# Stability Characteristics of Horizontal Wells in the Exploitation of Hydrate-Bearing Clayey-Silt Sediments

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}replacement [8,9]. In 2013, Japan completed the world’s first offshore NGH development in the Nankai Trough [10,11]. In 2017 [12] and 2020 [13], China completed two rounds of NGH production trials from the clayey-silt sediment in the northern South China Sea.

_{h}), the deviation angle, and the azimuth on the stability of the borehole are clarified. The results may have some significance for drilling design in the clayey-silt HBS in the northern South China Sea.

## 2. Mechanical Parameters of HBS-CS

_{h}range is between 20% and 60% [14], and hence, the predetermined S

_{h}is 15%, 30%, 45%, and 60% in the experiments. The effective confining pressure was set as 1 MPa, 2 MPa, and 4 MPa in the triaxial shear tests, respectively.

_{h}. For a detailed analysis of mechanical properties, refer to the literature [25,26].

## 3. Model Description

#### 3.1. Stress Distribution around the Wellbore

#### 3.1.1. Conversion of Axis Coordinates of Wellbore

_{2}, y

_{2}, z

_{2}) shall be converted into a wellbore axis coordinate system (x, y, z). The in situ stress coordinate system, corresponding to the Ox

_{2}axis, Oy

_{2}axis, and Oz

_{2}axis is consistent with the principal ground stresses σ

_{H}

_{,}σ

_{h}, and σ

_{ν}directions, respectively. In the wellbore axis coordinate system, axis Oz corresponds to the deviated wellbore axis and axes Ox and Oy are located in a plane perpendicular to the well axis, and ψ, and φ are the deviation angle and azimuth, respectively (Figure 2).

**M**

_{(φ,ψ)}, for which the expressions are listed as follows:

_{H}, σ

_{h}, and σ

_{ν}represent the in situ stresses in MPa; σ

_{xx}, σ

_{yy}, and σ

_{zz}are the principal stresses in MPa in directions, x, y, and z, respectively; and τ is the shear stress in MPa.

_{r}, σ

_{θ}, and σ

_{z}are the radial stresses of the reservoir, the tangential stress of the reservoir, and the vertical stress of the reservoir, respectively, in MPa.

#### 3.1.2. The Elastic Solution of the Stress around the Wellbore

_{H}, σ

_{h}, and σ

_{ν}on the surrounding strata of the wellbore is analyzed. It is assumed that the surrounding strata of the wellbore located in the HBS-CS are homogeneous, isotropic, linear–elastic, without creep, and independent from viscosity behavior. The stress of the original strata is in an isotropic state. The analytical solution is solved according to the principle of elasticity. The stress on the surrounding strata meets the plane-stress mechanics’ equilibrium and consistent equation [29], in which the plane-stress equilibrium equation can be expressed as:

_{i}, and principal stress, σ

_{xx}, σ

_{yy}, τ

_{xy}, τ

_{xz}, and τ

_{yz}. Equation (5) is substituted into Equations (6) and (7) to obtain the surrounding strata stresses of the wellbore (Table 2 and Table 3). In the vertical well, each component in Table 3 is 0.

_{z}and υ are the strain in direction z, and the Poisson’s ratio, respectively, and are dimensionless; E is the elastic modulus in MPa.

_{z}= 0 into Equation (8), the equation is transformed into:

_{H}, σ

_{h}, and σ

_{ν}are obtained by substituting the stress component of the wellbore axis coordinate system. These expressions are as follows:

_{r}is the principal stress, the deviated shaft wall is still a principal stress surface. To judge the location of a rock failure, the other two principal stress planes must be solved first.

_{r}, shear stress, τ, and each component is as follows:

_{θ}and σ

_{z}are the expressions as in Equation (11); p

_{p}is the pore pressure in MPa; α is the effective stress coefficient and is dimensionless.

