2022 Volume 63 Issue 8 Pages 1138-1143
This study developed an original constant-head permeability apparatus for rocks. This apparatus can freely adjust the confining pressure and hydraulic pressure (hydraulic gradient), and can directly measure the runoff volume using an electronic balance. This apparatus can measure the hydraulic conductivity more accurately than the conventional constant-head method that measures the runoff volume using a measuring cylinder. Second, this study measured the hydraulic conductivity of Inada granite specimens (50 mm in diameter and 40 mm in length) under confining pressure conditions using the constant-head permeability apparatus. The test was performed at 22 ± 1°C in a temperature-controlled room. As result, we found that the hydraulic conductivity of Inada granite, which was measured using this apparatus, is quite similar to that reported by a previous study using transient pulse method. Furthermore, the observed decline in hydraulic conductivity due to the confining pressure is consistent with the observations of the previous study. Therefore, the permeability measurement system used in this study is established and reliable. In addition, this study measured the hydraulic conductivity of various seven intact rocks (granite, basalt, dacite, sandstone, and tuff) under confining pressure conditions using a constant-head permeability apparatus, and we presented how the hydraulic conductivity changes as the confining pressure increases.
This Paper was Originally Published in Japanese in J. Soc. Mater. Sci., Japan 71 (2022) 221–227.
The deep-underground bedrock layer is utilized as underground space in large-scale projects, for example, long-term LPG stockpiling, CCS, and HLW geological disposal, and it is extremely important to understand the permeability of bedrock. So far, a significant amount of research has been conducted on the permeability of rocks and rock masses in in-situ and laboratory tests. In particular, laboratory tests have the significant advantage of being able to freely set measurement conditions such as temperature and pressure,1) therefore rock permeability tests under various conditions are often conducted. In general, constant-head, falling-head, transient pulse, flow pump, pore pressure oscillation, and other methods1) are employed to evaluate the permeability of rocks in laboratory. In particular, for rocks with low permeability, there are many studies that have evaluated permeability via the transient pulse method proposed by Brace et al.2) The details of the transient pulse method have already been described in many research papers published previously, therefore we will not discuss it further. Because the transient pulse method is extremely sensitive to the measured temperature, highly accurate temperature adjustment is required3) and minute temperature changes have a significant effect on experimental data.4) However, unlike the conventional method of measuring the flow rate, the transient pulse method is a method of measuring the change in pressure using a pressure gauge or differential pressure gauge with relatively higher measurement accuracy than the flow meter.5–8) Therefore, the measurement time is relatively short, and there is an advantage in that the permeability of low permeability rock can be evaluated with high accuracy. In contrast, rock permeability evaluation via the constant-head method is regarded as a classical method.3,9,10) However, this method is often applied to rocks with a relatively high permeability and hydraulic conductivity of approximately 10−5 m/s or more.11,12) The constant-head method is not suitable for low-permeability rocks, and is rarely implemented at present. It is presumed that this is because it is difficult to measure an extremely small runoff volume with a low-permeability material,10) and evaporation of the runoff volume cannot be ignored by long-term measurements. However, the constant-head method has the following three advantages3) over the transient pulse method: (1) stable measurement results of runoff volume can be obtained; (2) if there is a leak from a pipe or sleeve, it can be easily detected, and (3) the measurement method is simple and does not require any specialized competence. Recently, many studies have employed the constant-head method to evaluate the permeability of low-permeability materials (mainly clay samples and bentonite-based materials) with a hydraulic conductivity of approximately 10−10 m/s or less.13–18) We believe that the constant-head method can be applied to rock samples with comparable hydraulic conductivity, if problems such as leakage between the side surface of the specimen and the sleeve and evaporation of permeability are appropriately addressed.
In this study, we first attempted to develop a constant-head permeability test apparatus that was improved so that the permeability test device in Refs. 13–18) above could be applied to rock specimens. This apparatus can freely adjust the confining pressure and hydraulic pressure (hydraulic gradient), and can directly measure the runoff volume using an electronic balance. Second, the hydraulic conductivity of the intact Inada granite specimen was measured using this apparatus, and compared with previous research results (transient pulse method) to confirm the usefulness of the developed apparatus. Finally, the permeability of various intact rocks under confining pressure conditions was measured using the developed constant-head permeability apparatus, and we confirmed the consistency with the previous research results on the variation of the hydraulic conductivity of various rock specimens with increasing confining pressure.
Seven types of rock specimens were used in this study: Inada granite (biotite granite from Inada, Kasama, Ibaraki, Japan), Toyooka basalt (olivine basalt from Akaishi, Toyooka, Hyogo, Japan), Daisen dacite (biotite hornblende dacite from Daisen, Tottori, Japan), Shirahama sandstone (medium sandstone from Shirahama, Wakayama, Japan), Kimachi sandstone (tuffaceous sandstone from Kimachi, Shinji, Matsue, Shimane, Japan), Sapporo tuff (welded tuff from Sapporo, Hokkaido, Japan), and Shakudani tuff (lapilli tuff from Asuwa, Fukui, Japan) (Fig. 1).
