## Abstract

Fractures continuously extend and expand along bedding shale formations under the action of drilling fluid and eventually form a complex fracture network, which greatly reduces the strength of the rock. To determine the effect of the drilling fluid action time on the physical and mechanical properties of shale, nuclear magnetic resonance tests are carried out on shale soaked in oil-based drilling fluid for different soaking times. The fluid absorption rate of shale takes the form of a power function. The equations relating the shale mass, porosity, and permeability to soaking time are established. Then, in a sonic time-difference test, the change in the dynamic elastic parameters with the immersion time are observed. According to a triaxial strength test, the failure form and the deterioration degrees of the layered shale in different loading directions with immersion time are analyzed. Numerical simulation of the deterioration degree of shale under different water content conditions is carried out. When the water content increases, the collapse density of the surrounding rock of the well wall increases significantly. Finally, considering the anisotropy of bedding shale, the inclination angle, azimuth angle, and drilling fluid immersion time are substituted into the rock mechanics parameter deterioration model, the three pressure profiles of the formation are corrected, and the safe drilling fluid density window of the target interval is given.

## 1. Introduction

The instability of wellbores in bedding shale is a technical problem encountered in drilling engineering worldwide and is one of the core issues in the design of safe and efficient drilling practices [1, 2]. This is because there are a large number of microfractures in layered shale. The entry of drilling fluid causes the fractures to continue to extend and expand along the formation, eventually forming a complex network of fractures, which greatly reduces the strength of the rock [3, 4]. The water content near the well wall and the integrity of the rock cementation change the strength of the formation [5, 6]; they also change the stress field around the wellbore, causing stress concentrations; and if the wellbore fails to establish a new balance, instability of the well wall arises.

At present, abundant studies have been carried out on the influence of drilling fluids on shale strength. Such research focuses on the measurement of the adsorption and diffusion constants of shale, the numerical calculation of the wellbore stress, the measurement of the mechanical parameters of hydrated shale, and the simulation of the shale hydration reaction. A variety of wellbore collapse cycle calculation methods has been proposed [7–10]. Ong and Roegiers [11] analyzed the fracture pattern of deviated wells in anisotropic formations, which depends largely on anisotropy. Atkinson and Bradford [12] established a semianalytical model for predicting the near-well damage of strata. Jin et al. [13] and Hou et al. [14] analyzed the influence of anisotropy on the stress distribution around wells and studied the influence of the bedding dip angle, drilling azimuth, drilling time, and drilling fluid type on the wellbore collapse pressure in shale reservoirs. Ma and Chen [15] studied the influence of shale bedding on the wellbore stability of horizontal wells, established a layered wellbore stability model of horizontal wells, and analyzed the influence of water content on wellbore stability on this basis. Zhang et al. [16] carried out a series of compression tests on layered shale under four different confining pressures and obtained the comprehensive influence of anisotropy and hydration on strength. He found that anisotropy was the main controlling factor of shale geomechanical behavior. However, whether the pore structure, acoustic time difference, and strength of shale under fluid action change with time and the influence of strength deterioration on the wellbore collapse pressure are unclear. In this paper, laboratory experiments are carried out on bedding shale to analyze the deterioration mechanism of shale under the action of drilling fluid used in the field and to reveal the time-sensitive characteristics of the deterioration of bedding shale under the action of drilling fluid, which is of great significance for predicting the collapse pressure of shale reservoirs in the drilling process and establishing the collapse cycle of different well sections and the safety density window of drilling fluid.

## 2. Sample and Experiments

### 2.1. Sample

To study the deterioration trends of shale under the action of different fluids, a group of shale cores with typical bedding characteristics was selected to carry out laboratory experiments. The core photographs are shown in Figure 1. The observation of the core shows that shale bedding and fractures are obviously developed and that weak surfaces are clearly visible. A slight drop occurs when the core is touched with a hand. It is preliminarily judged that the cohesion between the bedding layers is low and that the angle between the bedding direction and the horizontal direction is less than 3°. Due to the particularity of shale, conventional processing methods cannot be used to cut and core it. Therefore, the core is processed by wire cutting, and the experimental standard specimens are prepared as shown in Figure 2.

