stress. Most interestingly, we have demonstrated that the pressure-dependent electrical conductivity and ultrasonic velocity exhibited strong linear correlations in both the intact and cracked samples cored from each direction (0°, 45° and 90° with respect to the layers and cracks), and a difference existed in the slopes between the samples with and without aligned cracks. The experimental results were plausibly explained and interpreted in terms of the distinct contributions of the pressure-induced deformation of cracks to the anisotropic elastic and electrical properties, and indicated that the anisotropic elastic and electrical properties were sensitive to the changes in the compliant and stiff pores with varying effective stress, respectively. The results have helped to gain new knowledge on the link between the anisotropic elastic and electrical properties in cracked rocks subject to varying pressure, and have also suggested the requirement for advanced theoretical models to fully understand the collected data.

ACKNOWLEDGEMENTS

The authors would like to acknowledge the financial support received from the National Natural Science Foundation of China (42174136, 41821002 and 41874151) and the Fundamental Research Funds for the Central Universities (18CX05008A).

DATA AVAILABILITY

Data presented in this paper are tabulated in Table 1 and will be available upon request from the corresponding author.

REFERENCES