Features of CO₂ fracturing deduced from acoustic emission and microscopy in laboratory experiments

2.1 Specimens and Experimental Setup

We used eight cubes (170 × 170 × 170 mm) of granite with a 20 mm diameter central hole. The granite is produced in Kurokami-jima Island in Seto Inland Sea in Southwestern Japan. The material is commonly known as Kurokami-jima granite. The modal composition of the samples for our experiments was about 40% potassium feldspar, 36% plagioclase, 21% quartz, and 3% micas and accessories. The mean grain size was about 2 mm, and some coarse potassium feldspar grains whose size more than 5 mm were observed.

To confirm the reproducibility of the experimental results, we used two specimens for each of the fracturing fluids: SC-CO₂, L-CO₂, water, and viscous oil (Table 1). The inherent rift plane of the granite specimen was oriented to correspond to the YZ plane in the Cartesian coordinate system (Figure 1). As shown in Table 1, the average P wave velocities measured along the Y and Z directions were around 5.0 km/s, whereas that along the X direction normal to the rift plane was around 4.5 km/s. The P wave velocities were measured before the experiments without any confining pressure. Results of Brazilian tests with the discs oriented to make fracture along the rift plane on 33 cylindrical samples of the same kind of Kurokami-jima granite, measuring 45 mm diameter and 30 mm length, showed an average tensile strength of 3.38 MPa with a standard deviation of 0.21 MPa [Ishida et al., 2005]. Effective porosity of the granite was 0.84%, where the pore and the bulk volumes were measured with the saturation and the buoyancy methods, respectively [International Society for Rock Mechanics, 1979], and its intrinsic permeability obtained by air permeability test for hollow cylinder samples was around 9 × 10⁻¹⁹ m² [Ishida et al., 2006]. The intrinsic permeability corresponds to 1 × 10⁻¹¹ m/s of hydraulic conductivity, which is within the extent from 10⁻¹² to 10⁻⁸ m/s for general granitic rock shown by Vutukuri and Katsuyama [1994]. To monitor AE events induced by the fluid injection, we glued four cylindrical lead zirconate titanate (PZT) elements 4 mm in diameter and 4 mm thick on each of the four lateral surfaces (total of 16 elements) of the specimen (Figure 1). To apply confining pressures, we covered each lateral surface with a 6 mm thick hard nylon sheet with four 5 mm diameter holes in the positions of the PZT elements. The PZT element wires were guided through grooves in the surface of the sheet, and the sheet was covered again with another 4 mm thick hard nylon sheet.

We placed the specimen in dry condition in a cylindrical pressure cell, except only the case of SC-CO₂ injection where we filled the cell with hot water to prevent the injected CO₂ from cooling. We inserted four bow-shaped spacer blocks between the specimen and the inner wall of the pressure cell and placed a flat jack between the specimen and each spacer block to apply pressure in the X and Y directions (Figure 2). In the Z direction, we placed flat jacks between the specimen and loading plates supported by the end caps on the top and bottom of the pressure cell. In all experiments, we applied confining pressures of 3, 6, and 4 MPa in the X, Y, and Z directions, respectively, to provide the deviatoric stress. The stress magnitudes of 3 and 6 MPa were selected following the solution by Kirsch [1898] so as to keep compressive stress larger than 3 MPa in the tangential direction all along the hole wall. The minimum tangential stress of 3 MPa induced at the points of the Y direction along the hole wall did not exceed the capacity of the injection pump and pipe line to induce HF, and the maximum stress of 15 MPa induced at those of the X direction was sufficiently smaller than that inducing the borehole breakout. The stress magnitude of 4 MPa in the Z direction was selected so as to be between 3 and 6 MPa in the X and Y directions. Although the confining pressures increase P wave velocities, we ignored the increases in calculation of AE source location, because they were expected only around 0.1 to 0.3 km/s from the measurements for granite under confining pressure from 0 to 200 MPa [Sano et al., 1992].

