Shale damage investigation is important in shale gas development. This paper is concerned with the experimental identification of ultrasonic wave velocities and damage mechanic parameters of Longmaxi shale under water-based mud soaking and confining pressure loading. The wave velocities increased with increasing confining pressure, while wave velocities decreased with increasing soaking time. The anisotropy of Young’s modulus decreases when confining pressure increases. As soaking time increases, the anisotropy coefficient increases. As soaking time and confining pressure rise, the damage parameters also show complex changes. The results are beneficial for shale gas development.

1. Introduction

During the drilling and development of shale gas, basic wave velocities and mechanical parameters play an important role [13]. The coupling effect of water-based mud (WBM) and confining pressure on the wave velocity and mechanical parameters of Longmaxi (LMX) shale is key to studying shale. The static mechanical properties of LMX shale have been largely studied for the past few years [46]. However, no elastic wave velocity data at WBM soaking and confining pressure loading are available in the literature for LMX shale. Indeed, elastic wave velocity measurements are well known as being very sensitive to damage in rocks [710]. The monitoring of elastic wave velocities in shale under mechanical loading is relatively common. Generally, most of the dynamic experimental studies reported in the literature on shale samples have been performed under hydrostatic loading conditions [9, 11, 12]. However, elastic wave velocity measurements on shale are reported by Yin [13] under triaxial and polyaxial loading and by Podio et al. [14] under uniaxial loading. In addition, Dewhurst and Siggins [15] reported elastic wave velocity data on shale samples under triaxial loading. Sarout and Guéguen [16, 17] studied the anisotropy of elastic wave velocities in deformed shale.

Nowadays, there are no studies on the coupling effect of WBM and confining pressure on the four-rank-order damage of LMX shale. Lots of experiments were carried out. The wave velocity data and anisotropy coefficients of this paper are different with those in previous works. The parameter (β1111, β1133, and β3333) analysis is different and deeper than in the previous work [1618]. The wave velocity test is an effective and well-tested method to interpret anisotropy and mechanical damage parameters [1923]. Shale is featured with the sensitivity of wave velocity, which is favorable for studying the change rules of mechanical parameters of LMX shale [2427]. To interpret quantitatively the elastic wave velocity data in terms of microstructural properties of rock, a micromechanical model developed by Sarout [16, 17], based on effective medium-theory concepts, is used in the investigation of this paper. The application of this model to experimental data allows us to discuss the evolution of damage parameters. The main outcomes of the experiments reported here are (1) the identification of dynamic elastic wave velocity measurements at various states of WBM soaking and confining pressure loading and (2) the assessment of elastic anisotropic extent and damage under various WBM soaking and confining pressure loadings.

2. Rock Sample and Methodology

2.1. Description and Preparation of Shale Specimen

The rock samples are LMX formation shale from Sichuan Basin. Three kinds of samples () at angles of 0°, 45°, and 90° to the bedding plane are prepared, as shown in Figure 1.

X-ray diffraction (XRD) analysis of 9 samples determines the characteristics of mineral components of LMX shale, as shown in Figure 2. In XRD analysis, the reported % composition of mineralogy is based on weight. The average content of clay minerals and quartz is 48.90% and 4.29%, respectively; the average content of dolomite is 4.29%. The scanning electron microscope (SEM) images of LMX shale is as shown in Figure 3. The results show that porous clay and inclusions are clearly visible and silty or sandy inclusions are randomly distributed in rock samples. The surface of rock samples is relatively flat with a few pores. The pores between clay particles are geometrical, and most of them are curved or reticulated. The shape of the organic matter (OM) hole of LMX shale samples is oval, microcrack, bubble-shaped, irregular, or round.

2.2. Preparation of Water-Based Mud

During drilling for the shale formation, WBM is most commonly used mud. The conventional process of preparing water-based mud for the experiment is as follows [28]. (1) Pre-hydrated bentonite slurry with solid content of 4% is prepared; (2) 400 g bentonite and anhydrous sodium carbonate containing 5% bentonite are added to 10000 ml hot water; (3) the mixture is shaken for 3-4 h at low speed; (4) the mixture to be used as the raw slurry is kept still for 24 h at room temperature; and (5) 0.5% sulfonated methypheuo formaldehyde is mixed in the raw slurry to be used as the base slurry.

2.3. Experimental Device and Process

The experimental devices consist of a high-pressure chamber, core holder, emission end (transmitting sensor), receiving end (receiving sensor), pressure-stabilizing servo system (confining pressure pump, pressure sensor, and control valve), and data collection and analysis system, which can provide the maximum confining pressure up to 90 MPa, as shown in Figure 4. The frequency of the solitary pulse in this experiment is 1 MHz. The test device is limited to provision of confining pressure, so shear failure will not occur in the rock sample. After the acoustic wave velocity is set at the starting point, the confining pressure will be increased gradually. The wave velocity is measured at the confining pressures of 0 MPa, 20 MPa, 40 MPa, and 60 MPa.