End face image of rock specimens (50 mm in diameter).
The end face images of the specimens (50 mm in diameter) and the properties (dry density, water absorption, effective porosity, and P-wave velocity under dry condition) of the rock samples are shown in Fig. 1 and Table 1. Three Inada granite specimens (A, B, and C) were prepared to confirm the degree of variation in the permeability test results. It is well-known that granite has three fragile planes that are orthogonal to each other (anisotropic),19,20) and are called rift, grain, and hardway planes. All three Inada granite specimens used in this study were obtained from the core in the direction orthogonal to the grain plane (G-direction core).
A schematic of the constant-head permeability apparatus is shown in Fig. 2. The permeability test was performed in a constant-temperature bath made of insulating material (IM) in a temperature-controlled room (TR; 22 ± 1°C). The apparatus mainly consists of an air compressor (CM), pressure water tank (PW; maximum allowable working pressure of 0.5 MPa), stainless steel (SUS304) pressure vessel (PV; outer diameter of 250 mm, thickness of 40 mm), stainless steel (SUS304) capillary tube (CT), hydraulic pump (HP; maximum allowable operating pressure of 30 MPa), electronic balance (EB; resolution of 0.1 mg), and a personal computer (PC). The cylindrical-shaped specimen (SP) has a diameter of 50 mm and a height of 40 mm, and a heat-shrinkable tube (HS) made of polyolefin was attached to the side surface of the specimen using a heat gun. In this apparatus, each part can be easily replaced, and the runoff volume can be measured directly using an electronic balance; therefore, it is possible to sequentially check the quality of the water that has passed through the specimen. In the future, it will be possible to easily conduct permeability tests under various measurement conditions.
Schematic diagram of the Constant-head permeability apparatus.
The permeability test was conducted by passing distilled water through the lower end face of the specimen at a constant water pressure using an air compressor and pressurized water tank. At this time, a constant confining pressure was applied to the side surface of the specimen through a heat-shrinkable tube. However, the water pressure was set to a value (0.45 MPa) smaller than the confining pressure in order to prevent water leakage from the gap between the side surface of the specimen and the heat-shrinkable tube. For leak check, a permeability test was conducted in advance using an impermeable cylinder acrylic material as the specimen, and it was confirmed that there was no leak. Each specimen was saturated using a water-filled decompression container. The runoff volume was measured at intervals of 60 s, and the data were transmitted from the balance to a personal computer. Figure 3 shows the runoff volume for the first 4 h in the permeability test (confining pressure Pc = 5 MPa) using Inada granite specimen A. After the water that has passed through the specimen is poured into the measuring cup (Fig. 3, upper right arrow), the runoff volume measured by the analytical balance decreases momentarily due to evaporation (Fig. 3, lower right arrow). In this example, it is poured at intervals of approximately 40 min. The decrease due to evaporation was added to the runoff volume when the data were organized, and the hydraulic conductivity was calculated as a correction value considering evaporation. The amount of water permeation under one set of measurement conditions was measured for ≥24 h after the first confirmation of water runoff. The hydraulic conductivity, k, was calculated using eq. (1) under the assumption that Darcy’s law holds.
| \begin{equation} k = \frac{QL}{hAt} \end{equation} | (1) |
Correction of runoff volume considering evaporation amount (e.g., Inada granite specimen A, confining pressure Pc = 5 MPa).
Figure 4 shows an example of the corrected value of hydraulic conductivity (Inada granite specimen A) with a measurement time of 24 h. Because the slope of the runoff volume is almost linear at any confining pressure, it can be confirmed that the hydraulic conductivity does not change with the passage of time during the test. It can be seen that the slope of the runoff volume decreases as the confining pressure increases. Because the amount of runoff volume that falls on the measuring cup on the electronic balance is almost the same, a small slope implies that the interval time corresponding to the amount of runoff volume that falls on the measuring cup is long. As shown in Fig. 5, this interval time increases exponentially as the confining pressure increases (that is, the hydraulic conductivity decreases, although there are some differences among the three Inada granite specimens.).
Corrected runoff volume in 24 hours of measurement time (e.g., Inada granite specimen A, confining pressure Pc = 1–12 MPa).
Interval time of measurement runoff volume at each effective confining pressure (e.g., Inada granite specimen).
