Sheng-Qi Yang, Yan-Hua Huang

State Key Laboratory for Geomechanics and Deep Underground Engineering, School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou, 221116, China

ABSTRACT In underground engineering, such as geological CO2 sequestration, unconventional oil and gas exploration, and radioactive waste storage, permeability of rock is important to evaluate the potential CO2 storage capacity,improve oil and gas production,and prevent leakage of radioactive waste.In this study,hydrostatic stress tests and triaxial compression tests with gas permeability measurements were carried out on intact and damaged sandstone specimens. Three series of experiment were designed to evaluate the permeability evolution laws of sandstone under different testing conditions. They included triaxial seepage tests on intact specimens under different confining pressures,triaxial seepage tests on damaged specimens with different extents of damage,and hydrostatic seepage tests on damaged specimens under increasing and decreasing gas pressures. Based on the experimental results, the effects of effective confining pressure, extent of damage and increasing and decreasing gas pressure on permeability of sandstone were investigated. It shows that the permeability of the intact sandstone specimens first decreased and then increased, followed by a constant value with increase in axial strain. The permeability of the sandstone specimens was observed to decrease with increase in effective confining pressure.The extent of damage affects the permeability evolution,but does not influence the failure patterns of damaged sandstone. As the gas pressure increased, the permeability of the damaged sandstone specimen increased. Under the same gas pressure condition, the permeability during the decreasing process is generally higher than that during the increasing process. These experiments are expected to enhance our understanding of seepage behavior in underground rock masses.

Keywords:Experimental study Sandstone Gas seepage Rock damage Loading and unloading

1. Introduction

Rock mass is often damaged or fractured due to the effect of high stress in underground engineering. Re-fractured mechanical behavior of damaged rock has been identified as one of the most important rock mechanics issues (Han and Yang, 2009). The strength,deformation and failure behaviors of fractured rock have been widely investigated (e.g. Rao and Ramana,1992; Heap et al.,2009; Yang and Jing, 2013). These experimental studies have shown that the re-fractured mechanical behavior of damaged rock is different from that of intact rock without damage. However,understanding the seepage behavior of damaged rock is not mature. Some researchers have measured the evolution of permeability in rock under unloading confining pressure condition(e.g. Yin et al., 2015; Ding et al., 2016; Zhang et al., 2017; Chen et al., 2018) and cyclic loading (Jiang et al., 2017), which can serve as reference to understand the seepage behavior of damaged rock. It is critically important to evaluate the seepage behavior of rock in design and construction stages of various rock engineering applications, such as high-level radioactive waste storage (Chen et al., 2014; Yang et al., 2020), geological sequestration of CO2(Rathnaweera et al., 2015; Huang et al., 2020a), deep geothermal energy extraction (Minissale et al., 2008), underground coal mining (Xue et al., 2017; Ma et al., 2019a, b), and unconventional oil and gas exploration(Liu et al.,2016).Potential sites for CO2and radioactive waste storage are directly determined by the permeability of the rock. Low-permeability rocks act as cap rocks or surrounding rocks to prevent the leakage of gas or radioactive waste. In contrast, to improve production of oil, gas and geothermal energy, the permeability of rock is increased by artificial cracks.

Fig.1. SEM images of sandstone with magnification of (a) 200 times, (b) 600 times, and (c) 1000 times (Yang et al., 2015a).

Various studies have been extensively carried out to investigate the permeability of rock under different conditions. In laboratory tests, the permeability of rock is generally measured under triaxial compression to investigate the variation of permeability during the development of deformation. Yang et al.(2017) tested the mechanical properties and permeability of thermally damaged sandstone specimens under different confining pressures.The permeability of sandstone specimen was observed to decrease at crack closure stage and increase at crack growth stage. Chen et al. (2017) experimentally measured the permeability of porous sandstone specimens under various confining pressures and water pore pressures.Their experimental results showed that the permeability of sandstone was significantly varied after yield stress when the specimens were subjected to different confining pressures, dependent on the failure modes after compression. Jia et al. (2018) investigated the evolutions of gas and water permeability in a compact sandstone specimen during the entire stress—strain process, and five stages were observed according to crack growth process. In the experiments performed by Fortin et al. (2011), it showed that the permeability of the basalt first decreased and then increased with the increase in axial deviatoric stress, and the change in permeability was small during the increasing stress stage. Some other similar studies on the permeability evolution of rock under triaxial compression have also been reported(e.g.Wang and Park,2002; Tan et al., 2014; Xu and Yang, 2016; Hu et al., 2016). However, change in permeability at the residual strength stage has been rarely studied. Yang et al. (2015a) concluded that the permeability of sandstone remained constant during the residual stage, whereas Wang et al. (2014) and Liu et al. (2018) found a decreasing trend. However, to date, the influence of the extent of damage on the evolution of permeability in damaged sandstone specimen during the complete stress—strain process has not previously been investigated. The complex issue of permeability evolution of rock at the post-peak residual stage indicates that further studies on permeability during the complete deformation process are needed.