#### 3.2. Failure Criteria

#### 3.2.1. The M-C Failure Criterion

^{2}is the influence coefficient of confining pressure on axial bearing capacity, $K=\mathrm{cot}\left(\frac{\pi}{4}-\frac{\varphi}{2}\right)$.

#### 3.2.2. The D-P Failure Criterion

_{1}(σ

_{ij}), and J

_{2}(S

_{ij}) are the plastic potential function, the first invariant of the stress tensor, and the second invariant of the stress partial tensor, respectively. Q

_{f}and K

_{f}are a function of cohesion C, and internal friction angle ϕ, respectively, as follows: ${Q}_{f}=\frac{\sqrt{3}\mathrm{sin}\varphi}{3\sqrt{3+{\mathrm{sin}}^{2}\varphi}}$, ${K}_{f}=-\frac{\sqrt{3}C\mathrm{cos}\varphi}{\sqrt{3+{\mathrm{sin}}^{2}\varphi}}$.

#### 3.3. Collapse Pressure and Fracture Pressure

_{i}that makes the equation hold was obtained, which is the collapse pressure of the wellbore under the M-C failure criterion.

_{k}can be negative values in Equation (16), the fracture pressure calculation expression is as follows:

_{t}is the uniaxial tensile strength of the HBS-CS in MPa.

## 4. Wellbore Stability Analyses

#### 4.1. Effect of S_{h} on Collapse Pressure of Wellbore

_{h}and the collapse pressure gradient by the two criteria is shown in Figure 7. The collapse pressure gradient increased with decreasing S

_{h}. When the saturation decreases from 60% to 15%, the collapse pressure gradient increases by 7–10%. Li et al. (2020) and Sun et al. (2018) obtained the same discovery from the analysis of stratum mechanical properties [17,20]. When the S

_{h}decreases, the strength of HBS decreases, the plastic zone increases, and the wellbore stability becomes worse. Therefore, considering the influence of the hydrate decomposition on wellbore stability, the equivalent density of drilling fluid should be appropriately increased to meet the needs of the wellbore stability after hydrate decomposition.

_{h}under low saturation (<45%) by the two criteria. The reason is that with decreasing S

_{h}, the formation pore–space increases, and the cementation ability of hydrate to the formation weakens, which results in a continuous increase in the collapse pressure gradient and the deterioration of the stability of the wellbore. At high saturation (>45%), the M-C failure criterion curve trend is the same as is seen at low saturation, while the D-P failure criterion curve is flat. At the same position, the calculated value of the D-P failure criterion is greater than that of the M-C failure criterion at low saturation, and the opposite is true at high saturation. It showed that the formation stability in high saturation is higher when the influence of the intermediate principal stress is fully considered. However, higher drilling fluid densities are required to maintain formation stability in low saturations.

#### 4.2. Influence of the Deviation Angle on the Collapse Pressure Gradient of the Wellbore

#### 4.3. Effect of the Azimuth on the Collapse Pressure Gradient of the Wellbore

_{h}as an example, the relationship between the azimuth and the collapse pressure gradient by the two criteria was obtained (see Figure 9). It was found that the collapse pressure gradient decreases and then increases with an increasing azimuth on the high inclination well sections (curves 2–6). The collapse pressure gradient reaches a minimum value in the direction of the minimum principal stress (azimuth of 90°). The same was reported in the literature [40]. With an increase in the deviation angle, the fluctuation of the curve is lower. That is, the difference in the collapse pressure gradient is not significant during drilling in any direction. When the deviation angle is 30° and 90°, the differences are 0.038 and 0.018 g/cm

^{3}, respectively. In the near-vertical sections (curve 1), the minimum collapse pressure gradient was obtained at an azimuth of 60°. In summary, the wellbore should be arranged along the azimuth between 60° and 120° for high wellbore stability.

