importance of temperature control in surrounding

Importance of Temperature Control in Surrounding Environment during Permeability Test for Measuring Hydraulic Constants of Rock†

by

Masaji KATO*, Yoshitaka NARA**, Daisuke FUKUDA*, Masanori KOHNO***, Toshinori SATO****, Tsutomu SATO***** and Manabu TAKAHASHI******

Because rock masses serve as natural barriers for geological disposal of radioactive waste, information about rock

permeability is essential. An understanding of the influence of the surrounding environment temperature on the results is necessary for highly accurate permeability measurements. Herein we describe how to perform precise permeability measurements. Then, to investigate the influence of the surrounding environment temperature, we show the results of permeability measurements under conditions with dramatic changes using the transient pulse method and a Toki granite sample obtained from Gifu Prefecture in central Japan. The measured permeability without a temperature change is used as a reference. A change in the surrounding environment temperature remarkably affects the pressure in the upstream and downstream reservoirs, their pressure difference, and the confining pressure. An increase in the experimental system temperature increases the pressure. This difference is directly related to the estimated permeability. To accurately measure the rock permeability, it is essential to minimize changes in the surrounding environment temperature because they significantly affect the pressure difference.

Key words: Permeability measurement system, Low-permeability rock, Hydraulic conductivity, Temperature control, Thermal expansion

1 Introduction

Rock masses with a low permeability are used as natural flow barriers for geological disposal of radioactive waste. The permeability of rock masses, including fractures and faults in the rock mass scale, are estimated via in situ hydraulic tests using bore holes1), while permeability tests in laboratory evaluate the permeability of intact rocks on the core size scale. In the latter case, permeability tests should be implemented without temperature variations or vibrations to evaluate the hydraulic constants (hydraulic conductivity and specific storage) of low permeability rocks. Temperature variations in the surrounding environment induce a temperature change in the experimental equipment and in fluids due to heat transfer. This leads to changes in the pressure of other fluids, which lessen the compatibility of the experimental data to the theory of permeability test method. Therefore, the influence of variations in the surrounding environment temperature on permeability test data has been widely investigated2)–4). Additionally, methods to control the temperature during permeability tests have been examined5)–10). However, the influence of the variation in the surrounding environment temperature on permeability test data has yet to be clarified quantitatively.

Here, we describe how to conduct a precise permeability measurement for low-permeability rocks with respect to controlling the surrounding environment temperature. Then, by conducting permeability measurements using a low-permeability rock sample, we evaluate the influence of a change in the surrounding environment temperature on the results of a laboratory permeability test to measure the hydraulic constants of rocks. Specifically, the influence of the temperature change on the measured values in the permeability test is shown. Next, the relation between the temperature change and measured pressures is discussed. Additionally, methods to shorten the test time are discussed to minimize the influence of the temperature variation on the test data. Finally, the results are analyzed using data obtained from a permeability test with dramatic temperature changes.

2 Method 2.1 Experimental apparatus

Figure 1 schematically illustrates the permeability measurement system. This system consists of a confining fluid controller, pore fluid controller, recorder, and independent temperature controller. It is applicable to several types of

† Received Apr. 8, 2020 2021 The Society of Materials Science, Japan

* Member: Faculty of Eng., Hokkaido Univ., Kita-ku, Sapporo, 060-8628 Japan ** Member: Graduate School of Eng., Kyoto Univ., Nishikyo-ku, Kyoto, 615-8540 Japan *** Graduate School of Eng., Tottori Univ., Koyamaminami, Tottori, 680-8552 Japan **** Member: Horonobe Underground Res. Center, Japan Atomic Energy Agency (JAEA), Horonobe, Hokkaido, 098-3224 Japan ***** Faculty of Eng., Hokkaido Univ., Kita-ku, Sapporo, 060-8628 Japan ****** Res. Inst. of Earthquake and Volcano Geology, National Inst. of Adv. Industrial Sci. and Technol. (AIST), Higashi, Tsukuba, 305-8567 Japan

permeability test methods. That is, it can sequentially apply the constant head method, falling head method, flow pump method, and transient pulse method.

It is essential to minimize the change in the surrounding environment temperature to precisely measure the permeability. For this purpose, the pressure vessel containing the rock specimen was set in the innermost chamber for the permeability measurement system, which was inside the triple-insulated chamber built in the experimental room (Fig. 2). To avoid a significant temperature change, the innermost chamber did not have a heat or light source. An air conditioner was installed at the insulated wall of the outermost chamber. These conditions maintained the temperature variation of the pressure vessel in the innermost chamber to ±0.1 °C during a measurement.

In some experiments, the inner and middle insulated doors were opened intentionally to conduct temperature change tests. Herein the temperature measured by the platinum resistance thermometer sensor near the pressure vessel in the innermost chamber was used as the index temperature.

Fig. 1 Schematic of the permeability measurement system (IC: Triple-insulated chamber, AC: Air conditioner, RT: Resistance thermometer, BR: Barometer, PT: Pressure transducer, DPT: Differential pressure transducer, PV: Pressure vessel, ER: Extra reservoir, UL: Upstream line, DL: Downstream line, SV: Separation valve, PV: Pressure pulse valve, EP: Evacuating port, AP: Air discharge port, WP: Water supply port, SC: Specimen, EC: End caps, HT: Heat-shrinkable tube, DP: Double plunger pump, SP: Syringe pump, CU: Controlling unit for syringe pumps, LG: Data logger, PC: Laptop computer. Confining fluid controller consists of DP and PV. Pore fluid is controlled by SP, CU, ER, UL, and DL. Recorder consists of LG, DPT, PTs, and PC. Temperature is controlled by RT and AC.)