In this study,triaxial compression tests with permeability measurements were carried out on sandstone specimens.Three series of experiments were conducted to investigate the permeability characteristics of rock under different testing conditions.The first series was triaxial compression tests with permeability measurements on intact sandstone specimens to investigate the influence of effective confining pressure on the mechanical and seepage behaviors of the rock. The second was triaxial compression tests with permeability measurements on damaged sandstone specimens to explore the effect of the extent of damage on the mechanical and seepage behaviors of rock. The last was hydrostatic stress tests with permeability measurements on damaged sandstone specimens to study the effect of the loading and unloading processes of gas pressure on the permeability of damaged sandstone specimens.

2. Experimental setup and loading procedure

2.1. Material and testing equipment

Sandstone sampled from Linyi,Shandong Province of China was used.Fig.1 shows the microscopic structure of the tested sandstone based on scanning electron microscope (SEM) observation, suggesting the fine-to medium-grained sandstone. The mercury intrusion porosimetry test indicated that the porosity is 5.3%. The bulk density, and P- and S-wave velocities of the sandstone are 2450 kg/m3, 2873 m/s and 1772 m/s, respectively. The X-ray diffraction analysis implied that the mineral components are feldspar, quartz and smectite, which were also observed in the thin section results (Fig. 2).

From Figs. 1 and 2, the grains are randomly distributed and the boundaries are irregular. Microcracks and micro-pores are observed among the grains, which may cause much less tensile and compression strengths. However, these micro-defects are the initial seepage path for fluid flow. Table 1 lists the principal parameters of sandstone and testing conditions. The diameter and height of the sandstone specimen are 25 mm and 50 mm,respectively.

All the tests were conducted using the rock mechanics servocontrolled system TAW-1000 with an axial load capacity of 1000 kN. As shown in Fig. 3, the system includes a mechanics loading system and permeability measurement system. In this experiment,the axial deformation was recorded by a displacement transducer. The capacities of the axial and radial displacement transducers are 4 mm and 2 mm, respectively.

2.2. Loading procedure

To understand the permeability characteristics of sandstone specimens subjected to various extents of damage, three experimental plans were designed, as indicated in Table 1. When the permeability of a rock is higher than or equals 10-7μm2, it is preferred to measure the permeability using steady-state method(Davy et al., 2007). Here,the permeabilitykis calculated by

Fig. 2. Thin section of the tested sandstone: (a) Orthogonal polarization, and (b) plane polarization.

whereQis the volume flow;p0is the atmospheric pressure;μ is the viscosity coefficient;His the height of specimen;Ais the crosssectional area;P1is the gas absolute pressure of the inlet; andP2is the gas absolute pressure of the outlet.In this study,the seepage medium is pure nitrogen (N2), and the corresponding viscosity coefficient μ is 1.758 × 10-5Pa s. The volume flow was measured using a soap bubble flowmeter with accuracy of ±0.1 cm3.

Plan A was designed to explore the confining pressure effect on the seepage behavior of intact specimens. In this plan, confining pressure σ3was set to 5 MPa, 15 MPa and 20 MPa. First, σ3was applied to the sandstone at a rate of 0.5 MPa/s (stress-controlled mode),and the specimens were then subjected to a gas pressurePgof 2 MPa.Then,the axial deviatoric stress was loaded stepwise at a rate of 0.04 mm/min(displacement-controlled mode),and at each stress increment, the volume flow was measured. During the test,σ3andPgwere kept constant.

Plan B was designed to explore the influence of the extent of damage on the seepage behaviors of damaged sandstone specimens. First, the sandstone specimens were loaded to 0.3 mm, 0.4 mm,0.5 mm and 0.65 mm(axial displacement)under σ3=20 MPa.Then, the axial deviatoric stress was unloaded to form damaged specimens with different extents of damage. After that, seepage tests were carried out during the reloading process at a rate of 0.04 mm/min (displacement-controlled mode).

