# A Novel Temperature Prediction Model Considering Stress Sensitivity for the Multiphase Fractured Horizontal Well in Tight Reservoirs

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## Abstract

**:**

## 1. Introduction

## 2. Mathematical Model

#### 2.1. Physical Model and Assumption

#### 2.2. Mathematical Model with Stress Sensitivity Effect

^{−1}; $p$ is the reservoir pressure, MPa; and the subscript 0 denotes the initial state.

^{2}·°C). $\gamma $ indicates the degree of the wellbore opening; $\gamma =1$ at the fracture, and $\gamma =0$ at the cementing section [30]. When the reservoir and the wellbore model are coupled, the diameter of the wellbore is much smaller than the size of the divided grid, and the grid containing the wellbore cannot directly describe the flow and heat exchange between the wellbore and the reservoir grid block. Hence, an equivalent radius is introduced to describe the flow between the reservoir grid block and the wellbore [31]:

^{2}) and the overall heat transfer coefficient (${\left.{U}_{T}\right|}_{r={r}_{eff}}$) of the effective radius into the above equation indicates the heat transfer from the reservoir to the wellbore. The following results can be obtained:

#### 2.3. Boundary Conditions and Initial Conditions

_{L}, Y

_{L}represents the boundaries of X and Y directions.

## 3. Analysis of Wellbore Temperature Sensitivity Factors

## 4. Field Application

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Physical model of multistage fractured horizontal well in tight reservoir:(

**a**) presents a multistage fractured horizontal well in an infinite reservoir; (

**b**) shows the simplified physical model.

**Figure 3.**Wellbore temperature profiles and $\mathrm{\Delta}T$ with different stress sensitivity coefficients.

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

Formation porosity | / | 0.1 |

Formation permeability | mD | 0.2 |

Formation temperature | °C | 100 |

Initial reservoir pressure | MPa | 20 |

Rock heat capacity | J/(kg·°C) | 1264 |

Rock heat conductivity | W/(m·°C) | 1.3 |

Oil density | kg/m^{3} | 0.641 × 10^{3} |

Oil viscosity | mPa.s | 0.8 |

Oil specific heat | J/(kg·°C) | 2193 |

Oil thermal conductivity | W/(m·°C) | 3.46 |

Water density | kg/m^{3} | 1.0 × 10^{3} |

Water viscosity | mPa.s | 0.317 |

Water heat capacity | J/(kg·°C) | 4194 |

Water heat conductivity | W/(m·°C) | 4.32 |

Wellhead temperature | °C | 14.7 |

Wellbore length | m | 800 |

Pipe inner | m | 0.01 |

Fracture permeability | D | 0.9 |

Fracture half-length | m | 100 |

Fracture width | m | 0.002 |

No. | ${\mathit{Q}}_{\mathit{w}}$ m³/d | $\mathit{k}$ mD | ${\mathit{\alpha}}_{\mathit{t}}$ W/(m ^{2}·K) | ${\mathit{L}}_{\mathit{f}}$ m | $\mathit{F}\mathit{C}\mathit{D}$ mD·m |
---|---|---|---|---|---|

1 | 0 | 0.1 | 336 | 40 | 10 |

2 | 5 | 0.15 | 436 | 60 | 15 |

3 | 10 | 0.2 | 536 | 70 | 20 |

No. | ${\mathit{Q}}_{\mathit{w}}$ | $\mathit{k}$ | ${\mathit{\alpha}}_{\mathit{t}}$ | ${\mathit{L}}_{\mathit{f}}$ | $\mathit{F}\mathit{C}\mathit{D}$ | $\mathrm{\Delta}\mathit{T}$ |
---|---|---|---|---|---|---|

1 | 2 | 1 | 3 | 3 | 1 | 0.276 |

2 | 1 | 1 | 1 | 1 | 1 | 0.314 |

3 | 1 | 3 | 1 | 2 | 1 | 0.344 |

4 | 2 | 1 | 1 | 1 | 3 | 0.282 |

5 | 1 | 2 | 3 | 1 | 3 | 0.256 |

6 | 3 | 2 | 2 | 1 | 1 | 0.373 |

7 | 2 | 2 | 1 | 2 | 2 | 0.356 |

8 | 3 | 1 | 1 | 1 | 2 | 0.295 |

9 | 1 | 1 | 2 | 2 | 3 | 0.309 |

10 | 3 | 3 | 1 | 3 | 3 | 0.336 |

11 | 1 | 2 | 1 | 3 | 1 | 0.324 |

12 | 2 | 3 | 2 | 1 | 1 | 0.261 |

13 | 1 | 1 | 2 | 3 | 2 | 0.336 |

14 | 1 | 1 | 1 | 1 | 1 | 0.288 |

15 | 3 | 1 | 3 | 2 | 1 | 0.326 |

16 | 1 | 3 | 3 | 1 | 2 | 0.355 |

K1 | 0.316 | 0.303 | 0.317 | 0.303 | 0.313 | / |

K2 | 0.294 | 0.327 | 0.320 | 0.334 | 0.336 | / |

K3 | 0.333 | 0.324 | 0.303 | 0.318 | 0.296 | / |

R | 0.039 | 0.024 | 0.017 | 0.031 | 0.022 | / |

Result | ${L}_{f}$ > ${Q}_{w}$ > $k$ > $FCD$ > ${\alpha}_{t}$ |

Wellbore Length (m). | 1174 |
---|---|

Porosity (%) | 0.1 |

Formation permeability (mD) | 0.037 |

Initial reservoir pressure (MPa) | 51.67 |

Initial reservoir temperature (°C) | 92.43 |

Fracture length (m) | 120 |

Fracture permeability (D) | 0.9 |

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**MDPI and ACS Style**

Duan, Y.; Zhang, R.; Wei, M.
A Novel Temperature Prediction Model Considering Stress Sensitivity for the Multiphase Fractured Horizontal Well in Tight Reservoirs. *Energies* **2021**, *14*, 4760.
https://doi.org/10.3390/en14164760

**AMA Style**

Duan Y, Zhang R, Wei M.
A Novel Temperature Prediction Model Considering Stress Sensitivity for the Multiphase Fractured Horizontal Well in Tight Reservoirs. *Energies*. 2021; 14(16):4760.
https://doi.org/10.3390/en14164760

**Chicago/Turabian Style**

Duan, Yonggang, Ruiduo Zhang, and Mingqiang Wei.
2021. "A Novel Temperature Prediction Model Considering Stress Sensitivity for the Multiphase Fractured Horizontal Well in Tight Reservoirs" *Energies* 14, no. 16: 4760.
https://doi.org/10.3390/en14164760