Fig. 2 Photo of the pressure vessel containing a specimen placed in the

innermost chamber in the permeability measurement system.

Fig. 3 Photo of the cylindrical specimen for the permeability measurement. Diameter and the length are 5.0 cm and 2.5 cm,

respectively. 2.2 Rock sample

The specimen, which was coarse-to-medium-grained biotite granite (Toki granite), was cored from the borehole (08MI14) drilled for geoscientific research as well as for the development and assessment of deep subsurface engineering techniques for geological disposal of high-level nuclear waste at the drift (GL-200 m) excavated normal to the ventilation shaft at the Mizunami Underground Research Laboratory. The laboratory is located in Mizunami, which is on Honshu Island of Japan. The specimen was cut into a cylindrical shape with a 5.0-cm diameter

｢材料｣ (Journal of the Society of Materials Science, Japan), Vol. 70, No. 4, pp. 300-306, Apr. 2021Technical Review

03-2020-0103-(p.300-306).indd 300 2021/02/09 15:36:52

Importance of Temperature Control in Surrounding Environment during Permeability Test for Measuring Hydraulic Constants of Rock†

by

Masaji KATO*, Yoshitaka NARA**, Daisuke FUKUDA*, Masanori KOHNO***, Toshinori SATO****, Tsutomu SATO***** and Manabu TAKAHASHI******

Because rock masses serve as natural barriers for geological disposal of radioactive waste, information about rock

permeability is essential. An understanding of the influence of the surrounding environment temperature on the results is necessary for highly accurate permeability measurements. Herein we describe how to perform precise permeability measurements. Then, to investigate the influence of the surrounding environment temperature, we show the results of permeability measurements under conditions with dramatic changes using the transient pulse method and a Toki granite sample obtained from Gifu Prefecture in central Japan. The measured permeability without a temperature change is used as a reference. A change in the surrounding environment temperature remarkably affects the pressure in the upstream and downstream reservoirs, their pressure difference, and the confining pressure. An increase in the experimental system temperature increases the pressure. This difference is directly related to the estimated permeability. To accurately measure the rock permeability, it is essential to minimize changes in the surrounding environment temperature because they significantly affect the pressure difference.

Key words: Permeability measurement system, Low-permeability rock, Hydraulic conductivity, Temperature control, Thermal expansion

1 Introduction

Rock masses with a low permeability are used as natural flow barriers for geological disposal of radioactive waste. The permeability of rock masses, including fractures and faults in the rock mass scale, are estimated via in situ hydraulic tests using bore holes1), while permeability tests in laboratory evaluate the permeability of intact rocks on the core size scale. In the latter case, permeability tests should be implemented without temperature variations or vibrations to evaluate the hydraulic constants (hydraulic conductivity and specific storage) of low permeability rocks. Temperature variations in the surrounding environment induce a temperature change in the experimental equipment and in fluids due to heat transfer. This leads to changes in the pressure of other fluids, which lessen the compatibility of the experimental data to the theory of permeability test method. Therefore, the influence of variations in the surrounding environment temperature on permeability test data has been widely investigated2)–4). Additionally, methods to control the temperature during permeability tests have been examined5)–10). However, the influence of the variation in the surrounding environment temperature on permeability test data has yet to be clarified quantitatively.

Here, we describe how to conduct a precise permeability measurement for low-permeability rocks with respect to controlling the surrounding environment temperature. Then, by conducting permeability measurements using a low-permeability rock sample, we evaluate the influence of a change in the surrounding environment temperature on the results of a laboratory permeability test to measure the hydraulic constants of rocks. Specifically, the influence of the temperature change on the measured values in the permeability test is shown. Next, the relation between the temperature change and measured pressures is discussed. Additionally, methods to shorten the test time are discussed to minimize the influence of the temperature variation on the test data. Finally, the results are analyzed using data obtained from a permeability test with dramatic temperature changes.

2 Method 2.1 Experimental apparatus

Figure 1 schematically illustrates the permeability measurement system. This system consists of a confining fluid controller, pore fluid controller, recorder, and independent temperature controller. It is applicable to several types of

† Received Apr. 8, 2020 2021 The Society of Materials Science, Japan

* Member: Faculty of Eng., Hokkaido Univ., Kita-ku, Sapporo, 060-8628 Japan ** Member: Graduate School of Eng., Kyoto Univ., Nishikyo-ku, Kyoto, 615-8540 Japan *** Graduate School of Eng., Tottori Univ., Koyamaminami, Tottori, 680-8552 Japan **** Member: Horonobe Underground Res. Center, Japan Atomic Energy Agency (JAEA), Horonobe, Hokkaido, 098-3224 Japan ***** Faculty of Eng., Hokkaido Univ., Kita-ku, Sapporo, 060-8628 Japan ****** Res. Inst. of Earthquake and Volcano Geology, National Inst. of Adv. Industrial Sci. and Technol. (AIST), Higashi, Tsukuba, 305-8567 Japan

permeability test methods. That is, it can sequentially apply the constant head method, falling head method, flow pump method, and transient pulse method.

It is essential to minimize the change in the surrounding environment temperature to precisely measure the permeability. For this purpose, the pressure vessel containing the rock specimen was set in the innermost chamber for the permeability measurement system, which was inside the triple-insulated chamber built in the experimental room (Fig. 2). To avoid a significant temperature change, the innermost chamber did not have a heat or light source. An air conditioner was installed at the insulated wall of the outermost chamber. These conditions maintained the temperature variation of the pressure vessel in the innermost chamber to ±0.1 °C during a measurement.