Table 1Principal parameters of sandstone specimens and testing conditions in the present study.

Fig. 3. Testing system of triaxial compression test with permeability measurement (modified from Yang et al., 2015a).

Fig. 4. Axial deviatoric stress—strain curves of sandstone tested under different confining pressures and gas seepage pressures.

Plan C was designed to explore the loading and unloading path effects on the seepage behavior of damaged sandstone specimens.First, sandstone specimens were loaded to 100 MPa,130 MPa and 160 MPa under confining pressure of 20 MPa. Then, the axial deviatoric stress was kept constant.After that,gas seepage pressure was first increased from 1 MPa to 6 MPa,and then decreased from 6 MPa to 1 MPa at an interval of 0.5 MPa.

3. Influence of confining pressure on seepage behavior of intact specimens

3.1. Influence of confining pressure on stress—strain curve and failure behavior

Fig. 4 shows the stress—strain curves of sandstone specimens under triaxial compression with respect to different gas pressures.The results for intact specimens under gas pressures of 0 MPa and 2 MPa were collected from Yang et al.(2015a).In the stress—strain curves,some small platforms were observed,which were caused by the permeability measurement.After the linear deformation stage,the axial deviatoric stress was increased to the yield stage. This provided an opportunity to measure the permeability near the peak strength. The stress—strain curves of the sandstone specimens tested with gas pressures were very similar to those of sandstone under conventional triaxial compression(Yang et al.,2015b;Huang et al.,2019).The deviatoric stress dropped to residual strength after it reached the peak strength. Furthermore, both the slope and the peak stress with gas pressures for the specimens were lower than those without gas pressures applied,which indicated the influence of gas injection on the mechanical behaviors of the sandstone specimens.

Based on the stress—strain curves of the sandstone specimens(Fig.4),the elastic modulus,peak strength and residual strength of the sandstone specimens were obtained. The effective confining pressure σeffcan be calculated using Eq.(2)when the permeability measurement tests are conducted with the steady-state method(Alam et al., 2014):

Fig. 5. Influence of effective confining pressure on strength and deformation parameters of sandstone: (a) Peak strength and residual strength, and (b) Elastic modulus.

Fig. 6. Influence of confining pressure on the failure mode of sandstone at gas seepage pressure of 2 MPa.

Fig. 7. Relationships between permeability and axial strain of sandstone under different confining pressures (Pg = 2 MPa).

Fig. 5 shows the relationships between the mechanical properties of the sandstone specimens and the effective confining pressure. As the effective confining pressure increased, the peak strength, residual strength and elastic modulus increased. For example, when σeffincreased from 4 MPa to 20 MPa, the peak strength of sandstone specimen increased from 109.18 MPa to 210.47 MPa. The correlation between the peak strength, residual strength and elastic modulus can be fitted by following linear functions:

Fig. 6 shows the failure patterns of the sandstone specimens subjected to various confining pressures. It shows that confining pressure influenced the failure pattern of the sandstone specimen.Under low confining pressure (5 MPa), specimen C1 showed a mixed tensile and shear failure mode.Multiple fractures including shear cracks, lateral tensile cracks and axial tensile cracks were observed in the specimen and the fracture extent of the sandstone was high. When the confining pressure was increased to a medium value (e.g. 15 MPa), a main shear fracture, in combination with local horizontal fracture and surface spalling, occurred in the front surface of specimen C3. When the confining pressure reached a high value (20 MPa), specimen C4 failed in form of a main shear fracture and a lateral tensile crack. However, only a shear fracture across the specimen was observed in specimen C15,which was compressed without gas pressure. The failure characteristics of the sandstone specimens tested were consistent with those of compact sandstone in gas seepage tests (Jia et al., 2018),but different from those of porous sandstone in water seepage tests (Chen et al., 2017).