The hydraulic conductivity of the Inada rock specimens under confining pressure (Pc = 1–12 MPa) is shown in Fig. 6. The hydraulic conductivity of three Inada granite under confining pressures of 1 to 12 MPa ranged from 2.9 × 10−11 to 1.8 × 10−12 m/s (specimen A), 2.1 × 10−11 to 2.1 × 10−12 m/s (specimen B), and 2.0 × 10−11 to 2.0 × 10−12 m/s (specimen C). The maximum standard deviation of the hydraulic conductivity at each effective confining pressure is 2.0 × 10−12 m/s (effective confining pressure Pec = 0.55 MPa). Although there is some variation in the hydraulic conductivity in the range of confining pressure Pc = 1 to 4 MPa, it can be ascertained that this variation is due to the inhomogeneity of the rock specimen. In three specimens, it was observed that the hydraulic conductivity tended to decrease as the effective confining pressure increased. At the effective confining pressure Pec = 11.55 MPa, the hydraulic conductivity decreased by approximately one order of magnitude with respect to Pec = 0.55 MPa. This tendency is consistent with the previous results.7,8,19) This is likely because micro-fractures inside the specimen (in the case of granite, the grain boundaries of mineral particles such as quartz, plagioclase, biotite, and others) gradually closed as the confining pressure increased.22)
Hydraulic conductivity of Inada granite specimen at each effective confining pressure, and comparison with transient pulse method.
Thereafter, we compared the hydraulic conductivity of Inada granite obtained in this study with the results of a previous study. Kato et al.8) adopted the nonlinear least squares method (Gauss-Newton method) as a method that is more versatile than the conventional analysis method in the transient pulse method. They proposed a method to calculate the hydraulic conductivity using an exact solution from the attenuation curve of the head difference obtained by the transient pulse method. Furthermore, in the experiment conducted by Kato et al.,8) a permeability test was conducted using Inada granite (cylindrical shape with a diameter of 50 mm and a height of 40 mm; the core in the direction orthogonal to the hardway plane (H-direction core)) under a strictly controlled temperature environment (±0.01°C). In addition, the reproducibility of the experiment was verified by conducting the experiment multiple times under the same measurement conditions. Therefore, we decided to confirm the usefulness of the developed test apparatus by comparing the hydraulic conductivity of Inada granite obtained in this study with the results of Kato et al.8) Comparing the experimental results in this study with the numerical value8) (Fig. 6 +) of the hydraulic conductivity of Inada granite obtained by the transient pulse method in the range of confining pressure Pc = 2 to 10 MPa, it is noted that the tendency of the hydraulic conductivity to decrease with increasing confining pressure is similar. Furthermore, it is observed that the values of hydraulic conductivity are approximately the same under the same confining pressure. Comparing the approximate line of numerical value8) (broken line in Fig. 6; H-direction core) with the hydraulic conductivity (G-direction core) in this study, the latter was larger, with a difference of approximately 30%. This difference indicates the difference (anisotropic) in the direction of the two cores. Comparing the mantissa parts of the hydraulic conductivity of both, the difference was 1.1 (effective confining pressure of 3.55 MPa) at maximum. Here, we examine the effect of anisotropy on the hydraulic conductivity of Inada granite specimen (cylindrical specimen with a diameter of 50 mm and a height of 25 mm).7) The hydraulic conductivity (effective confining pressure range of 1 to 9 MPa) between the H-direction core and the G-direction core is larger in the latter, and the difference is approximately 40%. This is approximately the same as the difference between the hydraulic conductivity in this study and the approximation line of Kato et al.8) In other words, if the hydraulic conductivity of the Inada granite specimen of the H-direction core is obtained using the apparatus in this study, it is presumed that it overlaps with the approximation line of Kato et al.8) Therefore, the permeability of low-permeability rocks can be evaluated effectively using the as-developed constant-head permeability test apparatus via the highly reliable transient pulse method.
3.2 Hydraulic conductivity of intact various rockThe hydraulic conductivities of seven types of intact rock specimens (including Inada granite) under confining pressure Pc = 1–12 MPa are shown in Fig. 7. The hydraulic conductivities of various rock specimens are 1.7 × 10−12 to 6.0 × 10−14 m/s (Toyooka basalt), 3.3 × 10−11 to 1.2 × 10−11 m/s (Kimachi sandstone), 1.5 × 10−10 to 6.1 × 10−11 m/s (Shirahama sandstone), 1.0 × 10−10 to 8.7 × 10−11 m/s (Shakudani tuff), 2.5 × 10−7 to 7.8 × 10−8 m/s (Daisen dacite), and 9.4 × 10−7 to 5.4 × 10−7 m/s (Sapporo tuff), respectively. In previous studies, the hydraulic conductivity k of Kimachi sandstone, Shirahama sandstone, and Sapporo tuff has been determined to be approximately 10−11 m/s5,23,24) and approximately 10−10 to 10−11 m/s6) (Kimachi sandstone), approximately 10−10 m/s25) and approximately 10−10 to 10−11 m/s6) (Shirahama sandstone), and approximately 10−7 m/s23) (Sapporo tuff). These studies differ from the current study in terms of the measurement conditions such as the specimen size, temperature, and pressure. Although it cannot be compared directly, the order of the hydraulic conductivities obtained in the previous studies and the hydraulic conductivities of the rocks (Kimachi sandstone, Shirahama sandstone, and Sapporo tuff) obtained in this study are almost comparable.