In some experiments, the inner and middle insulated doors were opened intentionally to conduct temperature change tests. Herein the temperature measured by the platinum resistance thermometer sensor near the pressure vessel in the innermost chamber was used as the index temperature.

Fig. 1 Schematic of the permeability measurement system (IC: Triple-insulated chamber, AC: Air conditioner, RT: Resistance thermometer, BR: Barometer, PT: Pressure transducer, DPT: Differential pressure transducer, PV: Pressure vessel, ER: Extra reservoir, UL: Upstream line, DL: Downstream line, SV: Separation valve, PV: Pressure pulse valve, EP: Evacuating port, AP: Air discharge port, WP: Water supply port, SC: Specimen, EC: End caps, HT: Heat-shrinkable tube, DP: Double plunger pump, SP: Syringe pump, CU: Controlling unit for syringe pumps, LG: Data logger, PC: Laptop computer. Confining fluid controller consists of DP and PV. Pore fluid is controlled by SP, CU, ER, UL, and DL. Recorder consists of LG, DPT, PTs, and PC. Temperature is controlled by RT and AC.)

Fig. 2 Photo of the pressure vessel containing a specimen placed in the

innermost chamber in the permeability measurement system.

Fig. 3 Photo of the cylindrical specimen for the permeability measurement. Diameter and the length are 5.0 cm and 2.5 cm,

respectively. 2.2 Rock sample

The specimen, which was coarse-to-medium-grained biotite granite (Toki granite), was cored from the borehole (08MI14) drilled for geoscientific research as well as for the development and assessment of deep subsurface engineering techniques for geological disposal of high-level nuclear waste at the drift (GL-200 m) excavated normal to the ventilation shaft at the Mizunami Underground Research Laboratory. The laboratory is located in Mizunami, which is on Honshu Island of Japan. The specimen was cut into a cylindrical shape with a 5.0-cm diameter

301Importance of Temperature Control in Surrounding Environment during Permeability Test for Measuring Hydraulic Constants of Rock

03-2020-0103-(p.300-306).indd 301 2021/02/09 15:36:52

and 2.5-cm length (Fig. 3). Precise permeability measurements require accurate shaping of a cylindrical sample. In particular, the top and bottom surfaces of the cylindrical specimen should be parallel. In addition, the circumferential side surface should be perpendicular to the top and the bottom surfaces. If not, water leakage may occur during a permeability measurement.

Before the measurement, the specimen was saturated with distilled water in a desiccator in a vacuum for several hours and subsequently kept in the water.

Fig. 4 Photo of the specimen set in the specimen closure. 2.3 Permeability measurement

Here, we explain the procedure for a permeability measurement. Because a permeability measurement of a low permeability rock requires a long experimental time, the transient pulse method was used11). Figure 4 shows the rock specimen in the specimen closure. The specimen was placed between end pieces with O-rings and covered with a thermally shrinkable tube to isolate it from the water when applying a confining pressure. Stainless-steel tubes were connected to the ports of the end pieces to control and monitor the behavior of the pore water. Then the specimen closure containing the rock specimen was set in the pressure vessel.

The tubes and valves for the pore water lines were evacuated to create a vacuum. Then the confining pressure was increased to about 1 MPa using the double plunger pump and kept constant. Then the confining pressure was raised up to 2 MPa and pore

water was supplied. The pore pressure was kept constant at 1 MPa by a syringe pump. While applying the pore pressure, we monitored the flow rate on the syringe pump to verify that water did not leak.

Next, we started monitoring the room temperature until the temperature variation became sufficiently small. After confirming no leakage and minimal temperature variations, the separating valve was slowly closed. If the differential pressure (difference of the pore pressure between the upstream and downstream) was stable, the preparation for the measurement by the transient pulse method was complete.

Finally, a pressure pulse was applied to the upstream side of the reservoir, and the differential pressure between both sides of the specimen decreased. 2.4 Measurement with a temperature change in the surrounding environment

We conducted some measurements with a change in the surrounding environment temperature for two months. To investigate the influence of a temperature change due to an air conditioner on the permeability measurement system, a measurement was conducted while keeping the innermost and middle insulated doors open, which allowed the air conditioner to generate a significant change of temperature. We quantified the effect of the temperature change on the measured values such as the pressure in the upstream and downstream reservoirs, their pressure difference, and the confining pressure. The measurement was conducted with a simple, monotonous temperature change to observe the effect of the surrounding environment temperature on the measurement.

3 Results

3.1 Variation of the measured values with a change in the surrounding environment temperature

Figure 5 shows the results of the measurement with a significant temperature change in the surrounding environment. “Room temperature” indicates the temperature in the vicinity of the pressure vessel in the innermost chamber. During the measurement, the innermost and middle insulated doors were kept open so that the air conditioner rapidly affected the measurement system. The upstream reservoir pressure agreed with the downstream reservoir pressure (Fig. 5). In the measurement system, the differential pressure was measured with a highly accurate sensor. Therefore, the change in the differential pressure was observed accurately and clearly in the measurement.

Fig. 5 Variation of the measured values with a temperature change (temperature transition with cooling at 22 °C, warming at 30 °C, and then the air conditioner stopped). Figure (b) is an enlarged view with

time of figure (a).

