# Study on Thermal Energy Conversion Theory in Drilling Process of Coal and Rock Mass with Different Stresses

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## Abstract

**:**

## 1. Introduction

## 2. Factors and Causes of Heat Generation in Drilling

## 3. Theory of Temperature Field Evolution of the Drill Bit

#### 3.1. Mechanical Analysis of the Drilling Process

- (1).
- The coal and rock mass is a homogeneous and isotropic continuous medium;
- (2).
- The drilling process follows the limit stress equilibrium condition;
- (3).
- The drill bit is a homogeneous isotropic continuous medium.

_{1}is the friction coefficient between the drill bit and the coal and rock (cuttings); $c$ is the length of the drilling head body, m; $m$ is the width of the drill head body, m; ${F}_{3}$ is the reaction force of the cut rock layer on the cutting edge of the bit, N; $\tau $ is the shear strength of rock material, Pa; ${S}_{1}$ is the shear area when a single cutting acts on the rock, m

^{2}.

#### 3.2. Generation and Distribution of Heat

_{1}is energy absorbed by rock in front of bit, J; Q

_{2}is energy absorbed by side rock of drill bit, J; Q

_{3}is energy absorbed by drill bit, J; Q

_{4}is energy absorbed by drilling cuttings, J.

#### 3.2.1. Generation of Friction Heat

_{c}, and, as the drilling hole gradually takes shape, the pressure of the drilling hole wall on the tire body gradually decreases until the drill bit is no longer subject to the stress of the coal body. Assuming that the pressure on the surface of the bit decreases uniformly from the coal stress value to zero along the opposite direction of the drill, then the average compressive stress on the surface of the drilling head body is as follows:

#### 3.2.2. Generation of Shear Heat

_{1}is the elastic modulus of the rock.

#### 3.2.3. The Distribution of Heat

^{3}; ${c}_{1}$ is the specific heat of the rock, J/(kg, °C); $\Delta {T}_{1}$ is the temperature variation of the rock, °C; $l$ is the axial length of the drill bit, m.

_{2}is the elasticity modulus of the bit.

#### 3.3. Bit Temperature Rise Condition Model

#### 3.4. The Relation between Coal Rock Stress and the Bit Temperature Rise

## 4. Verification of the Relationship between the Rate of Bit Temperature Change and the Stress of the Coal and Rock Mass

## 5. Conclusions

- (1).
- By studying the detection of the drilling process, the mechanism and factors of heat generation during the interaction between the drill bit and coal and rock mass are analyzed. The influences of coal and rock mass stress, coal and rock mass strength, bit motion parameters and bit material parameters on bit temperature change were obtained qualitatively, which provides a basis for the quantitative study of the relationship between the stress of coal and rock mass and the rate of bit temperature change.
- (2).
- On the basis of the mechanical analysis of the bit during drilling and the principle of energy conservation and thermal energy conversion theory, the conditional model of bit temperature rise and the coal stress identification model were established, and a linear expression between the coal stress and the bit temperature rate was obtained.
- (3).
- The variation law of bit temperature obtained from the stress identification model of the coal body is consistent with the experimental data, fully demonstrating the feasibility of using temperature as a discriminant stress index of coal. This provides a direct and effective reference for delineating dangerous areas of rock burst and testing the effect of anti-outburst measures.
- (4).
- In the process of using the bit temperature rate as the index to judge the coal stress value, a theoretical research method was adopted. The research results are preliminary and need to be further revised and deepened by practical application under specific engineering conditions.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Diagram of the relationship between the rate of temperature change of the bit and the influencing factors.

**Figure 7.**Diagram of the relationship between change rate of the bit temperature and the stress of the coal rock.

**Figure 10.**The relationship between the change rate of the bit temperature and the stress of the coal body.

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**MDPI and ACS Style**

Qiu, P.; Li, X.; Ning, J.; Wang, J.; Yang, S.
Study on Thermal Energy Conversion Theory in Drilling Process of Coal and Rock Mass with Different Stresses. *Energies* **2019**, *12*, 4282.
https://doi.org/10.3390/en12224282

**AMA Style**

Qiu P, Li X, Ning J, Wang J, Yang S.
Study on Thermal Energy Conversion Theory in Drilling Process of Coal and Rock Mass with Different Stresses. *Energies*. 2019; 12(22):4282.
https://doi.org/10.3390/en12224282

**Chicago/Turabian Style**

Qiu, Pengqi, Xuehui Li, Jianguo Ning, Jun Wang, and Shang Yang.
2019. "Study on Thermal Energy Conversion Theory in Drilling Process of Coal and Rock Mass with Different Stresses" *Energies* 12, no. 22: 4282.
https://doi.org/10.3390/en12224282