2.2 Method of Fluid Injection

Figure 3 shows the packer inserted into the central hole of the samples to inject the fracturing fluids, including CO₂. The packer had a 60 mm pressurizing section sealed with two O-rings at each end. The pressurizing section was centered along the hole. In all the experiments, we injected the fracturing fluid under the control of syringe pump to keep the same constant flow rate of 10 mL/min and stopped the injection just after HF was induced, which was indicated by a sudden pressure drop.

Figure 4 shows the injection system used for the HF experiments. To make SC-CO₂, we fed CO₂ from a bomb to a syringe pump cylinder, which had a capacity of 266 mL. To fill the cylinder as full as possible, we cooled the CO₂ to keep it in the liquid state by circulating coolant in a cooling unit above the cylinder. The phase diagram in Figure 5 shows that CO₂ becomes supercritical when the temperature is higher than 31.0°C and the pressure is greater than 7.38 MPa. After discharging L-CO₂ from the cylinder of the syringe pump at a constant flow rate of 10 mL/min, we heated it with a heater unit. We maintained the temperature at 55°C by bandaging electric resistance heating ribbon along the pipe connecting the heater unit to the packer (Figure 4). In addition, we filled the cell containing the specimen with hot water at a temperature of around 45°C to prevent the injected CO₂ from cooling. Although we did not measure the thermal properties of the Kurokami-jima granite, we believe that the temperature in the specimen did not easily increase within 1 h or so for the SC-CO₂ experiment, even when the outside of the specimen was warmed with the hot water and the wall of the injection hole wall with SC-CO₂. This expectation comes from our experiences in the heater test in a block of Inada granite whose thermal conductivity is 3.3 W/(m K), specific heat is 0.72 J/(g K), and density is 2.0 × 10³ kg/m³ [Ishida et al., 1990]. The similar tendency was also found in heater test in a block of Lac du Bonnet granite by Jansen et al. [1993]. Thus, during the experiment, it is most likely that the temperature of the specimen only in the vicinity of the surfaces and the hole wall was kept around 40°C, while the temperature in the specimen was kept at the room temperature around 20°C in which the specimen was left more than 1 week before the experiments. Although the specimen was soaked in hot water for around 1 h, the water was not expected to infiltrate around the injection hole owing to the specimen's low permeability, and the HF was induced under almost dry conditions based on our experience from similar previous experiments. For the other fluids, including L-CO₂, HF was also induced under dry conditions at room temperature, because we fed the fluids to the packer without heating or filling the cell with water.

2.3 Methods for Monitoring AE, Pressure, and Temperature

The PZT elements glued onto the specimen had a resonance frequency of 300 kHz, and they were covered with an aluminum sheet to avoid electromagnetically induced noise. They were also covered with heat shrinkable tubes and silicone rubber to provide a waterproof barrier for SC-CO₂ fracturing. We amplified the AE signals by 72 to 84 dB in total (36 dB in a preamplifier and 36 to 48 dB in a signal conditioner), processed them with a band-pass filter between 80 kHz and 1 MHz, and recorded them on a hard disk through an analog-to-digital (A/D) converter (PXI-5105, National Instruments Corp.) under the control of LabVIEW program. Since the A/D converter has 16 separate channels, the processed AE signals were digitized with 0.1 µs sampling time and had 2048 samples in the record length for each event for each sensor. We set the dead time after recording an event to 1 ms to prevent the hard disk from recording too much noise caused by “ringing,” which is the vibration following a large AE event. The recording of an AE event was triggered when one of the signals from the 16 AE sensors exceeded 3 V. In addition, we counted the number of AE events per second for each AE sensor when the signal exceeded 3 V.

Every 0.1 s, we measured the injected fluid pressure through transducers (PW-50MPA, Tokyo Sokki Kenkyujo Co., Ltd., with a full scale of 50 MPa and precision of 0.1 MPa) at the top of the packer, and the flat jack pressures in the X, Y, and Z directions through transducers (PW-20MPA with a full scale of 20 MPa and precision of 0.04 MPa) on the connecting pipes of opposing pairs of flat jacks. We measured the temperature changes with T-type thermocouples, which can measure temperature from −200 to 400°C with resolution of 0.5°C, glued to the injection pipe just above the packer in the hole and at both ends of the section of pipe covered with electric resistance heating ribbon only for SC-CO₂ injection (Figure 4).