### 2.2. Experimental Scheme

To characterize the anisotropy of bedding shale properties, cores are taken parallel (horizontal) and perpendicular (vertical) to the bedding, as shown in Figure 3.

First, the mineral composition analysis of shale is carried out to obtain the content of the brittle minerals and clay minerals to determine the type of hydration expansion in the shale samples. Then, the nuclear magnetic resonance (NMR) relaxation time of shale before and after drilling fluid immersion was tested to reveal the fluid absorption characteristics of shale and the variations in porosity and permeability. The acoustic time difference of the shale before and after immersion was tested to obtain the variation in dynamic rock mechanical parameters with immersion time. Finally, the time-sensitive characteristics of strength degradation were revealed according to the changes in the triaxial compressive strength of shale before and after immersion. Combined with fluid absorption characteristics, acoustic time difference, and logging data, the rock mechanical parameter profile of the whole well section under the action of drilling fluid was established, which provides basic data for calculating the collapse pressure of the formation, as shown in Figure 4. The drilling fluid used in the experiment was an oil-based drilling fluid obtained from the field.

## 3. Analysis of Experimental Results

### 3.1. Mineral Component Test

The composition and content of brittle minerals and clay minerals in shale samples were tested by X-ray diffraction analysis (X-RD). After statistical analysis of the data, the whole-rock mineral composition analysis diagram is obtained, as shown in Figure 5(a).

The main minerals of the sample are clay, quartz, and dolomite, with some calcite and plagioclase. Quartz and plagioclase are the main brittle minerals in shale, and their combined content is generally more than 50%, which is an important factor affecting the development of shale matrix pores and microcracks. When clay minerals encounter water, hydration expansion occurs. The high content of clay minerals indicates the possibility of hydration collapse. However, the hydration expansion capacity of each clay mineral is different, and the specific hydration collapse capacity needs to be judged according to the test results of each clay mineral content. The results of the clay mineral composition analysis performed in this work are shown in Figure 5(b).

The clay minerals of the samples are mainly illite and chlorite, with a small amount of illite/montmorillonite interlayers. Moreover, the montmorillonite content in the illite/montmorillonite interlayer is low, indicating that it has certain hydration characteristics, but the water absorption and expansion are not strong. Illite rapidly combines with water to generate hydration, forming high-intensity hydrogen bonds through free hydroxyl and shale self-associated hydroxyl groups. Water molecules form hydration films on the illite surfaces, resulting in surface hydration and the rapid expansion and extension of shale cracks, causing wellbore instability.

### 3.2. Testing of Shale Porosity and Permeability Variation under Drilling Fluid

The porosity and permeability of shale are much lower than those of conventional reservoirs. Traditional test methods cannot provide accurate measurements; the results of different experiments differ by 2~3 orders of magnitude. The relaxation time spectrum of NMR represents the pore size distribution of a formation, and the permeability of the formation rock has a certain relationship with the pore size (pore throat size) [17]. Therefore, this paper calculates the porosity and permeability of shale from the relaxation time spectrum of NMR.

The integrated area of the NMR relaxation time spectrum is directly proportional to the amount of fluid in the rock. As long as the relaxation time spectrum is appropriately scaled, the porosity and permeability of the rock can be obtained [18]. Figure 6 is a comparison chart of the relaxation time of shale at the initial time and after 10 d of immersion. The relaxation time at the initial time is less than 10 ms, indicating that the shale contains pores at the nanometer level. The relaxation time integral area of the shale after soaking for 10 d increases, indicating that the pores are open and that the cracks are propagating. With increasing immersion time, the internal pores of the shale obviously increase, but the cracks are all nanopores or microcracks, and the relaxation time is approximately 10 ms. This shows that the oil-based drilling fluid used in the field has a strong plugging ability.