Figure 5 shows that the changes in the measured values are constant until 0.9 hours. This is due to the stable temperature achieved by the air conditioner. The temperature around the pressure vessel was about 2 °C higher than the temperature set by the air conditioner due to the indirect airflow to the thermocouples. Upon suddenly changing the temperature from 22 °C to 30 °C, the temperature in the surrounding environment increased (time: 0.9–1.1 hours) and successively showed a plateau region with an irregular vibration (time: 1.1–3.5 hours). After that, all apparatuses in the insulated chamber were gradually heated, causing the temperature to oscillate (time: 3.5–5.8 hours). We stopped the air conditioner at 5.8 hours; then, the temperature gradually decreased

Figure 5 shows how a change in the surrounding environment temperature influences the other measured values, that is, the differential pressure, the reservoir pressure, and the confining pressure. The differential pressure was the most sensitive to a change in the surrounding environment temperature, while the reservoir pressure was more sensitive than the confining pressure.

3.2 Permeability measurements with a change in the surrounding environment temperature

Figure 6 shows the hydraulic head variation with an artificial temperature change during the measurement with the transient pulse method where the differential head is normalized by the initial value. Therefore, the normalized differential head corresponded to the differential pressure normalized by the initial differential pressure.

In this experiment, the pressure pulse was applied to the upstream reservoir at an initial temperature of 22.6 °C. The differential pressure decreased with elapsed time. When the differential pressure reached 80% of the initial value, we increased the room temperature using the air conditioner. Accordingly, the room temperature increased to 28.5 °C. Due to this temperature change, the dimensionless differential head increased to 1.1. Then the air conditioner was turned off, and we continued to measure the pressures and temperatures. The room temperature in Fig. 6 is the same as the temperature in the surrounding environment in Fig. 5.

The data obtained in this experiment is affected by the change in the surrounding environment temperature, demonstrating a low quality in the permeability measurement. Next, we checked the result of the permeability evaluation and its error using this low-quality data. Typically, experiments involving a low-permeable sample are complete before the differential pressure reaches 0 as the measurement requires a long-time. Therefore, we considered the influence of the data span on the permeability evaluation.

Figure 7 shows the hydraulic conductivity of granite obtained by the analysis using the difference in data span considering the influence of an artificial temperature change. In the data analysis, the analytical solution introduced by Brace et al.11) was used instead of the solution by Hsieh et al.12) for easy convergence in the nonlinear least-squares method. The reference on the left side in Fig. 7 shows the standard value obtained from the permeability measurement with the same pressure condition but without a temperature change. All the plots have error bars, which were estimated in the analysis. The reference value is one of the most precise results considering the error bar. Aside from the reference, the hydraulic conductivities were evaluated by the analysis with different data spans. Notations (A)–(K) in Fig. 7 are the same as those in Fig. 6. The hydraulic conductivity evaluated from the data span (A)–(B) in Fig. 7 was obtained from the data without the influence of the temperature change. The hydraulic conductivity evaluated from the data span (C)–(K) was obtained assuming that the experiment started from (C) where the dimensionless differential head was 1.1. These hydraulic conductivities were close to the reference and had smaller errors. For the other hydraulic conductivities, the evaluated values became smaller with a shorter data span, but the analytical error was larger.

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and 2.5-cm length (Fig. 3). Precise permeability measurements require accurate shaping of a cylindrical sample. In particular, the top and bottom surfaces of the cylindrical specimen should be parallel. In addition, the circumferential side surface should be perpendicular to the top and the bottom surfaces. If not, water leakage may occur during a permeability measurement.

Before the measurement, the specimen was saturated with distilled water in a desiccator in a vacuum for several hours and subsequently kept in the water.

Fig. 4 Photo of the specimen set in the specimen closure. 2.3 Permeability measurement

Here, we explain the procedure for a permeability measurement. Because a permeability measurement of a low permeability rock requires a long experimental time, the transient pulse method was used11). Figure 4 shows the rock specimen in the specimen closure. The specimen was placed between end pieces with O-rings and covered with a thermally shrinkable tube to isolate it from the water when applying a confining pressure. Stainless-steel tubes were connected to the ports of the end pieces to control and monitor the behavior of the pore water. Then the specimen closure containing the rock specimen was set in the pressure vessel.

The tubes and valves for the pore water lines were evacuated to create a vacuum. Then the confining pressure was increased to about 1 MPa using the double plunger pump and kept constant. Then the confining pressure was raised up to 2 MPa and pore

water was supplied. The pore pressure was kept constant at 1 MPa by a syringe pump. While applying the pore pressure, we monitored the flow rate on the syringe pump to verify that water did not leak.

Next, we started monitoring the room temperature until the temperature variation became sufficiently small. After confirming no leakage and minimal temperature variations, the separating valve was slowly closed. If the differential pressure (difference of the pore pressure between the upstream and downstream) was stable, the preparation for the measurement by the transient pulse method was complete.

Finally, a pressure pulse was applied to the upstream side of the reservoir, and the differential pressure between both sides of the specimen decreased. 2.4 Measurement with a temperature change in the surrounding environment

We conducted some measurements with a change in the surrounding environment temperature for two months. To investigate the influence of a temperature change due to an air conditioner on the permeability measurement system, a measurement was conducted while keeping the innermost and middle insulated doors open, which allowed the air conditioner to generate a significant change of temperature. We quantified the effect of the temperature change on the measured values such as the pressure in the upstream and downstream reservoirs, their pressure difference, and the confining pressure. The measurement was conducted with a simple, monotonous temperature change to observe the effect of the surrounding environment temperature on the measurement.

