# Fracture Interference and Refracturing of Horizontal Wells

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Decline in Production Capacity and Low Recovery

#### 1.2. Inter-Fracture Stress Interference

#### 1.3. Fracturing Fluid Filtration Loss and Variation of Pore Pressure

## 2. Theory and Model Design

#### 2.1. Calculation of Multi-Fracture Interference Stress Field

_{x}, u

_{y}is the displacement of the target point near the wellbore, m; n is the number of fractures; P

_{0,i}is the pressure of the fluid in the fracture, MPa; E is the Young’s modulus of the rock, GPa; ν is the Poisson’s ratio; r

_{1,i}, r

_{2,i}, and r

_{i}are the distances from the two endpoints and the midpoint of the fracture to the target point, m; θ

_{1,i}, θ

_{2,i}, and θ

_{i}are the angles from the two endpoints and the midpoint of the crack to the target point, respectively.

#### 2.2. Fracturing Fluid Flow and Filtration

_{f}is the local tangential flow rate within the fracture, m/s; w is the fracture aperture, m; μ is the fracturing fluid viscosity, mPa·s; and p

_{f}is the fluid pressure inside the hydraulic fracture, MPa.

_{t}and q

_{b}are the local fracturing fluid leak-off rates through the upper and lower fracture surfaces, m/s; c

_{t}and c

_{b}are the fluid leak-off coefficients on the upper and lower fracture surfaces; p

_{t}and p

_{b}are the formation pressures adjacent to the upper and lower fracture surfaces, MPa.

#### 2.3. Establishment of Fracturing Model

## 3. Multi-Cluster Fracturing Simulation

#### 3.1. Initial Fracturing Simulation

- Ground stress balance stage.
- Pump 150 m
^{3}(70 min) fracturing fluid, the cracks open and extend forward, and then stop the pump. - A 150-min simulation of fracturing fluid filtration loss and in situ stress field evolution.

#### 3.2. Refracturing Simulation

## 4. Discussion

#### 4.1. Fracturing Fluid Filtration Loss and Variation of Pore Pressure

#### 4.2. Changes of Fracture Size

#### 4.3. Evolution of Stress Field

#### 4.4. Refracturing

## 5. Conclusions

- There is stress concentration around the fractures during multi-cluster fracturing of horizontal wells due to formation deformation, which is more obvious between fractures. The hydraulic fracture’s effective influence radius on the external formation is about 15 m.
- The formation stress gradually recovers after the fracturing is completed, but it is still significantly higher than the original in situ stress. When refracturing is performed, it is recommended that stress relief be performed first, as this aids fracture initiation.
- Reperforating fracturing has a lower fracture extension pressure and a longer fracture length than in situ refracturing. As a result, it is recommended that reperforating fracturing be used first when refracturing is performed. With repeated stimulation, fracture temporary plugging technology increases the effective volume of reservoir stimulation and achieves high and stable production.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Particle paths (blue) after 1 month of production for a hydraulic fractured in the Permian Basin well. The hydraulic fracture stages are 250 ft apart and have a half-length of 100 ft. (

**a**) DRV around individual hydraulic fractures (

**b**) DRVs in a low productivity well [18] (Reproduced with permission from SEG, 2020).

**Figure 2.**Schematic illustration of the influence of stress shadow on the dynamic propagation of hydraulic fractures.

**Figure 3.**Pressure depletion (psi) progression for the central three fractures in a Wolfcamp shale well (Midland Basin, West Texas) constructed using a production history-matched CMG model. (

**a**) Map views of pressure depletion in production bench with wellbore horizontal in image and transverse fractures sets spaced at 60 ft. (

**b**) Pressure gradient normal to the fractures after 1 month [44]. (Reproduced with permission from Elsevier, 2019).

**Figure 4.**CAM model. (

**a**) Map view of velocity magnitude contours (ft/day) (

**b**) Vertical velocities measured at y = 0. (

**c**) Map view of normalized pressured depletion contours. (

**d**) Vertical profile of pressure magnitude variations along the well at y = 0 [18]. (Reproduced with permission from SEG, 2020).

**Figure 8.**Curves of fracture width and injection point pressure. The upper curve represents the pressure at the injection point, the lower curve represents the width of the fracture, and the red curve represents the intermediate injection point. The lateral curve is the projection of pressure and width of the five fractures.