Statistics of the experimental results show that the shale quality, porosity, and permeability in different directions change with time, as shown in Figure 7.

The definitions of symbols in Equation (1) as follows: $mc$ and $ms$ are vertical mass and horizontal mass, respectively, g; $PORc$ and $PORs$ are vertical porosity and horizontal porosity, respectively, %; and $Kc$ and $Ks$ are permeability in the vertical and horizontal directions, respectively, mD.

The quality, porosity, and permeability change curves in Figure 7 indicate the following. (1) The liquid absorption of the horizontal core gradually reaches saturation after 4 d, while the vertical core tends to be saturated after 2 d. This is because the fracture distribution of cores perpendicular to the bedding direction is greater than that of cores parallel to the bedding direction. This leads to a greater contact area between the cracks and drilling fluid in the vertical core [19]. (2) The porosity and permeability of shale rise rapidly in the early stage of immersion. This is due to the shedding of minerals by the drilling fluid, the increase in micropores in the rock, and the appearance of new pores aggravating rock hydration. The cracks are in full contact with the fluid, and hydration further increases the length and opening of the cracks. (3) Compared to other types of drilling fluids, oil-based drilling fluids more readily reduce the contact area between the fluid and the rock, enhance the cementing ability of minerals and clay, and inhibit the hydration of the rock surface.

### 3.3. Tests of the Acoustic Time Difference of Shale after Drilling Fluid Immersion

The acoustic velocity of the shale is tested with a sonic instrument, and the dynamic elasticity parameters of the rock can be obtained from the following formula according to the measurement of the wave speed of the vertical and horizontal waves of sonic waves propagating in the rock and the density of the rock [20].

#### 3.3.1. Dynamic Poisson’s Ratio

The definitions of symbols in Equation (2) are as follows: $\mu d$ is Poisson’s ratio, dimensionless; $\Delta ts$ and $\Delta tp$ are time differences of the shear and longitudinal waves in the rock, respectively, *μ*s/m.

#### 3.3.2. Dynamic Elastic Modulus

The definitions of symbols in Equation (3) are as follows: $Ed$ is the elastic modulus of the rock, MPa; $\rho $ is the density of the rock, g/cm^{3}.

Combined with the static mechanical parameters and logging data measured by the indoor triaxial stress experiment, the rock mechanical parameter profile of the entire well section was established.

After the shale cores were immersed in oil-based drilling fluid for different periods of time, the longitudinal and transverse time differences were tested with a sonic tester. The longitudinal and transverse wave time differences gradually increase with increasing immersion time. This is because when shale formations contact drilling fluid hydration, on the one hand, the formation water content increases, the rock mechanical strength and density decrease, and the clay mineral structure parameters and elastic modulus change [21, 22]; on the other hand, the internal stress of the shale formation increases. When the pressure of the overburden is constant, the acoustic velocity can be described with a power function of the effective stress. The reduction in the effective stress causes the propagation time of the formation acoustic wave to extend, which is reflected in the macrologging response value, increasing the acoustic time-difference logging value. The larger the amplitude is, the higher the degree of hydration [22]. The time differences of the shale longitudinal and transverse wave changes with time are shown in Figure 8.

Figure 8 shows that the increase in the acoustic time difference of the shale cored in the parallel bedding direction is significantly smaller than that of the shale cored in the vertical direction. For both directions, when the core has been immersed for more than 2 d, the acoustic waves are basically stable. The dynamic mechanical parameters of the abovementioned cores are calculated, and the calculation results are shown in Table 1.

The calculation results of the dynamic mechanical parameters of shale after oil-based drilling fluid immersion in Table 1 show that with increasing drilling fluid immersion time, the dynamic elastic modulus and shear modulus gradually decrease, and the bulk modulus increases. This shows that the soaked shale is more prone to elastic deformation when subjected to compressive stress and that shear failure occurs under smaller stresses [23].