3 Results

3.1 Variation of the measured values with a change in the surrounding environment temperature

Figure 5 shows the results of the measurement with a significant temperature change in the surrounding environment. “Room temperature” indicates the temperature in the vicinity of the pressure vessel in the innermost chamber. During the measurement, the innermost and middle insulated doors were kept open so that the air conditioner rapidly affected the measurement system. The upstream reservoir pressure agreed with the downstream reservoir pressure (Fig. 5). In the measurement system, the differential pressure was measured with a highly accurate sensor. Therefore, the change in the differential pressure was observed accurately and clearly in the measurement.

Fig. 5 Variation of the measured values with a temperature change (temperature transition with cooling at 22 °C, warming at 30 °C, and then the air conditioner stopped). Figure (b) is an enlarged view with

time of figure (a).

Figure 5 shows that the changes in the measured values are constant until 0.9 hours. This is due to the stable temperature achieved by the air conditioner. The temperature around the pressure vessel was about 2 °C higher than the temperature set by the air conditioner due to the indirect airflow to the thermocouples. Upon suddenly changing the temperature from 22 °C to 30 °C, the temperature in the surrounding environment increased (time: 0.9–1.1 hours) and successively showed a plateau region with an irregular vibration (time: 1.1–3.5 hours). After that, all apparatuses in the insulated chamber were gradually heated, causing the temperature to oscillate (time: 3.5–5.8 hours). We stopped the air conditioner at 5.8 hours; then, the temperature gradually decreased

Figure 5 shows how a change in the surrounding environment temperature influences the other measured values, that is, the differential pressure, the reservoir pressure, and the confining pressure. The differential pressure was the most sensitive to a change in the surrounding environment temperature, while the reservoir pressure was more sensitive than the confining pressure.

3.2 Permeability measurements with a change in the surrounding environment temperature

Figure 6 shows the hydraulic head variation with an artificial temperature change during the measurement with the transient pulse method where the differential head is normalized by the initial value. Therefore, the normalized differential head corresponded to the differential pressure normalized by the initial differential pressure.

In this experiment, the pressure pulse was applied to the upstream reservoir at an initial temperature of 22.6 °C. The differential pressure decreased with elapsed time. When the differential pressure reached 80% of the initial value, we increased the room temperature using the air conditioner. Accordingly, the room temperature increased to 28.5 °C. Due to this temperature change, the dimensionless differential head increased to 1.1. Then the air conditioner was turned off, and we continued to measure the pressures and temperatures. The room temperature in Fig. 6 is the same as the temperature in the surrounding environment in Fig. 5.

The data obtained in this experiment is affected by the change in the surrounding environment temperature, demonstrating a low quality in the permeability measurement. Next, we checked the result of the permeability evaluation and its error using this low-quality data. Typically, experiments involving a low-permeable sample are complete before the differential pressure reaches 0 as the measurement requires a long-time. Therefore, we considered the influence of the data span on the permeability evaluation.

Figure 7 shows the hydraulic conductivity of granite obtained by the analysis using the difference in data span considering the influence of an artificial temperature change. In the data analysis, the analytical solution introduced by Brace et al.11) was used instead of the solution by Hsieh et al.12) for easy convergence in the nonlinear least-squares method. The reference on the left side in Fig. 7 shows the standard value obtained from the permeability measurement with the same pressure condition but without a temperature change. All the plots have error bars, which were estimated in the analysis. The reference value is one of the most precise results considering the error bar. Aside from the reference, the hydraulic conductivities were evaluated by the analysis with different data spans. Notations (A)–(K) in Fig. 7 are the same as those in Fig. 6. The hydraulic conductivity evaluated from the data span (A)–(B) in Fig. 7 was obtained from the data without the influence of the temperature change. The hydraulic conductivity evaluated from the data span (C)–(K) was obtained assuming that the experiment started from (C) where the dimensionless differential head was 1.1. These hydraulic conductivities were close to the reference and had smaller errors. For the other hydraulic conductivities, the evaluated values became smaller with a shorter data span, but the analytical error was larger.


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When the temperature of the surrounding environment was constant, multiple measurements were conducted and the repeatability of results was confirmed. The hydraulic conductivity and specific storage of Toki granite obtained in the test were in the range of 21–2.6×10−11 m/s and 1.2–23×10−7 1/m, respectively, under the condition of an effective confining pressure in the range of 1–9 MPa and a constant pore pressure of 1 MPa.

Fig. 6 Dimensionless hydraulic head variation with the temperature change during a transient pulse permeability test. (A) 0 min, (B) 6 min, (C) 9 min, (D) 11 min, (E) 13 min, (F) 15 min, (G) 17 min, (H) 19 min,

(I) 23 min, (J) 65 min, and (K) 98 min.

Fig. 7 Hydraulic constants of granite obtained by analysis with different

data spans.

4 Discussion 4.1 Method to shorten the test time

Reducing the time needed for a permeability measurement can minimize the influence of a change in the surrounding environment temperature. Therefore, decreasing the experimental time is important for permeability measurements as the experimental time affects the precision of the test results. Here the methods to shorten the experimental time are discussed.

Shortening the experimental time in permeability measurement is equivalent to accelerating the decay of the differential head after applying a pressure pulse. Although the magnitude of the pressure pulse is not related to the decay rate

of the differential head, the influence of the temperature change on the experimental data becomes relatively small upon applying a large pressure pulse. To accelerate the decay of the pressure pulse during the permeability measurement by the transient pulse method, increasing the flow rate through a specimen is effective. According to Darcy’s law, shortening the height (that is, increasing the hydraulic gradient) or enlarging the cross-section area of the specimen will increase the flow rate under the condition of the same differential pressure with the same specimen. However, Darcy’s law may not be applicable if the rock-forming mineral size is larger than the specimen height. In such a case, seepage flow occurs only through relatively larger cracks. That is, channel flow occurs. In addition, the short specimen height makes the hydraulic gradient larger. The large difference of the hydraulic head between the upstream and downstream sides of the specimen yields a large difference in the effective confining pressure at both ends. Accordingly, the distribution of hydraulic conductivity within a specimen is not uniform because the permeability depends on the effective confining pressure. A large pressure pulse has the same influence. Therefore, we set the specimen size to 5.0-cm diameter × 2.5-cm length, and the magnitude of the pressure pulse was less than 5% of the effective confining pressure (usually less than 1%).