2.4 Observation of Cracks With Fluorescent Resin

After the HF experiment, we overcored the tested specimens with a diameter of 68 mm along the central injection hole (Figure 6). The overcored hollow cores were soaked in the thermosetting acrylic resin monomer containing a fluorescent compound under vacuum to allow the resin monomer to penetrate into the induced cracks and then heated to set the resin in the cores before sectioning. The cracks filled with the resin were visualized and observed under the ultraviolet light irradiation [Nishiyama and Kusuda, 1994]. We made two thin sections including hydraulically induced fractures on the plane where Z = 85 mm, corresponding to the center of the pressuring section. No secondary fractures caused by preparing the thin sections were detected because the above mentioned pretreatment was completed before sectioning.

3.1 Changes in Fluid Pressure and AE Count Rate

Figure 7 shows the changes in injected fluid pressure, confining pressure, and AE count rate during injection of SC-CO₂, L-CO₂, water, and viscous oil into the specimen. The temperature is shown only for SC-CO₂. In the injection of SC-CO₂ and L-CO₂, since we fed CO₂ from the bomb, the bomb pressure around 5 MPa applied in the hole just after the experiments have started. In contrast, in the injection of water and oil, the pressure increased gradually from zero. In all cases, we shut the return pipe after filling the fluids in the dry empty pressurizing section in the hole, and we kept to inject the fluids at the constant flow rate of 10 mL/min through the experiments. The elapsed time along the lateral axis is taken as zero when the breakdown pressure, which is defined as the peak pressure just before large sudden pressure drop, is recorded.

In Figure 7a for the case of SC-CO₂ injection, we show the temperature measured with a thermocouple glued on the injection pipe just above the packer in the hole. The temperature most likely indicates the CO₂ temperature, since the temperature always showed the same temperature measured at the both ends of the section of pipe covered with electric resistance heating ribbon (see Figure 4) even when the sudden temperature change of the CO₂ was induced. Since the temperature shows around 36°C, the test began with the CO₂ in the gas state in the borehole, referring to the phase diagram of CO₂ shown in Figure 5. The CO₂ should start to become into a supercritical state once the fluid pressure get closer to around the critical pressure, 7.38 MPa. This change could be inferred from the change in the increase rate of the fluid pressure under the constant flow rate as shown with the arrow in Figure 7a. This change was most likely caused by the decrease of the fluid compressibility due to the change from the gas to the supercritical state of CO₂. The fluid pressure decreased sharply to zero just after breakdown at 9.10 MPa. The pressure and temperature, 35.5°C, at the breakdown demonstrate that the HF was induced by CO₂ of a supercritical state. The pressure decrease, which was caused by leakage through fracturing-induced cracks, most likely changed the CO₂ from supercritical to gas state again. The temperature also decreased to 22.6°C just after breakdown, and came back to 27.9°C at 100 s after the breakdown. The temperature decrease was probably caused by adiabatic expansion of CO₂, because the measured temperature decrease from 35.2 to 22.6°C can be induced by 1.15 times larger expansion of the sealed volume of gas state CO₂, under an assumption of simple adiabatic expansion using Poisson's law. The AE count rate (average of the 16 AE sensors) increased sharply just after breakdown and events continued to occur for several tens of seconds. The confining pressures, S_H, S_V, and S_h (Figure 1), were kept nearly constant at 6, 4, and 3 MPa, respectively, with small fluctuations due to crack growth during breakdown.

Breakdown pressure was positively correlated with viscosity: 9.10 MPa for SC-CO₂, 11.96 MPa for L-CO₂, 12.96 MPa for water, and 23.07 MPa for viscous oil.

3.2 AE Source Locations

Figure 8 shows the locations of AE sources observed during the fluid injections projected onto the three orthogonal planes (XY, YZ, and ZX). All of the AE occurred within 15 s after breakdown. Waveforms of a typical AE event for the respective four fluids are shown in Figure S3 in the supporting information.