### 3.4. Triaxial Strength Test of Shale after Immersion in Drilling Fluid

#### 3.4.1. Triaxial Compressive Strength of Conventional Shale in Different Coring Directions

A TAW2000 microcomputer-controlled triaxial stress-testing machine was used for triaxial stress testing of the shale. The shale was processed into a standard core column of $\phi 25\xd750\u2009mm$ both parallel and perpendicular to the bedding direction. The confining pressures tested were 0 MPa, 12 MPa, and 24 MPa. Then, a triaxial compressive strength test on each as-cored sample was carried out.

Figure 9 shows the core fractures after loading the cores parallel and perpendicular to the bedding direction. The fracture morphologies of the parallel and horizontal shale cores are different. When the rock is loaded parallel to the direction of the shale, the core sample splits many times along the seams of the shale and forms multiple groups of fragments along the direction of the shale surface. However, loading in the direction perpendicular to bedding first produces shear cracks, and then, the shear cracks are connected with the microcracks along the bedding to form large volume fragmentation. Clearly, the rock loaded parallel to the bedding direction undergoes tensile failure along the structural planes when the vertical loading in the bedding direction overcomes the shear strength of the shale body [24, 25]. The conventional triaxial compressive strength test results are shown in Table 2.

The experimental results show that the compressive strength of vertical loading is much greater than that of horizontal loading. This reflects the anisotropy of the layered shale.

#### 3.4.2. Triaxial Compressive Strength of Shale after Soaking for Different Times

Soak shale with vertical and horizontal coring in oil-based drilling fluid. Triaxial tests were carried out after the core was soaked for 2 d, 4 d, and 10 d. Then, the cohesion and internal friction angle were calculated, and the experimental photographs are shown in Figure 10.

It can be seen from Figure 10 that the failure mechanism of shale does not change after drilling fluid immersion. The loading parallel to the bedding direction still produces multiple groups of fragments along the bedding orientation, indicating that tensile failure occurs. The vertical loading produces shear failure. The triaxial compressive strength is analyzed, and the stress–strain curve and Mohr circle are drawn for different immersion times, as shown in Figures 11 and 12.

When the loading is along the bedding direction, the triaxial strength of rock decreases by 18.8% and the cohesion decreases by 51.5% after 10 d of oil-based drilling fluid immersion. When the loading is perpendicular to the bedding direction, the triaxial strength decreases by 17%, and the cohesion does not change in 10 d. The overall strength remains high, indicating that the strength of the shale body is hardly affected by drilling fluid immersion. The deterioration degree of shale in the horizontal direction tends to be stable with soaking time. The relationship between the triaxial compressive strength under horizontal loading and the soaking time is shown in Figure 13.

The definitions of symbols in Equation (4) are as follows: $\sigma c$ is the triaxial compressive strength, MPa; $t$ is time, d.

## 4. Influence of the Deterioration of Layered Shale on Wellbore Stability

### 4.1. Theoretical Analysis of Layered Shale Deterioration

#### 4.1.1. Water Absorption Rate of Shale

The definitions of symbols in Equations (5) and (6) are as follows: $\u2207$ is the gradient operator; $Cf$ is the adsorption constant of the material, representing the nature of the drilling fluid and shale-related material, which can be measured from the water adsorption test.

Using the finite difference method to solve the above equations, the water content at different times and positions in the strata around the borehole can be obtained. Based on the above experimental results, the shale water absorption rate equation is corrected, and the water content of the shale formation around the borehole at different times and positions can be obtained by using numerical simulation methods.

#### 4.1.2. Anisotropy of Shale

The mechanical strength of the bedding interfaces of shale is much lower than that of the shale matrix, and the cohesion along these weak planes is usually much lower than the cohesion in the shale matrix. Therefore, the possibility of drilling failure along weak planes is greater than that in intact shale. The anisotropic characteristics of shale rock are mainly reflected in the two aspects of deformation and strength. To describe the mechanical characteristics of the weak surfaces of shale reservoirs, the single weak surface criterion proposed by Jaeger and Hoskins [27] was selected to evaluate the stability of the shale borehole wall. In other words, the shear failure modes of bedding rock are mainly divided into two types: the shear failure of the matrix or the bedding plane.