To downsize the volumes of both the upstream and downstream reservoirs, which increase the compressive storage capacity, can also shorten the experimental time. However, downsizing the reservoir volumes makes the reservoir pressure more sensitive to a change in the surrounding environment temperature. Therefore, the reservoirs were the cylinders (100 mL each) of syringe pumps.

4.2 Relation between the change in the surrounding environment temperature and the measured pressures

Here, we discuss the relation between the change in the surrounding environment temperature and the measured pressures. In particular, the differential pressure, which is the most important data for a permeability evaluation, is highly sensitive to such a change. In Fig. 5, the increase of 7 °C in temperature is followed by an increase of 27 kPa in the differential pressure. Then the increasing rate of the temperature decreases, and the differential pressure declines due to the penetration of water into the rock specimen. Similarly, other measurement values increase but to a lesser extent. The increase in the differential pressure indicates the pressure increases in the upstream reservoir, tubing, and valves more than those for the downstream reservoir side. This is because the heat transfer to the upstream reservoir, tubing, and valves occurs prior to that in the downstream reservoir sides. The small volume of the water in the upstream reservoir may also be another reason.

We quantitatively evaluated the influence of the change in the surrounding environment temperature on our apparatus. In

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our apparatus, the water in the reservoir, tubing, and valves expands (or shrinks) thermally due to the change in the surrounding environment temperature. This alters the pressure. That is, the influence of the temperature change on the reservoir pressure can be described as follows: (1) Change in the surrounding environment temperature ⇔

water volume changes in the reservoir, tubing, and valves, (2) Water volume change in the reservoir, tubing, and valves

⇔ reservoir pressure changes. First, the influence of (2) is discussed. In general, the relation

between the water volume change and pressure change can be calculated using the compressibility of water. However, it is not simple for this apparatus because not only the water compressibility but also the stiffness of the reservoir and tubing react to the temperature change8), 10). The stiffness of the reservoir and tubing is specific for the apparatus and it cannot be calculated from the design drawings. Therefore, we experimentally evaluated the compressive storage (fluid volume change per unit hydraulic head change) of the reservoir system, which includes the reservoir, tubing, and valves. The compressible storages of the downstream and upstream sides are the same, Sd = Su = 8.5×10-10 m2. For example, an infinitesimal change of water (10 µL) in the reservoir (compression) is followed by an increase of pressure (head) of 118 kPa (12 m(H2O)). Controversially, a pressure (head) change of 100 kPa (10.2 m(H2O)) is followed by an 8.7-µL volume change of water. The relation between the pressure pulse and infinitesimal volume change of water during the transient pulse permeability test was experimentally examined using the syringe pumps. The volume change of water with 5–8 µL in the upstream reservoir was observed for a pressure pulse of 60–80 kPa.

Next, we consider the influence of (1). The thermal expansion coefficient of water is 2.1×10-4 1/K at a temperature of 20 °C. On the other hand, the thermal expansion coefficient of stainless steel (SUS410) is 10.4×10-6 1/K, which is 1/20 of that of water. Here, only the thermal expansion of water is assumed to be affected by an environmental temperature change. For our apparatus, a 1-°C temperature change in reservoir water yields a 21-μL water volume change followed by a 247-kPa (25 m (H2O)) differential pressure change. Hence, a transient pulse permeability measurement with a pressure pulse of several tens kPa is invalid because the S/N ratio is less than 1.

The surrounding environment temperature change should be less than 0.02 °C to suppress the pressure change to 5 kPa (5% of pressure pulse) or less for a transient pulse permeability measurement with the pressure pulse of 100 kPa. Therefore, controlling the surrounding environment temperature during a permeability measurement is essential when using a low permeability rock as a sample material.

4.3 Influence of the change in the surrounding environment temperature on the permeability measurement results

The change in the surrounding environment temperature induces a pressure change in the reservoirs, altering its differential pressure. Additionally, it affects the permeability measurement results (Fig. 6), but it is difficult to quantify its influence. Figure 7, which indicates the precision using the analytical error, highlights the importance of temperature management in the experimental environment.

5 Conclusions We performed permeability measurements under the

conditions with significant changes in the surrounding environment temperature to investigate the influence of temperature changes on the experimental results. As a reference, the permeability was also measured without a change in the surrounding environment temperature. All measurements used Toki granite and the transient pulse method.

The change in the surrounding environment temperature affected the pressure in the upstream and downstream reservoirs, their pressure difference, and the confining pressure. All of these increased as the temperature of our experimental system increased. The differential pressure was affected immediately. This difference directly relates to the evaluation of the permeability (hydraulic conductivity). Because temperature changes significantly affect the differential pressure, it is essential to minimize the change in the surrounding environment temperature to accurately measure rock permeability.

This study was supported financially by the Radioactive Waste Management Funding and Research Center. In addition, we appreciate the support from Supporting Program for Interaction-based Initiative Team Studies (SPIRITS) of Kyoto University.