As a source location method, we used the iterative method with the least squares principle, which is called Geiger's method [Geiger, 1910, 1912] following the classification by Ge [2003a, 2003b]. Considering the anisotropy of the P wave velocity [Rothman et al., 1974], which was measured before the experiment shown in Table 1, the AE source locations were determined within an expected accuracy of several millimeters. This was possible because we chose the AE events satisfying the following criteria [Ishida and Sasaki, 2011]: (i) five or more P wave arrival times could be read and (ii) the standard deviation and the maximum of residuals of arrival times were within 3 µs. The number of sources that satisfied these conditions was 118 for SC-CO₂ (Figure 8a), 160 for L-CO₂ (Figure 8b), 116 for water (Figure 8c), and 73 for viscous oil (Figure 8d). Figure 8 also shows the cracks visible on the original surfaces of the cubic specimens with the located sources. Cracks were visible on the two opposite surfaces of the XY plane for SC-CO₂ (Figure 8a), the XY and ZX planes for L-CO₂ (Figure 8b), and the ZX plane for viscous oil (Figure 8d). The cracks contained in the two parallel planes are distinguished by using dark lines (near planes; Z = 170 mm for the XY and Y = 0 mm for the XZ planes) and light lines (far planes; Z = 0 mm for the XY and Y = 170 mm for the XZ planes). The other cracks were visible on one plane only, while no visible crack appeared on the YZ planes.

The AE sources were distributed along the cracks, as expected from the observed surface cracks. However, the AE sources in Figure 8a were more widely distributed rather than lying along a flat plane; this effect seemed to increase with the decrease of viscosity of the fracturing fluids. To present the differences quantitatively, the maximum likelihood flat plane for the AE distribution was first estimated for each specimen by minimizing the sum of squares of the distances from a source to the flat plane. After that, the average distance, L_av, from a source to the maximum likelihood plane was obtained. For the AE distributions shown in Figure 8, the L_av values were 12.06 mm for SC-CO₂, 10.78 mm for L-CO₂, 8.15 mm for water, and 7.39 mm for viscous oil.

We obtained also the fractal dimensions of the AE distributions with the correlation function method, following Hirata et al. [1987] and Grassberger [1983]. Theoretically, the fractal dimensions of an infinite number of points distributed on a line, on a plane, and in three-dimensional space are 1, 2, and 3, respectively. However, because the number of distributed points is finite, the fractal dimensions obtained by this method tend to be slightly lower than their respective dimensions [Ishida et al., 1998]. Nevertheless, fractal dimension is useful for characterizing the features of the AE distribution, and a larger fractal dimension suggests more extensive cracking in three dimensions. For the AE distributions shown in Figure 8, the fractal dimensions for SC-CO₂, L-CO₂, water, and viscous oil were 2.42, 2.17, 2.20, and 2.01, respectively. This suggests that a low-viscosity fracturing fluid such as SC-CO₂ induces cracking in three dimensions rather than in two by, for example, forming sinuous cracks with a greater number of secondary branches.

3.3 Induced Crack Patterns Observed With the Fluorescent Method

The cracks induced by HF in the experiments were subtle in the all cases, and they were barely identified by tracing segments where the fracturing fluid leaked on the surfaces of the cubic specimens, although they seemed to be observed the more clearly the more viscous the fracturing fluid became. Even when we overcored with a 68 mm diameter around the 20 mm diameter injection hole, the overcored hollow core still had substantial strength and did not break into two pieces for almost all of the cases, as seen in the experiments by Schmitt and Zoback [1992, 1993].