#### 4.4. Fracture Pressure Gradient and the Safe Drilling Fluid Density Window

_{h}as an example, the relationship curve between the azimuth and fracture pressure gradient was simulated, as shown in Figure 10. When the deviation angle was higher than 45° (curves 4–7), the fracture pressure gradient increased and then decreased with increasing azimuth, and the maximum value is in the direction of the minimum principal stress. When the deviation angle is less than 45° (curves 1–3), the fracture pressure gradient generally increases and then decreases with increasing azimuth, but the peak value exists between 120° and 150°. The azimuth corresponding to the peak decreases gradually with increasing deviation angle, closer to the direction of the minimum principal stress. During the drilling of horizontal wellbores, the drilling fluid density needs to meet the stability of the wellbore in all sections. Therefore, a drilling fluid density is selected in the yellow zone formed below the vertical and horizontal wellbore curves (curves 1 and 7), which can be safely drilled in any direction.

^{3}. The density window of the upper and lower belt regions is narrow, while the density window of the middle region is large. The maximum safe density window is the “crescent” region in the direction of the minimum principal stress. Drilling operations near this zone are most conducive to wellbore stability.

## 5. Conclusions and Suggestions

- The window distribution cloud chart of the collapse pressure gradient and the safe drilling fluid density of HBS-CS has a centrosymmetric distribution with a deviation angle and azimuth.
- Hydrate decomposition will lead to a higher collapse pressure and poorer stability of the formation. Therefore, the drilling fluid density should be appropriately increased by 7~10% during drilling to ensure the stability of formation after hydrate decomposition.
- The collapse pressure gradient increases by 7.2–9.2% from the vertical wellbore to the horizontal wellbore. From the perspective of preventing wellbore collapse, the safe density that satisfies the horizontal section can also ensure the wellbore stability of other sections. To prevent the wellbore fracture, a safe density that satisfies both the horizontal and vertical sections is necessary to ensure wellbore stability in all sections.
- Considering the combined effects of collapse, fracture pressure gradient, and safety density window, it is suggested that the borehole be arranged along the azimuth of 60–120°, which could greatly reduce the risk of the drilling operation.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**A comparison between the three-dimensional failure surface derived from the M-C criterion and the D-P criterion.

**Figure 6.**Cloud diagrams for the collapse pressure gradient distribution under the D-P failure criterion.

**Figure 7.**Hydrate saturation and collapse pressure gradient relationship curves by the two criteria.

**Figure 8.**The deviation angle and the collapse pressure gradient relationship curves by the two criteria.

S_{h} | σ_{3}/MPa | σ_{1}/MPa | Cohesion C/MPa | Friction Angle ϕ/° |
---|---|---|---|---|

15% | 1 | 1.62 | 0.0953 | 10.340 |

2 | 3.17 | |||

4 | 5.95 | |||

30% | 1 | 2.48 | 0.426 | 11.612 |

2 | 4.16 | |||

4 | 7.03 | |||

45% | 1 | 3.54 | 0.811 | 12.275 |

2 | 5.12 | |||

4 | 8.17 | |||

60% | 1 | 4.29 | 1.071 | 13.568 |

2 | 6.00 | |||

4 | 9.15 |

**Table 2.**Stress distribution expression for the surrounding strata caused by p

_{i,}σ

_{xx}, σ

_{yy}, τ

_{xy}, τ

_{xz}, and τ

_{yz}.

σ_{r} | σ_{θ} | τ_{θr} |
---|---|---|

$\frac{{R}^{2}}{{r}^{2}}{p}_{i}$ | $-\frac{{R}^{2}}{{r}^{2}}{p}_{i}$ | / |

$\left(1-\frac{{R}^{2}}{{r}^{2}}\right)\frac{{\sigma}_{xx}}{2}+\left(1-\frac{4{R}^{2}}{{r}^{2}}+\frac{3{R}^{4}}{{r}^{4}}\right)\frac{{\sigma}_{xx}}{2}\mathrm{cos}2\theta $ | $\left(1+\frac{{R}^{2}}{{r}^{2}}\right)\frac{{\sigma}_{xx}}{2}-\left(1+\frac{3{R}^{4}}{{r}^{4}}\right)\frac{{\sigma}_{xx}}{2}\mathrm{cos}2\theta $ | $-\left(1+\frac{2{R}^{2}}{{r}^{2}}-\frac{3{R}^{4}}{{r}^{4}}\right)\frac{{\sigma}_{xx}}{2}\mathrm{sin}2\theta $ |