**Figure 9.**The minimum principal stress nephogram of initial fracturing. The curve represents the minimum stress at the red horizontal point in the middle of the model.

**Figure 10.**Results of in situ refracturing. The four figures show the fracture morphology and stress field distribution at different times during the refracturing process. After pumping (70 min), the morphology of the five fractures in the in situ refracturing is more uniform than that of initial fracturing.

**Figure 11.**Results of reperforation hydraulic fracturing. The formation was reperforated in the middle of the five fractures of the initial fracturing, and the initial fracture was blocked by the temporary plugging technology, resulting in only four fractures during the refracturing.

**Figure 16.**The seepage field after the pump was stopped for 100 min. The fracturing fluid continues to filter out into the formation because the fluid pressure in the fracture is still greater than the pore pressure in the reservoir.

**Figure 17.**Variation of pore pressure along the central horizontal line. The pressure at the five injection points is always greater than the pore pressure in the nearby reservoir matrix.

**Figure 18.**Variation curve of minimum principal stress and pore pressure at monitoring points. The gray area represents the fracturing stage, and the pump stops after 70 min.

Geological Oroperties | Numerical Value |
---|---|

Young’s modulus | 20 GPa |

Poisson’s ratio | 0.25 |

Porosity | 10% |

Permeability | 1 mD |

Tensile strength | 6 MPa |

Horizontal minimum principal stress | 10 MPa |

Horizontal maximum principal stress | 20 MPa |

Injection Point | Breaking Pressure MPa | Fracture Pressure MPa | Average Fracture Width mm | Average Fracture Length m | |||
---|---|---|---|---|---|---|---|

Step2 | Step3 | Step2 | Step3 | Step2 | Step3 | ||

L/R-5 | 27.6 | 22.6 | 16.9 | 6.9 | 6.8 | 18 | 18 |

L/R-3 | 27.6 | 22.2 | 16.2 | 5.7 | 4 | 20 | 26 |

M-1 | 27.6 | 22.8 | 17 | 6.2 | 6.3 | 20 | 20 |

Data Information | Breaking Pressure/MPa | Extension Pressure/MPa | ||||
---|---|---|---|---|---|---|

Fracturing Method | Injection Point | Source of Stress Field | Injection Point | Source of Stress Field | ||

Step2 | Step3 | Step2 | Step3 | |||

reinject | M-1 | 33.5 | 32.5 | M-1 | 29.1 | 28.8 |

L/R-3 | 33.5 | 32.5 | L/R-3 | 28.4 | 27.1 | |

L/R-5 | 33.5 | 32.5 | L/R-5 | 28 | 27.6 | |

reperforation | L/R-2 | 33.4 | 32 | L/R-2 | 26.1 | 24.9 |

L/R-4 | 33.4 | 32 | L/R-4 | 25 | 24.2 | |

Data Information | Average Fracture Width/mm | Average Fracture Length/m | ||||

Fracturing Method | Injection Point | Source of Stress Field | Injection Point | Source of Stress Field | ||

Step2 | Step3 | Step2 | Step3 | |||

reinject | M-1 | 6.8 | 7.2 | M-1 | 17 | 17 |

L/R-3 | 6.4 | 6.5 | L/R-3 | 18 | 18 | |

L/R-5 | 7.4 | 7.4 | L/R-5 | 16 | 16 | |

reperforation | L/R-2 | 6.3 | 6.4 | L/R-2 | 22 | 19 |

L/R-4 | 6.7 | 6.3 | L/R-4 | 25 | 21 |

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**MDPI and ACS Style**

Lin, H.; Tian, Y.; Sun, Z.; Zhou, F.
Fracture Interference and Refracturing of Horizontal Wells. *Processes* **2022**, *10*, 899.
https://doi.org/10.3390/pr10050899

**AMA Style**

Lin H, Tian Y, Sun Z, Zhou F.
Fracture Interference and Refracturing of Horizontal Wells. *Processes*. 2022; 10(5):899.
https://doi.org/10.3390/pr10050899

**Chicago/Turabian Style**

Lin, Hai, Yakai Tian, Zhenwei Sun, and Fujian Zhou.
2022. "Fracture Interference and Refracturing of Horizontal Wells" *Processes* 10, no. 5: 899.
https://doi.org/10.3390/pr10050899