The basic experiment process is soaking samples, wave velocity testing, and dried samples. Each of them receives the immersion experiment at no soaking (0 h), soaking for 1 h, and soaking for 3 h in WBM, followed by wave velocity testing. The temperature (27°C) during the experiment is controlled at an accuracy of ±0.5°C.

3. Experiment Results

3.1. Effect of Wave Velocity of LMX Shale

The wave velocity and shapes of samples measured after soaking in WBM are shown in Figures 5 and 6. are wave velocities in different directions, as shown in Figure 1. The initial wave velocities at no confining pressure (0 MPa) and no soaking (0 h) are , , , , , and , respectively.

In order to study the wave velocity of LMX with different soaking time and confining pressure, the result of this paper is compared with previous work (Chicopee shale) [21]. As shown in Figures 6(a), 6(c), and 6(e), WBM has an obvious effect on wave velocity of shale. The change rule of the wave velocities at different directions for soaked sample is as consistent as that for the rock samples (0 h), . The change rule of Chicopee shale is the same as the change rule of LMX shale, but the wave velocities of Chicopee shale are larger than those of LMX shale. The investigation of Chicopee shale did not consider the effect of mud soaking. As the soaking time increases, the wave velocities of LMX shale in a given direction decrease. Wave velocities increase at the greatest rate for 1 h soaking in WBM. However, when the soaking time increases to 3 h, wave velocity presents a lower drop rate than at 1 h soaking. and are very much close at 1 h soaking and 3 h soaking; 1 h soaking is a threshold time.

With the confining pressure increasing, wave velocities increase in all directions and were divided into stage 1 and stage 2, as shown in Figures 5, 6(b), 6(d), and 6(f). In stage 1, the maximum increase rate in wave velocity occurs in the pressure range 0-20 MPa. In stage 2, the increase rate in wave velocity in the pressure range 20-60 MPa is slower than in stage 1. The experimental result shows that 20 MPa confining pressure is a special value of pressure conditions that affect the wave velocity of LMX shale. The experimental results mentioned above that there is an inverse relationship between hydration time and confining pressure in terms of the effect on wave velocity of shale; that is, the soaking time decreases wave velocity at a given confining pressure, while confining pressure increases wave velocity for a given soaking time. The conclusion above is different from the previous study [17, 1921], mainly because this experiment takes into account the soaking time in WBM and confining pressure loading.

3.2. Effect of Anisotropy Coefficient of LMX Shale

Three-plug methods have been used to study the mechanical properties by many authors [17, 1921], as shown in Figure 7.

The degree of anisotropy can be represented by the ratio of elastic modulus in different directions: where where and are the dynamic Young’s modulus; is the rock density; , , , , and are stiffness constants; and , , , , and are the measured ultrasonic wave velocities.

The anisotropy coefficient for Young’s modulus can be obtained using Eq. (1). The anisotropy coefficient of the initial elasticity modulus at 0 MPa is 1.33 (soaked 0 h), 1.41 (soaked 1 h), and 1.46 (soaked 3 h), respectively. The anisotropy of Young’s modulus decreases when confining pressure increases. As hydration increases, anisotropy coefficient increases, which indicates that difference increases as hydration time increases, as shown in Figure 8.

3.3. Effect of Damage Parameter of LMX Shale

The damage parameters , , , , and can be calculated by Eq. (A8)-Eq. (A12) [1921]. The damage parameters , , , , and were affected by the wave velocities. The detailed process of the reference is shown in the appendix. As shown in Figures 9 and 10, the initial damage parameters (0 MPa, no soaking) are (GPa-1), (GPa-1), (GPa-1), (GPa-1), and (GPa-1), respectively. As shown in Figures 9(a), 9(c), 10(a), and 10(c), the first direct observation to be reported here is that is always larger than , which indicates a higher amount of bedding-parallel cracks than bedding-orthogonal cracks. With the soaking time increasing, and increase. As shown in Figures 9(e) and 9(e), as the soaking time increases, the magnitude of increases, which is consistent with the increase in anisotropy with soaking time as reported in Figure 8. It can be noted that of the sample is greater than . At low confining pressure, may be ten times , and is always maintained at a low value and decreases when the confining pressure goes up. With the increasing of confining pressure, both and decrease in WBM.

As the confining pressure rises, show complex changes and can be divided into stage 1 and stage 2, as shown in Figures 9(b), 9(d), and 9(f). During stage 1, between 0 and 20 MPa, decrease with increasing confining pressure at 0 h soaking. When shale samples were soaked for 1 h and for 3 h, increase with the confining pressure increasing. During stage 2, between 20 and 60 MPa, decreases with increasing confining pressure with low decreasing rate. These experimental results draw a conclusion that an increase in confining pressure leads to smaller and even closed fractured pores. The microscopic pore structure of shale is direction-dependent.

As the soaking time rises, also show complex changes, as shown in Figures 10(b), 10(d), and 10(f). During 20-60 MPa, when soaking lasts longer, increase (0-1 h) and then decrease (1-3 h), while increases. However, when the confining pressure is 0 MPa, with the soaking time increasing, decrease. The experimental result shows that 1 h soaking is a special time condition for the damage of LMX shale.