$\left(1-\frac{{R}^{2}}{{r}^{2}}\right)\frac{{\sigma}_{yy}}{2}-\left(1-\frac{4{R}^{2}}{{r}^{2}}+\frac{3{R}^{4}}{{r}^{4}}\right)\frac{{\sigma}_{yy}}{2}\mathrm{cos}2\theta $ | $\left(1+\frac{{R}^{2}}{{r}^{2}}\right)\frac{{\sigma}_{yy}}{2}+\left(1+\frac{3{R}^{4}}{{r}^{4}}\right)\frac{{\sigma}_{yy}}{2}\mathrm{cos}2\theta $ | $\left(1+\frac{2{R}^{2}}{{r}^{2}}-\frac{3{R}^{4}}{{r}^{4}}\right)\frac{{\sigma}_{yy}}{2}\mathrm{sin}2\theta $ |

$\left(1-\frac{4{R}^{2}}{{r}^{2}}+\frac{3{R}^{4}}{{r}^{4}}\right){\tau}_{xy}\mathrm{sin}2\theta $ | $-\left(1+\frac{3{R}^{4}}{{r}^{4}}\right){\tau}_{xy}\mathrm{sin}2\theta $ | $\left(1+\frac{2{R}^{2}}{{r}^{2}}-\frac{3{R}^{4}}{{r}^{4}}\right){\tau}_{xy}\mathrm{cos}2\theta $ |

τ_{rz} | τ_{θz} |
---|---|

${\tau}_{xz}\left(1-\frac{{R}^{2}}{{r}^{2}}\right)\mathrm{cos}\theta $ | $-{\tau}_{xz}\left(1+\frac{{R}^{2}}{{r}^{2}}\right)\mathrm{sin}\theta $ |

${\tau}_{yz}\left(1-\frac{{R}^{2}}{{r}^{2}}\right)\mathrm{sin}\theta $ | ${\tau}_{yz}\left(1+\frac{{R}^{2}}{{r}^{2}}\right)\mathrm{cos}\theta $ |

Parameter | Value |
---|---|

Maximum principal stress, g/cm^{3} | 1.203 |

Minimum principal stress, g/cm^{3} | 1.159 |

Overburden rock stress, g/cm^{3} | 1.282 |

Poisson’s ratio | 0.45 |

Effective stress factor | 0.6 |

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**MDPI and ACS Style**

Sun, X.; Hu, Q.; Li, Y.; Chen, M.; Zhang, Y. Stability Characteristics of Horizontal Wells in the Exploitation of Hydrate-Bearing Clayey-Silt Sediments. *J. Mar. Sci. Eng.* **2022**, *10*, 1935.
https://doi.org/10.3390/jmse10121935

**AMA Style**

Sun X, Hu Q, Li Y, Chen M, Zhang Y. Stability Characteristics of Horizontal Wells in the Exploitation of Hydrate-Bearing Clayey-Silt Sediments. *Journal of Marine Science and Engineering*. 2022; 10(12):1935.
https://doi.org/10.3390/jmse10121935

**Chicago/Turabian Style**

Sun, Xiaofeng, Qiaobo Hu, Yanlong Li, Mingtao Chen, and Yajuan Zhang. 2022. "Stability Characteristics of Horizontal Wells in the Exploitation of Hydrate-Bearing Clayey-Silt Sediments" *Journal of Marine Science and Engineering* 10, no. 12: 1935.
https://doi.org/10.3390/jmse10121935