3.2. Influence of confining pressure on permeability evolution

Fig. 7 shows the evolution of permeability with axial strain under different effective confining pressures. The permeability of the sandstone exhibited a similar trend with respect to different confining pressures applied. The permeability of the sandstone specimens first decreased and then increased, followed by a constant value with increase in axial strain; this process could be divided into three stages (Fig. 7c). To explain the evolution of permeability, a sketch of microcracks during the whole loading process is plotted in Fig.7d.During stage I(Fig.7c),at the stages of initial and elastic deformation, the denser structure of the sandstone specimens caused by the closure of original micro-pores and fissures induced decrement in permeability. During stage II(Fig. 7c), microcracks were initiated from the pre-existing closed pores and fissures when the stress exceeded the material strength,resulting in enhancement of permeability. Abrupt increment in permeability at the post-peak stage resulted from the coalescence of cracks.However,during stage III(Fig.7c),at the residual strength stage, the pore structure of the sandstone specimens did not change, indicating that the permeability was constant. However,some researchers (e.g. Yang et al., 2015a; Jia et al., 2018) reported that the evolution of rock permeability in complete stress—strain curves had five stages according to the critical stress. The overall variation of permeability in the tested sandstone was similar to the results of previous studies(e.g.Xu and Yang,2016;Cai et al.,2018).

Fig. 8. Relationships between permeability and volumetric strain of sandstone under different confining pressures (Pg = 2 MPa).

Fig. 8 shows the evolution of permeability in sandstone specimens during the volumetric strain process with respect to effective confining pressures. The volumetric strain of the sandstone was calculated as the axial strain pluses twice the circumferential strain.Crack damage threshold is defined as the stress when the volumetric strain transforms from compaction to dilation (Martin,1997). The crack damage threshold is helpful in analysis of the evolution of permeability and porosity in rock (Fortin et al., 2011).Fig. 8 shows that the permeability of the sandstone specimens decreases at the volume compaction stage,as a result of reduction in seepage channels. When the specimens were loaded to the volumetric dilation stage, the permeability increased due to the initiation and propagation of microcracks.

Fig.9 shows the influence of effective confining pressure on the permeability of the sandstone specimens. Permeability was observed to decrease with the increase in effective confining pressure. When the effective confining pressures were 4 MPa,14 MPa and 19 MPa, the initial permeability values were 0.553 × 10-3μm2, 0.459 × 10-3μm2and 0.283 × 10-3μm2,respectively. The decrement in permeability can be explained by the densification of the sandstone material under higher confining pressure. The final permeability values were measured 18.2 × 10-3μm2,13.257 × 10-3μm2and 6.452 × 10-3μm2in the sandstone specimens when the effective confining pressures were 4 MPa,14 MPa and 19 MPa, respectively. These results correspond to the ultimate failure modes shown in Fig.6.The extent of fracture decreased with increasing effective confining pressure, indicating that the seepage channels decreased under high effective confining pressure.

4. Influence of damage on seepage behavior of sandstone specimens

The extent of damageDgis defined by the ratio of the deviatoric stress at unloading to the peak deviatoric stress, as expressed by

Fig.9. Influence of effective confining pressure on the permeability evolution curve of sandstone (Pg = 2 MPa).

Fig.10. Relationships between permeability and axial strain of sandstone specimens with different extents of damage.

Fig.11. Ultimate failure modes of sandstone specimens with different extents of damage.

where (σ1-σ3)unloadingis the deviatoric stress at the unloading point, and σpis the peak deviatoric stress.

Fig. 10 presents the evolution of permeability in damaged sandstone specimens during the entire deformation process. The first permeability value in each figure was measured in the damaged sandstone just before reloading. For comparison, the evolution of permeability in undamaged sandstone (specimen C4)is also plotted in Fig.10.Compared with the undamaged sandstone,the evolution laws for the damaged sandstone specimens were different.For the specimen C8 with a low extent of damage of 0.468 as shown in Fig. 10a, the permeability was observed to increase significantly at the beginning of reloading. Afterward, the permeability of the damaged sandstone decreased with the increase in axial strain. This occurred due to the fact that the unloading point was at the elastic deformation stage whenDg=0.468 for specimen C8. Microcracks were not initiated when the deviatoric stress was unloaded.Then, the permeability of the damaged sandstone specimens increased, and the increment rate also increased with the axial strain. The maximum permeability value occurred after the peak stress.Similar to the intact specimens,the permeability of the damaged sandstone remained constant during the residual strength stage.

Fig.12. Microscopic observations of shear and tensile cracks of sandstone specimens.

For the specimens C9 and C10 with extents of damage of 0.692 and 0.886, as shown in Fig. 10b and c, respectively, the evolution trend of permeability was similar to that of specimen C8 with a low extent of damage. It is seen that the permeability increased significantly at the beginning of reloading. However, when the extent of damage increased to 0.924 (Fig.10d), the evolution of permeability was different from that of the sandstone with a relatively low extent of damage. The permeability of the specimen C11 increased slowly with the increase in axial strain at the initial stage of reloading.This finding can be explained by the initiation of cracks caused by the initial loading at the yield stage for specimen C11.