4. Discussion

The degree of shale damage shows a drastic change under soaking time and confining pressure loading. A higher degree of damage occurs in the vertical direction. The damage quantity α33 (horizontal direction) is much higher than α11 (vertical direction), which means that most of the crack-like pores or microcracks in shale are subhorizontal, while there are fewer of them in the vertical direction; this is why confining pressure has less effect on . increases more than does with soaking time at a given confining pressure. The microcrack further expands, propagates, converts, and connects to be macrocrack that becomes wider and extends to be fracture, which will develop until breaking. For 0-20 MPa, the pore direction, size, and structure of LMX shale are sensitive to confining pressure. For 20-60 MPa confining pressure, the sensitivity of pore to confining pressure is lower than that at 0-20 MPa. LMX shale shows a complex change in nonhorizontal and nonvertical directions.

The wave velocities and damage of LMX shale are sensitive to the soaking time. As the soaking time increases, the wave velocities in a given direction decrease. Wave velocities drop at the greatest rate for 1 h soaking in WBM. However, when the soaking time increases to 3 h, wave velocity presents a lower drop rate than 1 h soaking. The anisotropy coefficient of the elasticity modulus increases with soaking time increasing. When WBM enters the rock matrix, the damage of shale matrix occurs in short time.

5. Conclusion

The ultrasonic wave velocities of LMX shale under WBM and confining pressure were measured and analyzed. The shale damage mechanic parameters were determined by means of ultrasonic velocity measurements. With the confining pressure increasing, wave velocities increase in all directions, while wave velocities decreased with increasing soaking time. The anisotropy of Young’s modulus decreases when the confining pressure increases. As soaking time increases, the anisotropy coefficient increases, while the damage parameters also show complex changes. In the future, the soaking time and pressure conditions should be increased to study the coupled effect on the wave velocities and mechanic damage.


Shale can be simplified as a rock element with many spherical pores [2022]. For one pore in the shale element, the volume of transversely isotropic media is , and the elastic attribute is . When is inserted, the elastic attribute is , as shown in Figure 11. The equatorial plane of the pore is parallel to the shale bedding, which is assumed to coincide with the symmetry plane of the TI rock, and the effect of bulk modulus of fluid in the pore uniformity is lower than that of the bulk modulus of the solid phase on the same.

Additional stress sources from the fractured pore throughout the process of medium deformation. The far-field stress is , and in the absence of pore, the stress of the microscopic representative volume element (RVE) is , and the additional stress brought from the pore is . For RVE, we have where and refer to the flexibility tensors of background medium and fractured pore, respectively. is the flexibility tensor of the elliptical pore, and the Eshelby tensor is denoted as . The average displacement of fractured pore is expressed with flexibility tensor and stress field . where is the unit vector at discontinuity in the vertical direction as shown in Figure 12.

The flexibility tensor at discontinuity of infinite medium may be expressed with normal component and tangential component

The pore-induced additional compliance tensor can be expressed as where is the tensor in Kronecker symbol, is the count constant, and is the microfracture area , in m2.

The second-order tensor and the four-order tensor and are defined as

Under macroscopic conditions, the additional compliance tensor is expressed as

and parameters are directly related to fracture density and aspect ratio, where closely correlates to void, while correlates to fluids in the void. and may be used as the evaluation parameters of fracture change within shale and defined as damage parameters.

It can be drawn from the expressions that the conditions for obtaining the damage parameter are to first calculate the additional compliance tensor associated with the presence of spheroidal pores (crack-like), which requires the calculation of the rock compliance tensor that can be obtained by laboratory experiment or logging data. However, as shown in Eq. (A1), the compliance tensor of the whole medium consists of two parts: compliance tensor of the background medium (ignoring the crack-like pores) and compliance tensor associated with the presence of spheroidal pores (crack-like). The compliance tensor of the background medium is measured at high confining pressure when all crack-like pores are assumed to be closed. When the confining pressure decreases, any changes of the compliance tensor may be attributed to pore deformation. For extra compliance, therefore, the damage parameters , , , , and can be calculated.

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Authors’ Contributions

Ping Chen, Heyi Yuan, and Guangjian Dong designed the study. Heyi Yuan and Yudi Lu conducted the experiments and analyzed the data.


This work is supported by the National Science and Technology Major Project (Grant Nos. 2016ZX05022001 and 2016ZX05028001), Major National Basic Research Development Program of China (973 Program) (Grant No. 2013CB228003), the Science and Technology Support Program of Sichuan Province (Grant No. 2015SZ0003), the Basic Research Subject of the State Key Laboratory of Oil & Gas Reservoir Geology and Exploitation (Southwest Petroleum University) (Grant No. G3-1 and Grant No. G3), and China Scholarship Council (CSC) (No. 201808510213). We thank Dr. Tao Huang who helped us to prepare the WBM. We are immensely grateful to the anonymous reviewers and editors for their constructive comments and suggestions to improve this paper.