References 1) S. Takeuchi, R. Takeuchi and K. Ando, “Study on

hydrogeological conceptualization in a fractured rock based on the cross-hole hydraulic test”, Proceedings of the Institute of Natural Sciences, Nihon University, No.48, pp.95-110 (2013).

2) Y. Bernabé, “Technical Note: A wide range permeameter for use in rock physics”, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, Vol.24, No.5, pp.309-315 (1987).

3) M. Takahashi and Z. Xue, “On problem in measuring permeability of rocks using pulse method”, Chisitsu News, No.421, pp.46-54 (1989).

4) K. Nakano, A. Saito and M. Nishigaki, “Laboratory measurement technique for low permeability of rock sample”, Soils and Foundations, Vol.31, No.3, pp.164-174 (1991).

5) H. J. Sutherland and S. P. Cave, “Argon gas permeability of New Mexico rock salt under hydrostatic compression”, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, Vol.17, No.5, pp.281-288 (1980).


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When the temperature of the surrounding environment was constant, multiple measurements were conducted and the repeatability of results was confirmed. The hydraulic conductivity and specific storage of Toki granite obtained in the test were in the range of 21–2.6×10−11 m/s and 1.2–23×10−7 1/m, respectively, under the condition of an effective confining pressure in the range of 1–9 MPa and a constant pore pressure of 1 MPa.

Fig. 6 Dimensionless hydraulic head variation with the temperature change during a transient pulse permeability test. (A) 0 min, (B) 6 min, (C) 9 min, (D) 11 min, (E) 13 min, (F) 15 min, (G) 17 min, (H) 19 min,

(I) 23 min, (J) 65 min, and (K) 98 min.

Fig. 7 Hydraulic constants of granite obtained by analysis with different

data spans.

4 Discussion 4.1 Method to shorten the test time

Reducing the time needed for a permeability measurement can minimize the influence of a change in the surrounding environment temperature. Therefore, decreasing the experimental time is important for permeability measurements as the experimental time affects the precision of the test results. Here the methods to shorten the experimental time are discussed.

Shortening the experimental time in permeability measurement is equivalent to accelerating the decay of the differential head after applying a pressure pulse. Although the magnitude of the pressure pulse is not related to the decay rate

of the differential head, the influence of the temperature change on the experimental data becomes relatively small upon applying a large pressure pulse. To accelerate the decay of the pressure pulse during the permeability measurement by the transient pulse method, increasing the flow rate through a specimen is effective. According to Darcy’s law, shortening the height (that is, increasing the hydraulic gradient) or enlarging the cross-section area of the specimen will increase the flow rate under the condition of the same differential pressure with the same specimen. However, Darcy’s law may not be applicable if the rock-forming mineral size is larger than the specimen height. In such a case, seepage flow occurs only through relatively larger cracks. That is, channel flow occurs. In addition, the short specimen height makes the hydraulic gradient larger. The large difference of the hydraulic head between the upstream and downstream sides of the specimen yields a large difference in the effective confining pressure at both ends. Accordingly, the distribution of hydraulic conductivity within a specimen is not uniform because the permeability depends on the effective confining pressure. A large pressure pulse has the same influence. Therefore, we set the specimen size to 5.0-cm diameter × 2.5-cm length, and the magnitude of the pressure pulse was less than 5% of the effective confining pressure (usually less than 1%).

To downsize the volumes of both the upstream and downstream reservoirs, which increase the compressive storage capacity, can also shorten the experimental time. However, downsizing the reservoir volumes makes the reservoir pressure more sensitive to a change in the surrounding environment temperature. Therefore, the reservoirs were the cylinders (100 mL each) of syringe pumps.

4.2 Relation between the change in the surrounding environment temperature and the measured pressures

Here, we discuss the relation between the change in the surrounding environment temperature and the measured pressures. In particular, the differential pressure, which is the most important data for a permeability evaluation, is highly sensitive to such a change. In Fig. 5, the increase of 7 °C in temperature is followed by an increase of 27 kPa in the differential pressure. Then the increasing rate of the temperature decreases, and the differential pressure declines due to the penetration of water into the rock specimen. Similarly, other measurement values increase but to a lesser extent. The increase in the differential pressure indicates the pressure increases in the upstream reservoir, tubing, and valves more than those for the downstream reservoir side. This is because the heat transfer to the upstream reservoir, tubing, and valves occurs prior to that in the downstream reservoir sides. The small volume of the water in the upstream reservoir may also be another reason.

We quantitatively evaluated the influence of the change in the surrounding environment temperature on our apparatus. In

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Time (min)

Heating to 30 oC

No air conditioning

Room temperature

(A)

(B)

(C)

(D)(E)

(F)

(G)(H)

(I)

(J)(K)

our apparatus, the water in the reservoir, tubing, and valves expands (or shrinks) thermally due to the change in the surrounding environment temperature. This alters the pressure. That is, the influence of the temperature change on the reservoir pressure can be described as follows: (1) Change in the surrounding environment temperature ⇔

water volume changes in the reservoir, tubing, and valves, (2) Water volume change in the reservoir, tubing, and valves

⇔ reservoir pressure changes. First, the influence of (2) is discussed. In general, the relation

between the water volume change and pressure change can be calculated using the compressibility of water. However, it is not simple for this apparatus because not only the water compressibility but also the stiffness of the reservoir and tubing react to the temperature change8), 10). The stiffness of the reservoir and tubing is specific for the apparatus and it cannot be calculated from the design drawings. Therefore, we experimentally evaluated the compressive storage (fluid volume change per unit hydraulic head change) of the reservoir system, which includes the reservoir, tubing, and valves. The compressible storages of the downstream and upstream sides are the same, Sd = Su = 8.5×10-10 m2. For example, an infinitesimal change of water (10 µL) in the reservoir (compression) is followed by an increase of pressure (head) of 118 kPa (12 m(H2O)). Controversially, a pressure (head) change of 100 kPa (10.2 m(H2O)) is followed by an 8.7-µL volume change of water. The relation between the pressure pulse and infinitesimal volume change of water during the transient pulse permeability test was experimentally examined using the syringe pumps. The volume change of water with 5–8 µL in the upstream reservoir was observed for a pressure pulse of 60–80 kPa.