Fig.11 shows the ultimate failure modes of damaged sandstone specimens with different extents of damage. All the damaged sandstone specimens failed under shear modes. Some local horizontal tensile cracks could be seen in the compressed sandstone specimens. The extent of damage showed no sound influence on the failure patterns of the damaged sandstone specimens,compared with the intact sandstone specimen under the same testing condition (specimen C4 in Fig. 6). However, a slight increment in the fracture angle between the main shear fracture and the horizontal direction was observed with the increase in extent of damage. Furthermore, microscopic observations of the main shear fracture and horizontal tensile fracture are shown in Fig. 12. The shear fracture was relatively smooth, whereas the tensile fracture was relatively rough.

Fig.13 shows the evolution of permeability in damaged sandstone specimens during the increase and decrease in gas pressure.Similar evolution trends were found for the damaged sandstone specimens with different extents of damage. As the gas pressure increased (increasing process), the permeability in the damaged sandstone specimens decreased,which is consistent with previous studies on intact sandstone specimens (Huang et al., 2020b) and fractured coal specimens (Ju et al., 2016). This increase in permeability resulted from the decrement in effective stress applied to the specimens when the gas pressure increased and confining pressure remained constant. As the gas pressure decreased, the permeability of the damaged sandstone specimens decreased, which was a result of increment in the effective confining pressure. Moreover, the permeability in the decreasing process was generally higher than that in the increasing process with the same gas injection pressure, mainly due to the gradual increase of permeability channel (similar to scouring effect) in the first increasing process of gas pressure.

Fig. 14 shows the influence of the extent of damage on the permeability of the damaged sandstone specimens in the increasing and decreasing processes of gas pressure.It is clear from Fig.14 that as the extent of damage increased, the permeability of sandstone specimens increased in both the increasing and decreasing processes of gas pressure.This increase in permeability occurred because more microcracks were initiated under greater extents of damage. The slope of the permeability curve with gas pressure increased with increasing extent of damage, indicating that the sensitivity of permeability to the gas pressure increased with the extent of damage.

Fig. 13. Relationships between permeability and gas seepage pressure of sandstone specimens with different extents of damage.

Fig.14. Influence of the extent of damage on the permeability of sandstone specimens in the (a) increasing and (b) decreasing processes of gas pressure.

To explain the influence of the pre-loading on the evolution of the permeability of sandstone,a parameter of extent of damage was defined. However, the extent of damage was calculated by stress ratio in this study,which is an indirect response for rock damage.If the extent of damage defined as the crack ratio, it provides direct evidence for rock damage induced by pre-loading. Therefore, how to obtain the crack distribution in rock should be the emphasis of further work. Computed tomography (CT) scanning and nuclear magnetic resonance (NMR) may be effective methods. Moreover,how to maintain a constant gas pressure during the whole loading process is another important issue,because the initial permeability and the permeability after macro-failure initiation differ significantly. Artificially adjusting the injection pressure is a conventionally used method at present; however, the results may be influenced by the technicians’ experience. It would be better to develop a servo valve at the gas inlet.

5. Conclusions

(1) As the effective confining pressure increased, the peak strength, residual strength and elastic modulus of the sandstone specimens increased. With the increase in axial strain, the permeability of the sandstone specimens first decreased and then increased,followed by a constant value.The permeability of the sandstone specimens was observed to decrease with the increase in effective confining pressure.

(2) The evolution of the permeability of damaged sandstone specimens was related to the extent of damage. When the extent of damage was relatively low, the permeability exhibited a decreasing trend after reloading;however,when the extent of damage was relatively high, the permeability increased with the axial strain after the reloading. The damaged sandstone specimens failed under shear mode,which was independent of the extent of damage.

(3) As the gas pressure increased,the permeability of the damaged sandstone specimens increased.As the gas pressure decreased,the permeability of the damaged sandstone specimens decreased.Moreover,the permeability in the decreasing process of gas pressure was generally higher than that in the increasing process with the same injected gas pressure.

Declaration of Competing Interest

The authors wish to confirm that there are no known conflicts of interests associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.

Acknowledgments

This research was supported by the National Natural Science Foundation of China(Grant Nos.41272344 and 51909260),and the Fundamental Research Funds for the Central Universities(Grant No.2020ZDPYMS34). The authors would also like to express their sincere gratitude to the editor and two anonymous reviewers for their valuable comments which have greatly improved this paper.