# Risk Assessment Method for Analyzing Borehole Instability Considering Formation Heterogeneity

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## Abstract

**:**

## 1. Introduction

## 2. Prediction Model of Borehole Instability

#### 2.1. Stress Distribution around Borehole

#### 2.2. Strength Criterion

#### 2.3. Model Solution

_{3}is the minimum principal stress around the borehole, in MPa; and σ

_{t}is the tensile strength of the rock around the borehole, in MPa.

## 3. Quantitative Characterization of Stratigraphic Heterogeneity

^{4}, the probability density and cumulative probability distribution curves of cohesion and internal friction angle are obtained, as shown in Figure 3. This indicates that smooth probability density and cumulative probability distribution curves can be obtained when the sampling frequency reaches 10

^{4}, and the distribution characteristics of the input parameters are stable. Therefore, the sampling times in this analysis were all set to 10

^{4}.

## 4. Risk Analysis of Borehole Instability

#### 4.1. Influence of Single Parameter on the Risk of Borehole Instability

#### 4.2. Influence of Multiple Parameters on the Risk of Borehole Instability

^{3}, and the probability that the borehole wall will not collapse or break is 95.895%. The stability and reliability of the borehole wall are the highest at this drilling fluid density, but the safety density window is extremely narrow. Considering construction measures such as the start and stop of drilling fluid pumps and the lifting and dropping of drilling tools, it is difficult to maintain the equivalent drilling fluid density at 1.61 g/cm

^{3}. In practice, the equivalent drilling fluid density has a certain window, and the larger the window of the equivalent drilling fluid density that the borehole wall can withstand, the better the stability of the borehole wall. Similarly, by controlling the equivalent drilling fluid density window, the reliability of borehole stability can be controlled within a certain range, and the higher the reliability of borehole stability, the better. When the borehole stability reliability is 90% (that is, the cumulative probability of no borehole collapse or fracture and instability is 90%), the equivalent drilling fluid density window is 1.55~1.67 g/cm

^{3}, indicating that the drilling fluid density variation range is only 0.16 g/cm

^{3}. When the borehole stability reliability is reduced to 80%, the equivalent drilling fluid density window changes to 1.46~1.79 g/cm

^{3}, and the safe drilling fluid density range is 0.33 g/cm

^{3}. When the borehole stability reliability is 70%, the equivalent drilling fluid density window is 1.43~1.85 g/cm

^{3}, and the safe drilling fluid density range is 0.42 g/cm

^{3}. When the stability reliability of the borehole wall is further reduced to 60%, the safe drilling fluid density ranges from 1.36 g/cm

^{3}to 1.97 g/cm

^{3}, and the safe drilling fluid density range is 0.61 g/cm

^{3}. With an increase in drilling fluid density window, the risk of borehole instability gradually increases.

^{3}, and the reliability of borehole stability is 87.43%, which indicates that the horizontal well in this block has a higher risk of borehole instability and a narrower window of the safe drilling fluid density than the vertical well. When the borehole stability reliability is 80%, the equivalent drilling fluid density window is 1.73~1.82 g/cm

^{3}, and the safe drilling fluid density variation range is only 0.09 g/cm

^{3}, which is obviously difficult to achieve for the current borehole pressure control ability. When the borehole stability reliability is reduced to 70%, the equivalent drilling fluid density window is 1.67~1.94 g/cm

^{3}, and the safe drilling fluid density variation range is 0.27 g/cm

^{3}. When the wall stability reliability is further reduced to 60%, the equivalent drilling fluid density window is 1.61~2.12 g/cm

^{3}, and the safe drilling fluid density variation range is 0.51 g/cm

^{3}. At this time, the pressure control of the fluid column in the borehole is easier, but the risk of borehole instability is as high as 40%.

^{3}, the upper limit is 2.13 g/cm

^{3}, and the range of the safe drilling fluid density is 0.8 g/cm

^{3}. For the horizontal well, the lower limit of the safe drilling fluid density is 1.58 g/cm

^{3}, the upper limit is 2.24 g/cm

^{3}, and the range of the safe drilling fluid density is 0.66 g/cm

^{3}. It can be seen that compared to the results of the conventional borehole stability analysis, although the overall change trend is consistent after considering the influence of parameter uncertainty, the obtained safe drilling fluid density window is further narrowed. If the safe drilling fluid density window is designed according to the conventional borehole stability analysis method, the reliability of borehole stability will be reduced and the risk of instability will be significantly increased. Conventional borehole stability analysis methods cannot evaluate the impact of uncertainty of input parameters and construction parameters. However, the evaluation model of borehole instability risk established in this paper can quantitatively evaluate the impact of parameter uncertainty on borehole instability risk, which can provide more accurate and effective decision-making basis for drilling technicians and construction personnel.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**The failure envelops the characteristics of the modified Lade criterion in the principal stress space and π-plane. (

**a**) Yield surface in the principal stress space. (

**b**) Yield curve in the π-plane (Blue line).

**Figure 3.**Distribution characteristics of input parameters: (

**a**) cohesion and (

**b**) internal friction angle.

**Figure 5.**Sensitivity analysis of factors affecting borehole collapse for the horizontal well drilled in the direction of the maximum in situ stress.