Next, we consider the influence of (1). The thermal expansion coefficient of water is 2.1×10-4 1/K at a temperature of 20 °C. On the other hand, the thermal expansion coefficient of stainless steel (SUS410) is 10.4×10-6 1/K, which is 1/20 of that of water. Here, only the thermal expansion of water is assumed to be affected by an environmental temperature change. For our apparatus, a 1-°C temperature change in reservoir water yields a 21-μL water volume change followed by a 247-kPa (25 m (H2O)) differential pressure change. Hence, a transient pulse permeability measurement with a pressure pulse of several tens kPa is invalid because the S/N ratio is less than 1.

The surrounding environment temperature change should be less than 0.02 °C to suppress the pressure change to 5 kPa (5% of pressure pulse) or less for a transient pulse permeability measurement with the pressure pulse of 100 kPa. Therefore, controlling the surrounding environment temperature during a permeability measurement is essential when using a low permeability rock as a sample material.

4.3 Influence of the change in the surrounding environment temperature on the permeability measurement results

The change in the surrounding environment temperature induces a pressure change in the reservoirs, altering its differential pressure. Additionally, it affects the permeability measurement results (Fig. 6), but it is difficult to quantify its influence. Figure 7, which indicates the precision using the analytical error, highlights the importance of temperature management in the experimental environment.

5 Conclusions We performed permeability measurements under the

conditions with significant changes in the surrounding environment temperature to investigate the influence of temperature changes on the experimental results. As a reference, the permeability was also measured without a change in the surrounding environment temperature. All measurements used Toki granite and the transient pulse method.

The change in the surrounding environment temperature affected the pressure in the upstream and downstream reservoirs, their pressure difference, and the confining pressure. All of these increased as the temperature of our experimental system increased. The differential pressure was affected immediately. This difference directly relates to the evaluation of the permeability (hydraulic conductivity). Because temperature changes significantly affect the differential pressure, it is essential to minimize the change in the surrounding environment temperature to accurately measure rock permeability.

This study was supported financially by the Radioactive Waste Management Funding and Research Center. In addition, we appreciate the support from Supporting Program for Interaction-based Initiative Team Studies (SPIRITS) of Kyoto University.

References 1) S. Takeuchi, R. Takeuchi and K. Ando, “Study on

hydrogeological conceptualization in a fractured rock based on the cross-hole hydraulic test”, Proceedings of the Institute of Natural Sciences, Nihon University, No.48, pp.95-110 (2013).

2) Y. Bernabé, “Technical Note: A wide range permeameter for use in rock physics”, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, Vol.24, No.5, pp.309-315 (1987).

3) M. Takahashi and Z. Xue, “On problem in measuring permeability of rocks using pulse method”, Chisitsu News, No.421, pp.46-54 (1989).

4) K. Nakano, A. Saito and M. Nishigaki, “Laboratory measurement technique for low permeability of rock sample”, Soils and Foundations, Vol.31, No.3, pp.164-174 (1991).

5) H. J. Sutherland and S. P. Cave, “Argon gas permeability of New Mexico rock salt under hydrostatic compression”, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, Vol.17, No.5, pp.281-288 (1980).


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6) D. Trimmer, “Laboratory measurements of ultralow

permeability of geologic materials”, Review of Scientific Instruments, Vol.53, No.8, pp.1246-1254 (1982).

7) Y. Bernabé, “The effective pressure law for permeability in Chelmsford granite and Barre granite”, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, Vol.23, No.3, pp.267-275 (1986).

8) M. Zhang, M. Takahashi, R. H. Morin and T. Esaki, “Evaluation and application of the transient-pulse technique for determining the hydraulic properties of low-permeability rocks − part 2: experimental application”, Geotechnical Testing Journal, Vol.23, No.1, pp.91-99 (2000).

9) Y. Nara, P. G. Meredith, T. Yoneda and K. Kaneko, “Influence of macro-fractures and micro-fractures on permeability and elastic wave velocities in basalt at elevated pressure”, Techtonophysics, Vol.503, No.1, pp.52-59 (2011).

10) M. Kato, M. Takahashi and K. Kaneko, “Highly precise evaluation of hydraulic constants of low-permeability rocks using the transient pulse method”, Journal of MMIJ, Vol.129, No.7, pp.472-478 (2013).

11) W. F. Brace, J. B. Walsh and W. T. Frangos, “Permeability of granite under high pressure”, Journal of Geophysical Research, Vol.73, No.6, pp.2225-2236 (1968).

12) P. A. Hsieh, J. V. Tracy, C. E. Neuzil, J. D. Bredehoeft and S. E. Sillman, ”A transient laboratory method for determining the hydraulic properties of ‘tight’ rocks − I. theory”, International Journal of Rock Mechanics and Mining Sciences & Geomechanical Abstracts, Vol.18, No.3, pp.245-252 (1981).


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importance of temperature control in surrounding

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