Figure 9 shows crack propagation patterns observed on the thin sections cut from the hollow cores soaked in the acrylic resin containing a fluorescent compound. Although preliminary observations, except for the L-CO₂ injection, have already been reported [Chen et al., 2015], we examine the crack patterns in relation to the results of AE monitoring. Figures 9a(i) and 9b(i), 9b(ii), 9c(i), and 9d(i) show fluorescent images of the thin section taken under ultraviolet light [Nishiyama and Kusuda, 1994]. The bright and bluish white regions correspond to cracks. Figures 9a(ii), 9b(iii), 9c(ii), and 9d(ii) show sketches of the main crack induced by the injection. The crack propagates from right to left in all figures. The periphery of the injection hole is shown with a red line on the right side of the sketch. The observed area corresponds to the area from Y coordinate of 95 to 119 mm in Figure 6, and the left side almost corresponds to the inner wall of the overcoring hole. The sketch was made by connecting segments of the main crack identified with the fluorescence method under ultraviolet light, considering the continuity in the direction of the crack propagation. Although it was easy to identify the main cracks in the photos of SC-CO₂, water, and viscous oil (Figures 9a(i), 9c(i), and 9d(i)), it is difficult only in the photo of L-CO₂ (Figure 9b(i)); therefore, we used an enlarged photo (Figure 9b(ii)). The sketches of the main cracks in Figures 9a(ii), 9b(iii), 9c(ii), and 9d(ii) show that the cracks are tortuous and never propagate straight, although they propagate along the direction of the maximum compressive stress and along the rift plane where the main preexisting microcracks align. Fluids with lower viscosity induce cracks with higher tortuosity, because intermittent and stepwise crack extensions become more conspicuous.

To examine the correlations between crack patterns and the constituent mineral grains of the specimens, photomicrographs of the crack patterns on thin sections for SC-CO₂ and oil injection in the boxes in Figure 9 were taken using a petrographic microscope in crossed-polarized light (crossed Nicols). The cracks induced by SC-CO₂ propagate mainly along the grain boundaries of the constituent minerals (Figure 10a). In contrast, Figure 10b shows that the cracks induced by oil cut through many mineral grains. This is most likely a reason why the crack pattern depends on the viscosity of the fracturing fluid.

Crack aperture shown in Figure 10a is larger than that in Figure 10b, although Ishida et al. [2004] and Stanchits et al. [2014] showed that the higher viscosity fracturing fluid tends to induce cracks having larger aperture. Ishida et al. [2004] injected water and viscous oil into blocks of Kurokami-jima granite with monitoring pressure change of the flat jacks applying the confining pressure. Stanchits et al. [2014] injected two kinds of silicon oil having thousandfold different viscosity into low permeability blocks of Colton sandstone with monitoring volume of the injected fluid. Their results both indicated that the higher viscosity tends to induce the larger aperture cracks, which is inconsistent with our results shown in Figure 10. Although we did not monitor changes of the flat jack pressure and the injected volume, the large aperture observed in the SC-CO₂ injection was probably caused by expansion of CO₂ with the phase change from SC-CO₂ to gas due to the pressure decrease after the crack extension to the lateral free surface of the specimen.

4.1 Breakdown Pressure and Apparent Tensile Strength

Figure 11a shows the dependency of breakdown pressure on fracturing fluid viscosity. This figure clearly shows that breakdown pressure increases with viscosity. The tendency is consistent with the experimental results by Morita et al. [1996] using water-based and oil-based muds and, in addition, the numerical simulation by Bunger et al. [2010].

Schmitt and Zoback [1992, 1993] discussed carefully the effect of pore pressure on crack initiation of HF through laboratory experiments using hollow cylinder of westerly granite and glass, where they changed the pressurization rate and the magnitude of the confining pressure applying the outer surface of the cylinder. Here we discuss the effect in the much simpler way than Schmitt and Zoback [1992, 1993], using the following equation proposed by Scheidegger [1962] for a vertical borehole:

(1)

where P_b the breakdown pressure, P_p the pore pressure, T the tensile strength, S_hmin the minimum horizontal stress, and S_Hmax the maximum horizontal stress. In our experiments, S_hmin and S_Hmax correspond to S_h and S_H, respectively, as shown in Figure 1. By putting that S_h min = S_h, S_H max = S_H and P_P = αP_b,the equation 1 becomes

(2)

The case that α = 0 corresponds to the state that no pore pressure applies without infiltration of fracturing fluid, while the case that α = 1 corresponds to the state that the pore pressure equal to the fracturing fluid pressure applying on the wall of the injection hole. The magnitude of S_h fluctuated at the breakdown, because a specimen expanded in the X direction, due to intrusion of fracturing fluid into a crack induced along the Y direction, and resulted to push the flat jacks applying the confining pressure, S_h. However, since the fluctuation is not so large as shown in Figure 7, by substituting 3 MPa for S_h and 6 MPa for S_H, the equation 2 becomes

(3)

where a unit for T and P_b is MPa and α is a coefficient having no dimension.

