# Study on the Erosion of Choke Valves in High-Pressure, High-Temperature Gas Wells

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Simulation Model of Erosion

#### 2.1. Flow Equation of Liquid Phase

#### 2.2. Movement Equation of Particle Phase

#### 2.3. Equation of Erosion

^{−9}[19,20] because the size of the particles in this paper is mono; $\alpha $ is the impact angle between the particle motion path and the wall surface of the structure; $f\left(\alpha \right)$ is the angle of the impact function of the particles; $v$ is the relative velocity of the particles; $b\left(v\right)$ is a function of the relative velocity of the particles, and the solid particles in this article are quartz sand, which take the value of 2.6 [21,22,23]; ${A}_{\mathrm{face}}$ is the wall area of the wall surface of the particle collision wall, which is defined during the process of simulation based on the effect of the angle and the velocity of the particles; and ${R}_{\mathrm{erosion}}$ is the erosion quality of the particles on the wall surface of the structure per unit area per unit time. The choke impact angle function $f\left(a\right)$ was proposed by Huser and Kvemvold.

## 3. Model Creation with Parameter Setting

#### 3.1. Choke Valve Geometry and Meshing

#### 3.2. Initial Boundary Condition Setting

^{3}. The continuous phase in a high-pressure gas well is mainly methane, which is less dense, and the effect of gravity can be ignored. Furthermore, the energy equation states are open, avoiding standard wall functions, no-slip conditions, and particles bouncing off after collision avoidance. The amount of momentum reduction is determined by the collision model. Thus, the solution method adopts the SIMPLE algorithm to solve the pressure–velocity coupling, the others adopt the second-order windward format, and the mean residual convergence standard is set to the recommended value of 10

^{−5}. High temperature and high pressure frequently occur together, and a high pressure generally indicates a high rate of gas well production. The change in pressure and flow directly affects the quantity of the fluid and particles impacting the nozzle wall. In comparison to a low flow rate, erosion at a high flow rate is more noticeable and causes bigger priority at the production sites. The simulation and conclusions in this paper are more applicable to high-pressure and high-production gas wells.

#### 3.3. Mesh Independence Verification

## 4. Choke Valve Erosion Numerical Simulation

#### 4.1. Pure Gas Phase Erosion

#### 4.1.1. Wall Pressure Distribution

#### 4.1.2. Velocity Vectors at Different Openings

#### 4.2. Simulation of Sand Erosion

#### 4.2.1. Effect of Gravel Diameter on Wear

#### 4.2.2. The Influence of Sand Volume on Wear

^{−8}, 7.18 × 10

^{−7}, and 9.73 × 10

^{−6}, respectively. The erosion velocity of the choke valve spool surface is within an order of magnitude, and the maximum erosion speed point is randomly distributed around the pore size. The erosion is uniform and correlates positively with the amount of sand produced. The results show that, in the case of fine silt sand, the erosion is positively correlated with the amount of sand, the distribution of the erosion locations does not change, and all of them are more commonly abraded.

#### 4.3. Comparison of Simulation Results with On-Site Results

## 5. Conclusions

- (1)
- The position of the high-risk point of the choke valve under different opening conditions is obtained through simulation, which can help choke manufacturers optimize the shape and material of choke valves.
- (2)
- In the case of a certain amount of sand, the increase in grit particle size concentrates the erosion position at the edge of the hole, which manifests as the concentrated erosion of the edge of the small hole. Consistent with the erosion pit at the edge of the actual small hole, the grit’s large particle size seems to be more significant in the erosion process.
- (3)
- In the case of a certain grain size of sand and gravel (0.1 mm for fine silt sand), and under the condition that the amount of sand changes, the erosion rate of the surface facing the current is positively correlated with the amount of sand. Additionally, the maximum erosion speed point is randomly distributed around the pore size, resulting in a uniform erosion.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

Symbol | Definition |

ρ | density (kg/m^{3}) |

${\mathrm{u}}_{\mathrm{i}}$ | velocity component parallel to the axis ${\mathrm{x}}_{\mathrm{i}}$ (m·s^{−1}) |

p | pressure (Pa) |

${\mathsf{\tau}}_{ij}$ | viscous stress tensor (N·m^{−2}) |

g | acceleration of gravity (m·s^{−2}) |

${F}_{i}$ | generalized volumetric force (N) |

$\mathrm{k}$ | turbulent kinetic energy (J·kg^{−1}) |

${\mathsf{\mu}}_{t}$ | turbulence viscosity (Pa·s) |

$\mathsf{\mu}$ | fluid dynamic viscosity (Pa·s) |

${G}_{k}$ | turbulent flow energy generated by the average speed gradient |

${G}_{b}$ | turbulent flow energy generated by the buoyancy |

${Y}_{m}$ | effect of the compressible turbulence fluctuation |

ε | turbulent flow energy consumption dissipation power |

${\sigma}_{k}$ | turbulent kinetic energy (m^{2}·s^{−1}) |

${\sigma}_{\mathsf{\epsilon}}$ | turbulent flow Plant number (m^{2}·s^{−1}) |

${u}_{P}$ | particle velocity component |

${\rho}_{P}$ | particle density (kg/m^{3}) |

${F}_{D}$ | flow resistance of the particle (N) |

${F}_{P}$ | other forces affected by the particle (N) |

${d}_{P}$ | particle diameter (mm) |

$\mathrm{Re}$ | relative Reynolds number |

${C}_{D}$ | resistance coefficient |

${m}_{P}$ | average mass flow of the particles (kg·s^{−1}) |

N | number of particles |

$C\left({d}_{P}\right)$ | particle diameter function |

$f\left(a\right)$ | The function of the relative velocity of particles |

${A}_{\mathrm{face}}$ | wall area of the wall surface of the particle collision tube (mm^{2}) |

${R}_{\mathrm{erosion}}$ | erosion quality of particles on the wall surface (kg·s^{−1}·mm^{2}) |

${\mathsf{\epsilon}}_{n}$ | normal recovery coefficient |

${\mathsf{\epsilon}}_{t}$ | tangential recovery coefficient |

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**MDPI and ACS Style**

Guo, L.; Wang, Y.; Xu, X.; Gao, H.; Yang, H.; Han, G.
Study on the Erosion of Choke Valves in High-Pressure, High-Temperature Gas Wells. *Processes* **2022**, *10*, 2139.
https://doi.org/10.3390/pr10102139

**AMA Style**

Guo L, Wang Y, Xu X, Gao H, Yang H, Han G.
Study on the Erosion of Choke Valves in High-Pressure, High-Temperature Gas Wells. *Processes*. 2022; 10(10):2139.
https://doi.org/10.3390/pr10102139

**Chicago/Turabian Style**

Guo, Ling, Yayong Wang, Xiaohui Xu, Han Gao, Hong Yang, and Guoqing Han.
2022. "Study on the Erosion of Choke Valves in High-Pressure, High-Temperature Gas Wells" *Processes* 10, no. 10: 2139.
https://doi.org/10.3390/pr10102139