**Figure 7.**Sensitivity analysis of factors affecting borehole breakout for the horizontal well drilled in the direction of the maximum in situ stress.

**Figure 10.**Influence of multi-parameter uncertainty on borehole instability risk of horizontal well.

Inputting Parameters | Cohesion/MPa | Internal Friction Angle/° | Horizontal Maximum In Situ Stress/MPa | Horizontal Minimum In Situ Stress/MPa | Vertical In Situ Stress/MPa | Pore Pressure/MPa | Poisson’s Ratio |
---|---|---|---|---|---|---|---|

Mean value | 6.38 | 30.42 | 30.54 | 23.32 | 35.5 | 17.15 | 0.25 |

Standard deviation | 2 | 2 | 2 | 2 | 2 | 2 | 2 |

Well Type | Vertical Well | Horizontal Well | ||||
---|---|---|---|---|---|---|

Influencing Factors | Mean Value (g/cm^{3}) | Standard Deviation (g/cm ^{3}) | Coefficient of Variation (%) | Mean Value (g/cm^{3}) | Standard Deviation (g/cm ^{3}) | Coefficient of Variation (%) |

Cohesion | 1.331 | 0.115 | 8.613 | 1.577 | 0.114 | 7.209 |

Internal friction angle | 1.333 | 0.026 | 1.986 | 1.577 | 0.041 | 2.599 |

Horizontal maximum in situ stress | 1.37 | 0.192 | 7.34 | 1.5 | 0.292 | 0.000 |

Horizontal minimum in situ stress | 1.333 | 0.033 | 2.45 | 1.576 | 0.033 | 2.073 |

Vertical in situ stress | 1.332 | 0 | 0 | 1.576 | 0.098 | 6.243 |

Pore pressure | 1.333 | 0.067 | 5.023 | 1.576 | 0.067 | 4.227 |

Poisson’s ratio | 1.127 | 0 | 0 | 1.126 | 0.00004 | 0.004 |

Well Type | Vertical Well | Horizontal Well | ||||
---|---|---|---|---|---|---|

Influencing Factors | Mean Value (g/cm^{3}) | Standard Deviation (g/cm^{3}) | Coefficient of Variation (%) | Mean Value (g/cm^{3}) | Standard Deviation (g/cm^{3}) | Coefficient of Variation (%) |

Cohesion | 1.63 | 0.05 | 2.88 | 1.74 | 0.19 | 10.63 |

Internal friction angle | 1.63 | 0.01 | 0.37 | 1.74 | 0.02 | 1.38 |

Horizontal maximum in situ stress | 1.62 | 0.3 | 8.04 | 1.74 | 0 | 0 |

Horizontal minimum in situ stress | 1.63 | 0.2 | 12.23 | 1.75 | 0.2 | 11.42 |

Vertical in situ stress | 1.63 | 0 | 0 | 1.74 | 0.13 | 7.57 |

Pore pressure | 1.63 | 0.13 | 7.74 | 1.74 | 0.09 | 5.4 |

Poisson’s ratio | 1.63 | 0 | 0 | 1.74 | 0 | 0 |

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## Share and Cite

**MDPI and ACS Style**

Gao, X.; Wang, M.; Shi, X.; Li, C.; Zhang, M.
Risk Assessment Method for Analyzing Borehole Instability Considering Formation Heterogeneity. *Processes* **2024**, *12*, 70.
https://doi.org/10.3390/pr12010070

**AMA Style**

Gao X, Wang M, Shi X, Li C, Zhang M.
Risk Assessment Method for Analyzing Borehole Instability Considering Formation Heterogeneity. *Processes*. 2024; 12(1):70.
https://doi.org/10.3390/pr12010070

**Chicago/Turabian Style**

Gao, Xiangsen, Min Wang, Xian Shi, Cui Li, and Mingming Zhang.
2024. "Risk Assessment Method for Analyzing Borehole Instability Considering Formation Heterogeneity" *Processes* 12, no. 1: 70.
https://doi.org/10.3390/pr12010070