The apparent tensile strength, T, obtained from the equation 3 is shown in Table 2 for the cases that α = 0. Even in the case that α = 0, the apparent tensile strength, T, becomes from 6 to 22 MPa, which is much larger than Brazilian tensile strength of the Kurokami-jima granite, 3.38 MPa. In the case that α = 1, the apparent tensile strength, T, becomes still much larger.

In Brazilian test, the tensile stress uniformly distributes along the fracture plane, while in our HF experiment, the tensile stress in the circumference direction is the largest on the wall of the injection hole and decreases with the square of the distance from the center of the hole [Kirsch, 1898]. When the difference of the stress distribution is taken account by introducing a concept of “risk of rupture” proposed by Weibull [1939a, 1939b] under the assumption of uniform distribution of Griffith cracks, the breakdown pressure, P_b, becomes 1.45 times larger than that of the Brazilian tensile strength [Ishida et al., 2005]. The difference of 1.45 times showed good agreement with that of 1.47 obtained in their experiments [Ishida et al., 2005]. However, the difference is still small to explain the difference between the apparent tensile strength and the Brazilian tensile strength.

The cracks induced in our HF experiments seemed to extend instantaneously to the lateral surface of the specimen. Discussion on the crack extension considering the stress intensity factors at a crack tip, as described by Ishida et al. [1997] following Zoback et al. [1977] and Zoback and Pollard [1978], may help to interpret the difference in the apparent tensile strength depending on the viscosity of the fracturing fluid. Figure 12 (left column) depicts the case in which hydrostatic pressure, σ, applies throughout an ellipsoidal crack surface. In this case, K_I = σ(πl)^1/2, where K_I is the stress intensity factor of mode I at a crack tip and l is half of the crack length. According to this relation, the stress intensity factor at a crack tip increases with crack length; in other words, a crack never stops once it starts to extend. Figure 12 (right column) depicts the case in which a pair of point loads, F, are applied at the center of an ellipsoidal crack. In this case, K_I = F(πl)^− 1/2, which indicates that stress intensity factor at a crack tip decreases with crack length; that is, a crack never extends without an additional increase in applied loads. It can be expected that the fracturing fluid pressure reaches the closer to a crack tip, the lower the viscosity becomes. Thus, the low-viscosity fluid injection would make state close to that hydrostatic pressure, σ, applies throughout an ellipsoidal crack surface, while the high-viscosity fracturing fluid injection would make state close to that a pair of point loads, F, applies at the center of an ellipsoidal crack. Consequently, the difference of the apparent tensile strength, T, in other words, the difference of the breakdown pressure, P_b, among the fracturing fluids, is most likely caused by the differences of their viscosity. From the above discussion, in field operations for the same rock type stratum under the same in situ stress condition and flow rate, the breakdown pressure for injecting a low-viscosity fluid, such as SC-CO₂, is expected to be lower than that of water and much lower than that of high-viscosity fluid such as gel.

4.2 AE Distribution

Figure 11b shows the dependency on viscosity of the average distance, L_av, from a source to the maximum likelihood plane. This figure clearly indicates that L_av decreases with viscosity. This suggests that low-viscosity fracturing fluids induce cracks that propagate farther away from a flat plane, whereas viscous fluids, such as gels, tend to induce cracks along a flat plane. Figure 11c shows that the fractal dimension, FD, of the AE distributions decreases with viscosity, suggesting that low-viscosity fracturing fluids induce cracks that propagate three dimensionally, rather than two dimensionally along a flat plane.

