# Development of Hydraulic Turbodrills for Deep Well Drilling

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Development of Mathematical Model

- ${c}_{1u}={c}_{z}\xb7ctg\alpha $—equivalent speed in the rotor, m/s,
- ${c}_{2u}=u-{c}_{z}\xb7ctg\beta $—equivalent speed in the stator, m/s,
- ${c}_{z}=\frac{Q}{\pi \xb7D\xb7l}$—axis velocity of the liquid, m/s,
- $u=\pi \xb7D\xb7{n}^{\prime}$—district fluid velocity, m/s,
- $M$—torque, Nm,
- $\rho $—density, kg/m
^{3}, - $Q$—drilling fluid flow rate, m
^{3}/s, - $D$—medium turbine diameter, m,
- $\alpha $—stator blade angle of inclination, n’,
- $\beta $—rotor blade angle of inclination, n’,
- ${n}^{\prime}$—rotation frequency, rev/s,
- $l$—radial length of turbodrill blades, m.

## 3. Simulation of the Investigated Object

#### 3.1. Study of the Mathematical Model

- $P$—power, W,
- $\omega $—rotation frequency, rad/s,
- $n$—rotation frequency, rpm.

- $q$—generalized variables of the desired values,
- $y$—valid speed values of rotation,
- $f\left(q\right)$—rotation frequency function values for a set of generalized variables,
- ${R}^{q}$—real space with the length of the q vector.

- h, g—restriction function,
- $\mu $—positive barrier parameter, variable s is to be positive.

- e—single vector-pillar,
- S—diagonal matrix,
- ${A}_{h,g}\left(x\right)$—vector line components of the gradient corresponding to the restriction function.

#### 3.2. Results of Mathematical Modeling

#### 3.3. Testing the Research Results Using the Finite Element Method

## 4. Comparative Analysis of the Developed Turbodrill

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Modeling a working turbine pair: (

**a**)—Model of a turbodrill, where H—section height, and z—gap between sections; (

**b**)—Display of the flow of fluid flows in the developed turbine pair.

Rotation Frequency, rpm | Torque, Nm | Power, kW | Pressure Drop, kPa |
---|---|---|---|

0 | 167.6 | 0.0 | 0.0 |

500 | 150.8 | 7.9 | 157.9 |

1000 | 134.0 | 14.0 | 280.7 |

1500 | 117.3 | 18.4 | 368.5 |

2000 | 100.5 | 21.1 | 421.1 |

2500 | 83.8 | 21.9 | 438.6 |

3000 | 67.0 | 21.1 | 421.1 |

3500 | 50.3 | 18.4 | 368.5 |

4000 | 33.5 | 14.0 | 280.7 |

4500 | 16.8 | 7.9 | 157.9 |

5000 | 0.0 | 0.0 | 0.0 |

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

Rotor blade angle, n’. | 12.18 |

Stator blade angle, n’. | 12.18 |

Flow rate, L/s | 50.00 |

Turbine pressure drop, kPa | 438.65 |

No. | Indicator | Model of Turbodrill | ||
---|---|---|---|---|

TSSh-178T | Neyrfor 2 7/8 | Developed Turbodrill | ||

1 | Outer diameter of the case, mm | 178 | 73 | 195 |

2 | Turbodrill length, mm | 7100 | 4572 | 520 |

3 | Drilling fluid flow rate, l/s | 28–38 | 6.3–7.5 | 45–55 |

4 | Drilling mud density, g/cm^{3} | 1.0 | Before 2.16 | 1.0 |

5 | Torque, Nm | 1630–3000 | Before 203 | 679–1013 |

6 | Operating speed, rpm | 945–1283 | 2000–2500 | 2250–2750 |

7 | Turbine pressure drop, MPa | 5.4–9.2 | 7.6–11.4 | 3.6–5.3 |

8 | Maximum power, kW | 80–201 | 24–43 | 160–292 |

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**MDPI and ACS Style**

Dvoynikov, M.V.; Sidorkin, D.I.; Kunshin, A.A.; Kovalev, D.A. Development of Hydraulic Turbodrills for Deep Well Drilling. *Appl. Sci.* **2021**, *11*, 7517.
https://doi.org/10.3390/app11167517

**AMA Style**

Dvoynikov MV, Sidorkin DI, Kunshin AA, Kovalev DA. Development of Hydraulic Turbodrills for Deep Well Drilling. *Applied Sciences*. 2021; 11(16):7517.
https://doi.org/10.3390/app11167517

**Chicago/Turabian Style**

Dvoynikov, Mikhail V., Dmitry I. Sidorkin, Andrey A. Kunshin, and Danil A. Kovalev. 2021. "Development of Hydraulic Turbodrills for Deep Well Drilling" *Applied Sciences* 11, no. 16: 7517.
https://doi.org/10.3390/app11167517