Relationship between effective confining pressure and hydraulic conductivity for intact rock specimens.
It was observed that the hydraulic conductivity of all rock specimens tended to decrease as the effective confining pressure increased, although the degree was different. This is the same tendency as that for the granite specimen. A decrease in hydraulic conductivity with an increase in effective confining pressure has also been reported in Kimachi sandstone,5,6) Shirahama sandstone6,25) that is consistent with the results of these studies. In order to confirm the difference in the degree of decrease in hydraulic conductivity with the increase in effective sealing pressure, Fig. 8 shows the hydraulic conductivity change ratio of various rocks based on the hydraulic conductivity at an effective confining pressure Pec = 0.55 MPa. In Toyooka basalt that has a small effective porosity of only a few percent, the degree of decrease in hydraulic conductivity with an increase in effective confining pressure was large, and the decrease rate at Pec = 11.55 MPa was 96.5% that was approximately equal to that of Inada granite. Next, the specimens with the largest decrease were three types of rocks, Daisen dacite, Shirahama sandstone, and Kimachi sandstone that had an effective porosity of more than 10%, and the decrease rate at Pec = 11.55 MPa was approximately 60%. The hydraulic conductivity of the Shakudani tuff did not change significantly with an increase in the effective confining pressure. This is because the effective porosity of Shakudani tuff is relatively large at 26.93% (Table 1) that is probably because the voids are not sufficiently closed to have a large effect on the hydraulic conductivity in the range of effective confining pressure Pec = 0.55 to 11.55 MPa. However, although the effective porosity of Sapporo tuff is much larger than that of Shakudani tuff, the degree of decrease in hydraulic conductivity with an increase in the effective confining pressure is large. As can be seen from the physical properties shown in Table 1, the values of the dry density and P-wave velocity of Sapporo tuff are much smaller than those of the Shakudani tuff. From this, it can be inferred that the particle skeleton structure of Sapporo tuff is fragile, and in addition to the blockage of voids, the compression of the specimen itself is larger than that of the Shakudani tuff. This is believed to have led to a decrease in the hydraulic conductivity.
Hydraulic conductivity change ratio as the effective confining pressure Pec increases based on the hydraulic conductivity of Pec = 0.55 MPa.
As described above, the constant-head permeability test apparatus developed in this study afforded results consistent with those of the previous studies. More specifically, it has been found that there is a tendency for the hydraulic conductivity to decrease as the confining pressure increases, and there is a difference in the degree of decrease in the hydraulic conductivity owing to the difference in rock types.
In this study, we first developed a constant-head permeability test apparatus that can be used to examine low-permeability rock specimens. Second, the hydraulic conductivity of various intact rock specimens (diameter 50 mm, height 40 mm) under a confining pressure of 1–12 MPa was measured. Furthermore, the usefulness of the test apparatus was validated by confirming consistency with the results of previous studies on the changes in hydraulic conductivity with increasing confining pressure. When the hydraulic conductivity of the three Inada granite specimens was compared with the hydraulic conductivity of Inada granite determined by the transient pulse method in a previous study, the tendency of the decrease in hydraulic conductivity with the increase in confining pressure was found to be similar. In addition, the hydraulic conductivity values were comparable under the same confining pressure. Therefore, the permeability of low-permeability rocks can be evaluated effectively using the as-developed constant-head permeability test apparatus via the highly reliable transient pulse method. In addition, in various other rock specimens, the tendency of the hydraulic conductivity to decrease with increasing confining pressure and the difference in the degree of decrease in hydraulic conductivity due to the difference in rock type were consistent with the previous research results. Accordingly, we conclude that it is possible to evaluate the permeability of rocks (hydraulic conductivity in the range of 10−5 to 10−14 m/s) using the developed constant-head permeability test apparatus.
In the future, the relationships between the runoff volume, hydraulic conductivity, and measurement time and the hydraulic gradient will be clarified, and the measurable area (confining pressure, hydraulic pressure, and specimen size) of the specimen will be examined.
This work was supported by the Ministry of Economy, Trade and Industry (METI) of Japan. We are grateful to Dr. Masaji Kato (Assistant Professor, Division of Sustainable Resources Engineering, Faculty of Engineering, Hokkaido University) for providing the numerical data presented in Fig. 6 (Reference No. 8).