The definitions of symbols in Equation (9) are as follows: $\sigma \u2032$ is the normal stress on the weak bedding plane, MPa; $\tau \u2032$ is the shear stress on the weak bedding plane, MPa; $c0\u2032$ is the cohesion of the weak bedding plane, MPa; and $\phi \u2032$ is the internal friction angle of the layered weak surface, °.

The definitions of symbols in Equation (10) are as follows: $\sigma $ is the normal stress on the failure surface, MPa; $\tau $ is the shear stress on the failure surface, MPa; $c0$ is the cohesion of the rock matrix, MPa; and $\phi $ is the internal friction angle of the rock matrix, °.

### 4.2. Collapse Pressure Simulation of Layered Shale after Degradation

According to the test results of the rock mechanical parameters after soaking in oil-based drilling fluid, due to the existence of shale and microfractures, the shale strength is degraded after soaking. Since the conductivity of the structural surface is much higher than that of the original rock, the penetration of drilling fluid along the structural surface directly weakens the strength of the structural surface [28]. According to the previous experimental results, the change in cohesion and internal friction angle can be used to indicate the weakening of shale strength. Therefore, a force-chemical coupling finite element numerical simulation model was obtained, and the stress contour maps of some simulation results are shown in Figure 14.

In the drilling process of shale formations, the rock strength decreases, and the bearing capacity decreases. An increase in the stress leads to an increase in the rock collapse trend around the well. This is quantitatively reflected in an increase in the collapse pressure, which leads to wellbore instability [29]. Therefore, it is more intuitive to analyze the influence of fluid content on shale degradation and wellbore stability by using finite element numerical simulation to calculate the equivalent density of the collapse pressure of shale at different water contents. Wellbore collapse pressure distributions under different well inclinations, azimuths, and fluid contents are shown in Figure 15.

The equivalent density chart of the collapse pressure around wells with different fluid contents in Figure 15 shows that the change range of the collapse density is 1.02~1.53 g/cm^{3} without shale deterioration. When the water content of the shale reservoir increases, the shale strength value changes, and the equivalent density of the wellbore collapse pressure increases rapidly. When the water content is 10%, the collapse density increases from 0.15 to 0.22 g/cm^{3}, and when the water content is 15%, the collapse density increases from 0.31 to 0.45 g/cm^{3}.

### 4.3. Triaxial Pressure Profile Description of Real Shale Formations under Fluid Action

In actual engineering drilling, the formation at each depth point has been soaked by drilling fluid since it was drilled. The on-site drilling fluid immersion time corresponding to a certain well depth is the time at the end of the whole drilling process minus the time when drilling began at the well depth. Thus, the drilling log of the work area was extracted and summarized, and the action time of the field drilling fluid on the shale formation in the studied block was analyzed. Taking horizontal well G as an example, the relationship between the drilling fluid action time and well depth was obtained by analyzing its construction period, as shown in Figure 16.

The definitions of symbols in Equation (11) are as follows: $t$ is the time, h; $H$ is the well depth, m.

In the drilling process of shale formations, the drilling fluid action time decreases with depth. The immersion time of the field drilling fluid decreases almost linearly with increasing well depth. Therefore, the immersion time of the field drilling fluid for different depths can be continuously calculated using Formula (11). The longer the formation is immersed in the field drilling fluid, the more obvious the hydration effect, the greater the impact on the internal structure of the rock, and the more serious the adverse impact on wellbore stability. Therefore, the immersion time of the drilling fluid decreases linearly with the formation around the well in the vertical direction. This factor should be considered in actual engineering drilling, the performance and density of the drilling fluid should be adjusted, and a reasonable drilling speed should be planned.