4.3 Fracturing Mechanism Deduced From P Wave First Motion Polarity of AE

The differences in the crack features possibly arose from a difference in fracture mechanism. Thus, we compared ratios of the P wave first motion polarity of approximately 30 AE events that were detected by at least seven sensors, allowing P wave arrivals to be determined for a source location. A calibration test, in which a small steel ball was dropped onto the upper surface of a thick steel plate and the resultant waveforms were recorded by sensors glued onto the plate's lower surface, showed that compression corresponded to an upward trace and dilation to a downward trace. In Figure S3 in the supporting information, the closed triangles indicate compression in P wave first motion showing upward trace, while the open triangles indicate dilatation. For example, in the case of Figure S3a, since the number of compression is four and that of dilatation is four, the compression ratio in P wave first motion for this AE event becomes 50%. Figure 11d shows the compression ratio in P wave first motion tends to increase with viscosity. The ratio would be 50% for a pure shear fracture and 100% for a pure tensile fracture. Thus, the results suggest that a low-viscosity fracturing fluid tends to induce shear dominant fractures, whereas viscous fluids tend to induce tensile dominant fractures.

As shown in Figure 10a, the cracks induced by SC-CO₂ propagate mainly along the grain boundaries of the constituent minerals, producing many small cracks inclined in the direction of the maximum compressive stress, S_H, which is the propagating direction of a main crack. As shown in Figure 8, the induced main cracks extended in planes almost parallel to the Z direction (the direction of the intermediate principal stress, S_V) in the all experiments, and we observe the cracks on XY plane normal to the Z direction in Figure 10a. Thus, ignoring effect of the intermediate principal stress and considering the two-dimensional stress condition, because shear stress develops on a plane inclined in the direction of the maximum compressive stress, S_H, the inclined cracks are easy to be induced by shear fracture. In contrast, Figure 10b shows that the cracks induced by viscous oil injection cut through many mineral grains and propagate almost straight along the direction of the maximum compressive stress without bending. Because shear stress does not develop on a plane parallel to the direction of the maximum compressive stress, the cracks are probably induced by tensile fracture rather than by shear. In addition, in the oil injection, because the cracks extended to the both lateral surfaces of the specimens as shown in Figure 8d and the injected oil seeped out from the induced cracks on the specimen surfaces, the tensile cracks are most likely induced by the intrusion of the viscous oil.

4.4 Crack Features Deduced From Direct Observation

Figure 11e shows the dependency on viscosity of the tortuosity, L/L₀, where L is the crack length measured by connecting 0.05 mm long line segments, namely, a divider, along the main crack, and L₀ is the length of the straight line from the initiation point of the crack on the wall of the injection hole to its end point on the inner wall of the overcoring (Figure 9a). The main cracks are traced in both directions from the fracturing hole, from Y coordinates of 75 to 51 mm and from 95 to 119 mm (Figure 6). The tortuosity for each specimen is the average of the tortuosities obtained in the two opposite directions. Although the results for the two specimens for each fracturing fluid are plotted, only one result is plotted for the water injection. This is because the cracks in specimen G1103 for water injection could not be filled with the fluorescent resin, and no observation was obtained. The tortuosity of the induced cracks tended to increase with the decrease of fracturing fluid viscosity, which is consistent with the crack propagation patterns in Figure 9.

Figure 11f shows the dependency on viscosity of an average of the crack numbers, which were counted when the induced cracks crossed the scanning lines at intervals of 1 mm from the injection hole to the inner wall of the overcoring. We counted the cracks excluding preexisting cracks, voids, and other defects with checking the propagation direction and continuity of the cracks through careful observation of crack width, fluorescent resin brightness, and constituent mineral grains under polarized and ultraviolet light. The cracks were counted in the two opposite directions from the fracturing hole, and the number plotted is the average obtained in the both directions. Thus, the number corresponds roughly to an average number of crack branches. The number of induced cracks increased with the decrease in fluid viscosity, although the number is large for oil injection in specimen G1112. This is an exceptional case, because our observation of this specimen showed that one of the main crack propagations was obstructed by a large biotite grain near the injection hole and the crack branches were in many directions.

The trends in Figures 11e and 11f are consistent with those obtained from the AE distribution, where the average distance, L_av, and the fractal dimensions, FD, increased with the decrease of fluid viscosity (Figures 11b and 11c).