# Mechanisms and Influence of Casing Shear Deformation near the Casing Shoe, Based on MFC Surveys during Multistage Fracturing in Shale Gas Wells in Canada

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## Abstract

**:**

## 1. Introduction

## 2. Overview of Casing Shear Deformation in Simonette

#### 2.1. Field Description

#### 2.2. Casing Shear Deformation

^{3}of fracturing fluid, with a displacement of 12–14 m

^{3}/min and pumping pressure of over 70 MPa. 5 pads including 28 wells were investigated by MFC surveys. Casing deformation occurred in 16 wells during multistage fracturing. 23 deformed points were found, and there were five different types of deformed points, including extrusion deformation, shear deformation, bending deformation, buckling, and casing holes, as shown in Figure 2. Statistical data showed that 52.2% of all of the deformed points were shear deformation.

#### 2.3. Difference Between Measurement Results and Actual Shear Deformation

## 3. Mechanisms of Casing Shear Deformation induced by Multistage Fracturing

#### 3.1. Mechanisms of Casing Shear Deformation

#### 3.2. Verification of Fault Slipping

_{n}represents the coefficient of friction, dimensionless. And according to Zoback [28], the value range of f

_{n}is from 0.6 to 1. σ

_{n}represents the effective normal stress (MPa); S represents the rock cohesive strength (MPa).

_{n}can be expressed as

_{p}is the pore pressure in MPa, and S

_{n}is the normal stress perpendicular to the interface.

_{w}is equal to the yield density in (g/cm

^{3}). ψ is the angle between the interface and the maximum horizontal principal stress (degree). The normal stress has been resolved into horizontal (σ

_{H}) and vertical (σ

_{v}) components.

## 4. Numerical Simulation

#### 4.1. Model Geometry and Discretization

#### 4.2. Boundary Conditions and Simulation Steps

#### 4.3. Geological and Mechanical Parameters

^{3}, then the casing’s inner pressure in the interface was about 115 MPa. The discharge of fracturing fluid is 12 m

^{3}/min, and the fracturing time is 4 h. Other geological and mechanics parameters are shown in Table 1 and Table 2.

## 5. Results

#### 5.1. Engineering Verification of the Numerical Simulation

#### 5.2. Sensitivity Analysis of Casing Shear Deformation

#### 5.2.1. Influence of Slip Distance

#### 5.2.2. Influence of Casing Inner Pressure

#### 5.2.3. Influence of Casing Thickness

#### 5.2.4. Influence of Cement Sheath Mechanical Parameters

## 6. Results Comparison and Mitigation Method

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

_{H}, σ

_{h}and σ

_{v}, MPa). Although the stress field in the vertical section of the shale gas well was stay the same with in-situ stress, the mechanical state in the inclination section was different. For the reason that the research object was located in the inclination section, the in-situ stress should be converted to the stress tensor in the wellbore coordinate system.

_{y}and L

_{z}represent the direction cosine matrixes rotating around y-axis and z-axis based on the right-hand rule.

_{ij}) in the wellbore coordinate could be calculated by

^{T}represents the transposition of L, dimensionless.

## Appendix B

_{z}represents formation temperature at a certain depth, °C, T

_{b}represents land surface temperature, °C, α represents the geothermal gradient, °C/m, z represents reservoir depth, m; b represents the benchmark depth, m.

_{j}represents the heat generated by friction between the fracturing fluid and casing wall, J; Q represents the displacement of fracturing fluid, m

^{3}/min, ρ represents density, kg/m

^{3}, C represents specific heat, J/(kg·°C), r is the radius, m; ΔH

_{j}represents the height of the control unit body, m; U represents the convective heat transfer coefficient between the fracturing fluid and casing wall, w/(m

^{2}·°C); and λ

_{fj}represents the casing friction coefficient, dimensionless.

_{t}is the Stanton number (dimensionless), K

_{0}is the heat conductivity coefficient (w/(m·°C); D is the casing diameter (m); D

_{eff}is the equivalent diameter of casing (m); n is the liquidity index, dimensionless; K

_{con}is the consistency (Pa/s

^{n}); C

_{0}represents the specific heat of the fracturing fluid (J/(kg·°C)).

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Component | Outer Diameter (mm) | Young Modulus (GPa) | Poisson’s Ratio | Cohesive Strength (MPa) | Internal Friction Angle(°) |
---|---|---|---|---|---|

Production Casing | 139.7 | 210 | 0.3 | \ | \ |

Cement Sheath (2) | 171 | 10 | 0.17 | 8 | 27 |

Intermediate Casing | 193.7 | 210 | 0.3 | \ | \ |

Cement Sheath (1) | 222 | 10 | 0.17 | 8 | 27 |

Formation | \ | 22 | 0.23 | 5 | 39 |

Materials | Coefficient of Heat Conduction (W·(m·°C)^{−1}) | Specific Heat (J·(kg·°C)^{−1}) | Density (kg·m^{−3}) | Coefficient of Thermal Expansion (10^{−6}·°C^{−1}) |
---|---|---|---|---|

Casing | 45 | 461 | 7800 | 13 |

Cement sheath | 0.98 | 837 | 3100 | 11 |

Formation | 1.59 | 1256 | 2600 | 10.5 |

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**MDPI and ACS Style**

Xi, Y.; Li, J.; Liu, G.; Li, J.; Jiang, J.
Mechanisms and Influence of Casing Shear Deformation near the Casing Shoe, Based on MFC Surveys during Multistage Fracturing in Shale Gas Wells in Canada. *Energies* **2019**, *12*, 372.
https://doi.org/10.3390/en12030372

**AMA Style**

Xi Y, Li J, Liu G, Li J, Jiang J.
Mechanisms and Influence of Casing Shear Deformation near the Casing Shoe, Based on MFC Surveys during Multistage Fracturing in Shale Gas Wells in Canada. *Energies*. 2019; 12(3):372.
https://doi.org/10.3390/en12030372

**Chicago/Turabian Style**

Xi, Yan, Jun Li, Gonghui Liu, Jianping Li, and Jiwei Jiang.
2019. "Mechanisms and Influence of Casing Shear Deformation near the Casing Shoe, Based on MFC Surveys during Multistage Fracturing in Shale Gas Wells in Canada" *Energies* 12, no. 3: 372.
https://doi.org/10.3390/en12030372