The definitions of symbols in Equation (12) are as follows: $Pb$ is the collapse pressure, MPa; $\sigma H$ is the maximum horizontal stress, MPa; $\sigma h$ is the minimum horizontal formation stress, MPa; $Pp$ is the formation pore pressure, MPa; $C0$ is the cohesion, MPa; $\phi 0$ is the angle of internal friction, °; and $\alpha $ is the effective stress coefficient.

The definitions of symbols in Equations (13) and (14) are as follows: $Cw$ is the shale bedding cohesion after drilling fluid immersion, MPa; $\phi w$ is the internal friction angle of shale after drilling fluid immersion, °.

By combining Formulas (9)–(14), the shale collapse pressure under oil-based drilling fluid can be obtained. Then, the inclination angle, azimuth angle, and drilling fluid soaking time are substituted into the rock mechanics parameter deterioration model to correct the three pressure profiles, and the collapse pressure deterioration correction results under the actual bottom hole conditions of well G are obtained, as shown in Figure 17. The maximum collapse pressure equivalent density of horizontal well G increases from 1.35 g/cm^{3} to 1.66 g/cm^{3}, and the minimum fracture pressure is 1.85 g/cm^{3}. Therefore, if the construction period after drilling is less than 25 d and the bottom hole rock meets the requirements, the recommended drilling fluid density of the target layer is 1.66~1.71 g/cm^{3}, which is consistent with the actual drilling fluid density of this block to maintain wellbore stability.

## 5. Conclusion

In this paper, through porosity, permeability, acoustic time difference, and triaxial compressive strength experiments on layered shale with different immersion treatments of oil-based drilling fluid that is used in the field, the time-sensitive characteristics of shale deterioration are revealed, and the influence of shale strength deterioration on wellbore stability is analyzed. The following conclusions are reached:

- (1)
The liquid absorption rate of shale takes the form of a power function, and equations for mass, porosity, and permeability with soaking time are proposed

- (2)
The longitudinal and transverse wave time differences of shale gradually increase with increasing immersion time, and the increase in the acoustic time difference of shale coring in the parallel bedding direction is significantly lower than that of shale coring in the vertical direction

- (3)
After 10 d of oil-based drilling fluid soaking, the triaxial strength of the rock drops by 18.8% and the cohesion drops by 51.5%; with the loading in the direction perpendicular to bedding, the triaxial strength drops by 17% and the cohesion remains unchanged after 4 d, and the overall strength is higher, indicating that there is still a certain degree of anisotropy. The degree of rock deterioration tends to stabilize with increasing immersion time

- (4)
When the water content of shale reservoirs increases, the shale strength value changes, and the equivalent density of the wellbore collapse pressure increases rapidly. The collapse densities at 10% and 15% water contents increase in the ranges of 0.15~0.22 g/cm

^{3}and 0.31~0.45 g/cm^{3}, respectively - (5)
The collapse pressure is corrected by using the time-sensitive characteristics of shale deterioration combined with field construction logs and logging data. When the construction period of the drilling shale section is 25 d, the equivalent density of the collapse pressure increases by 0.31 g/cm

^{3}; thus, a reasonable equivalent density window of drilling fluid for actual drilling construction is obtained

## Data Availability

Data used to support the results of this study can be found in this manuscript text.

## Conflicts of Interest

The authors declare that they have no conflicts of interest.

## Authors’ Contributions

Wang Changhao analyzed the data and wrote the paper; Zhang Ling and Liang Kai carried out the experiments; Zhao Huizhi, Wang Xiaoming, and Wang Chunhua provided field data and experimental cores; and Li Shibin supervised the research work and provided helpful suggestions.

## Acknowledgments

This study was jointly supported by the Heilongjiang Postdoctoral Fund (No. LBH-Z20120), Northeast Petroleum University Youth Science Fund (No. 2019QNL-24), and National Natural Science Foundation of China (No. 51874098).